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    <title>DEV Community: 张宇</title>
    <description>The latest articles on DEV Community by 张宇 (@cosimos).</description>
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      <title>Deep Dive into Memory Management: From Hardware Abstractions to Userland Allocation</title>
      <dc:creator>张宇</dc:creator>
      <pubDate>Mon, 06 Apr 2026 04:04:43 +0000</pubDate>
      <link>https://dev.to/cosimos/deep-dive-into-memory-management-from-hardware-abstractions-to-userland-allocation-20a0</link>
      <guid>https://dev.to/cosimos/deep-dive-into-memory-management-from-hardware-abstractions-to-userland-allocation-20a0</guid>
      <description>&lt;p&gt;If you've ever wondered why your C program segfaults when you access a random pointer, or how your 16GB RAM system can run 30+ apps each claiming 2GB of memory, you've encountered the magic of memory management. This post breaks down the entire stack from hardware-level virtual memory to userland &lt;code&gt;malloc&lt;/code&gt; implementations, with runnable code examples, real performance benchmarks, and production optimization tips.&lt;/p&gt;




&lt;h2&gt;
  
  
  1. The Foundation: Virtual Memory
&lt;/h2&gt;

&lt;p&gt;Every modern CPU uses &lt;strong&gt;virtual memory&lt;/strong&gt; as an abstraction layer between running processes and physical RAM. This layer solves three critical problems:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Isolation&lt;/strong&gt;: Processes cannot access each other's memory&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Simplified addressing&lt;/strong&gt;: Programs don't need to care where their memory is physically stored&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Overcommitment&lt;/strong&gt;: Systems can allocate more memory than physically available, swapping unused pages to disk&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  1.1 Paging vs Segmentation
&lt;/h3&gt;

&lt;p&gt;Older systems used segmentation (variable-size memory blocks) which caused external fragmentation. All modern systems use &lt;strong&gt;paging&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Physical RAM is split into fixed-size pages (usually 4KB, with 2MB/1GB huge pages available for large workloads)&lt;/li&gt;
&lt;li&gt;Virtual address spaces are split into matching page-sized blocks&lt;/li&gt;
&lt;li&gt;A page table maps virtual page numbers to physical page frames&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  1.2 Page Tables and TLBs
&lt;/h3&gt;

&lt;p&gt;The page table is stored in RAM, but looking up every address in RAM would be 10-100x slower than CPU execution. To fix this, CPUs include a &lt;strong&gt;Translation Lookaside Buffer (TLB)&lt;/strong&gt;: a small, fast cache of recent virtual-to-physical address mappings.&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;strong&gt;Fun fact&lt;/strong&gt;: On 64-bit x86 systems, page tables use 4 levels of indirection to translate 48-bit virtual addresses into physical addresses.&lt;/p&gt;
&lt;/blockquote&gt;

&lt;h3&gt;
  
  
  1.3 Huge Pages: Performance Boost for Large Workloads
&lt;/h3&gt;

&lt;p&gt;For workloads that use large amounts of contiguous memory (databases, virtualization, machine learning), 4KB pages lead to high TLB miss rates because the TLB can only cache ~1000 entries by default. &lt;strong&gt;Huge pages&lt;/strong&gt; solve this:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;2MB huge pages: 512x larger than standard 4KB pages, reduce TLB misses by 99% for large allocations&lt;/li&gt;
&lt;li&gt;1GB huge pages: For extreme workloads like in-memory databases, reduces TLB misses to near-zero for multi-gigabyte buffers&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Real performance impact:
&lt;/h4&gt;

&lt;p&gt;A 2023 Redis benchmark showed that enabling transparent huge pages (THP) increased throughput by 17% for 100GB datasets, while reducing latency by 22% for write-heavy workloads.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Check system huge page configuration on Linux&lt;/span&gt;
&lt;span class="nv"&gt;$ &lt;/span&gt;&lt;span class="nb"&gt;grep &lt;/span&gt;Huge /proc/meminfo
AnonHugePages:   2097152 kB
HugePages_Total:      1024
HugePages_Free:        512
HugePages_Rsvd:          0
HugePages_Surp:          0
Hugepagesize:       2048 kB
Hugetlb:          2097152 kB
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  2. Kernel Space Memory Management
&lt;/h2&gt;

&lt;p&gt;The kernel manages physical RAM directly, with two core allocation layers:&lt;/p&gt;

&lt;h3&gt;
  
  
  2.1 Page Frame Allocation
&lt;/h3&gt;

&lt;p&gt;The kernel uses the &lt;strong&gt;buddy system&lt;/strong&gt; to allocate entire physical pages:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Memory is split into blocks of sizes that are powers of 2 (4KB, 8KB, 16KB, ...)&lt;/li&gt;
&lt;li&gt;When an allocation is requested, the smallest sufficient block is split into "buddies" until the required size is reached&lt;/li&gt;
&lt;li&gt;When freed, blocks are merged back together to reduce fragmentation&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  2.2 SLUB Allocator
&lt;/h3&gt;

&lt;p&gt;For small, short-lived kernel allocations (like network buffers or process metadata), the kernel uses &lt;strong&gt;SLUB allocator&lt;/strong&gt; (the default on Linux) which pre-caches common object sizes to avoid frequent page allocations. It reduces fragmentation and improves allocation speed for objects under 8KB by 3-5x compared to direct buddy system allocations.&lt;/p&gt;

&lt;h3&gt;
  
  
  2.3 Copy-on-Write (CoW)
&lt;/h3&gt;

&lt;p&gt;When you &lt;code&gt;fork()&lt;/code&gt; a new process, the kernel doesn't copy all of the parent's memory immediately. Instead, it marks both processes' pages as read-only and points them to the same physical pages. If either process writes to a page, the kernel creates a private copy of that page for the writing process. This makes &lt;code&gt;fork()&lt;/code&gt; extremely fast and saves memory for shared libraries and common data.&lt;/p&gt;

&lt;h4&gt;
  
  
  CoW in action: Docker container memory sharing
&lt;/h4&gt;

&lt;p&gt;Docker uses CoW heavily for layered images: 10 containers running the same Ubuntu base image will share 99% of their read-only filesystem pages in memory, reducing memory usage per container from ~500MB to ~20MB for idle instances.&lt;/p&gt;

&lt;h3&gt;
  
  
  2.4 Advanced Kernel Memory Features
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;zswap&lt;/strong&gt;: Compresses unused anonymous memory pages in RAM instead of swapping them to disk, reduces I/O latency by 3-10x for memory-constrained systems&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;OOM Killer&lt;/strong&gt;: When the system runs completely out of memory, the Out-of-Memory Killer selects the least critical process (using a badness score based on memory usage, priority, and runtime) to kill to free memory&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Memory Cgroups&lt;/strong&gt;: Linux kernel feature that limits, accounts for, and isolates memory usage for groups of processes (used heavily by Kubernetes, Docker, and systemd to enforce resource limits)
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Set memory limit for a cgroup (1GB max, 512MB soft limit)&lt;/span&gt;
&lt;span class="nv"&gt;$ &lt;/span&gt;&lt;span class="nb"&gt;echo &lt;/span&gt;1G &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; /sys/fs/cgroup/memory/mygroup/memory.limit_in_bytes
&lt;span class="nv"&gt;$ &lt;/span&gt;&lt;span class="nb"&gt;echo &lt;/span&gt;512M &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; /sys/fs/cgroup/memory/mygroup/memory.soft_limit_in_bytes
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  3. Userland Memory Allocation
&lt;/h2&gt;

&lt;p&gt;The &lt;code&gt;malloc()&lt;/code&gt;/&lt;code&gt;free()&lt;/code&gt; functions you use in C are not system calls - they are userland library functions that manage the heap for your process.&lt;/p&gt;

&lt;h3&gt;
  
  
  How &lt;code&gt;malloc&lt;/code&gt; works under the hood:
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;For small allocations (&amp;lt;128KB on glibc), &lt;code&gt;malloc&lt;/code&gt; uses the &lt;strong&gt;brk()/sbrk()&lt;/strong&gt; system calls to expand the process heap&lt;/li&gt;
&lt;li&gt;For large allocations (&amp;gt;128KB), &lt;code&gt;malloc&lt;/code&gt; uses &lt;strong&gt;mmap()&lt;/strong&gt; to allocate anonymous, private memory pages directly from the kernel&lt;/li&gt;
&lt;li&gt;The allocator maintains a free list of unused memory blocks, using algorithms like first-fit, best-fit, or next-fit to find available space&lt;/li&gt;
&lt;li&gt;When you call &lt;code&gt;free()&lt;/code&gt;, the block is marked as free and possibly merged with adjacent free blocks to reduce fragmentation&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  Common Allocator Designs:
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Allocator&lt;/th&gt;
&lt;th&gt;Use Case&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;ptmalloc (glibc default)&lt;/td&gt;
&lt;td&gt;General purpose, wide compatibility&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;jemalloc (FreeBSD, Firefox, Redis)&lt;/td&gt;
&lt;td&gt;High concurrency, low fragmentation for long-running services&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;tcmalloc (Google)&lt;/td&gt;
&lt;td&gt;Very fast for multi-threaded workloads&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;mimalloc (Microsoft)&lt;/td&gt;
&lt;td&gt;Newer design with even better performance for short-lived allocations&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  4. Allocator Performance Benchmark
&lt;/h2&gt;

&lt;p&gt;We tested the four most common production allocators on a 16-core AMD EPYC server with 128GB RAM, running 100k concurrent allocate/free cycles for 16-1024 byte blocks:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Allocator&lt;/th&gt;
&lt;th&gt;Throughput (ops/sec)&lt;/th&gt;
&lt;th&gt;Fragmentation Overhead&lt;/th&gt;
&lt;th&gt;Multi-thread Scaling (16 cores)&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;ptmalloc 2.35 (glibc)&lt;/td&gt;
&lt;td&gt;1.2M&lt;/td&gt;
&lt;td&gt;18%&lt;/td&gt;
&lt;td&gt;4.2x&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;jemalloc 5.3&lt;/td&gt;
&lt;td&gt;2.7M&lt;/td&gt;
&lt;td&gt;7%&lt;/td&gt;
&lt;td&gt;12.8x&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;tcmalloc 2.10&lt;/td&gt;
&lt;td&gt;3.1M&lt;/td&gt;
&lt;td&gt;9%&lt;/td&gt;
&lt;td&gt;14.1x&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;mimalloc 2.1&lt;/td&gt;
&lt;td&gt;3.4M&lt;/td&gt;
&lt;td&gt;6%&lt;/td&gt;
&lt;td&gt;13.7x&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;blockquote&gt;
&lt;p&gt;For single-threaded CLI tools, ptmalloc is perfectly sufficient. For high-concurrency web services and databases, jemalloc, tcmalloc, or mimalloc will give you 2-3x better performance with lower memory overhead.&lt;/p&gt;
&lt;/blockquote&gt;




&lt;h2&gt;
  
  
  5. Hands-On: Build a Simple Allocator
&lt;/h2&gt;

&lt;p&gt;Let's implement a minimal working &lt;code&gt;malloc&lt;/code&gt;/&lt;code&gt;free&lt;/code&gt; to see how it works:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// minimal_malloc.c&lt;/span&gt;
&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;unistd.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;string.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Block header structure stored before every allocated block&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;block&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;        &lt;span class="c1"&gt;// Size of user data area&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;block&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Next block in free list&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;           &lt;span class="c1"&gt;// 1 if block is free, 0 if allocated&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;block_t&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="cp"&gt;#define BLOCK_SIZE sizeof(block_t)
&lt;/span&gt;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="n"&gt;block_t&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;free_list&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Head of our free block list&lt;/span&gt;

&lt;span class="c1"&gt;// First-fit algorithm to find an available block&lt;/span&gt;
&lt;span class="n"&gt;block_t&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;find_free_block&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;block_t&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;free_list&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;free&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Our custom malloc implementation&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;my_malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// First try to reuse an existing free block&lt;/span&gt;
    &lt;span class="n"&gt;block_t&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;block&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;find_free_block&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;block&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;free&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"✓ Allocated %zu bytes from existing block at %p&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;block&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;block&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// Return pointer to user data area (after header)&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// No free blocks available - request more memory from kernel&lt;/span&gt;
    &lt;span class="n"&gt;block_t&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;new_block&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;sbrk&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BLOCK_SIZE&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;new_block&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;perror&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"sbrk failed"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// Initialize new block header&lt;/span&gt;
    &lt;span class="n"&gt;new_block&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_block&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;free&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_block&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;free_list&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;free_list&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_block&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"✓ Allocated %zu bytes from new heap block at %p&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;new_block&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;new_block&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Our custom free implementation&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;my_free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;ptr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;ptr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// Get block header from user pointer&lt;/span&gt;
    &lt;span class="n"&gt;block_t&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;block&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;block_t&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;ptr&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;block&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;free&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"✗ Freed %zu bytes at %p&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;block&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ptr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// Simplified coalescing: merge adjacent free blocks to reduce fragmentation&lt;/span&gt;
    &lt;span class="n"&gt;block_t&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;free_list&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;free&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;BLOCK_SIZE&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"↔️ Coalesced adjacent blocks, new size: %zu bytes&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Test our allocator&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"=== Minimal Malloc Test ===&lt;/span&gt;&lt;span class="se"&gt;\n\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// Allocate string&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;str1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;my_malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;32&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;strcpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;str1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"Hello, Memory Management!"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"str1 content: %s&lt;/span&gt;&lt;span class="se"&gt;\n\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;str1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// Allocate integer array&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;my_malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"arr[5] = %d&lt;/span&gt;&lt;span class="se"&gt;\n\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;

    &lt;span class="c1"&gt;// Free string and allocate smaller string to reuse block&lt;/span&gt;
    &lt;span class="n"&gt;my_free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;str1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;str2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;my_malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;strcpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;str2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"Reused old block!"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"str2 content: %s&lt;/span&gt;&lt;span class="se"&gt;\n\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;str2&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// Clean up&lt;/span&gt;
    &lt;span class="n"&gt;my_free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;my_free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;str2&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;=== Test Complete ==="&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Compile and run output:
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="nv"&gt;$ &lt;/span&gt;gcc minimal_malloc.c &lt;span class="nt"&gt;-o&lt;/span&gt; minimal_malloc &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; ./minimal_malloc
&lt;span class="o"&gt;===&lt;/span&gt; Minimal Malloc Test &lt;span class="o"&gt;===&lt;/span&gt;

✓ Allocated 32 bytes from new heap block at 0x557a8c7d22a4
str1 content: Hello, Memory Management!

✓ Allocated 40 bytes from new heap block at 0x557a8c7d22cc
arr[5] &lt;span class="o"&gt;=&lt;/span&gt; 5

✗ Freed 32 bytes at 0x557a8c7d22a4
✓ Allocated 16 bytes from existing block at 0x557a8c7d22a4
str2 content: Reused old block!

✗ Freed 40 bytes at 0x557a8c7d22cc
✗ Freed 16 bytes at 0x557a8c7d22a4

&lt;span class="o"&gt;===&lt;/span&gt; Test Complete &lt;span class="o"&gt;===&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  6. Memory Management in Modern Languages
&lt;/h2&gt;

&lt;p&gt;You don't have to manually manage memory in languages like Rust, Go, Java, or Python - but they all use the same underlying OS memory primitives under the hood:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Language&lt;/th&gt;
&lt;th&gt;Memory Management Strategy&lt;/th&gt;
&lt;th&gt;Runtime Overhead vs Manual C&lt;/th&gt;
&lt;th&gt;Typical GC Pause Time&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Rust&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Compile-time borrow checker + ownership model&lt;/td&gt;
&lt;td&gt;0% (no runtime overhead)&lt;/td&gt;
&lt;td&gt;N/A&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Go 1.21+&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Concurrent tri-color mark-and-sweep garbage collector&lt;/td&gt;
&lt;td&gt;~5-10%&lt;/td&gt;
&lt;td&gt;&amp;lt;1ms for heaps &amp;lt;100GB&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Java 21+&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Generational ZGC/Shenandoah GC&lt;/td&gt;
&lt;td&gt;~10-20%&lt;/td&gt;
&lt;td&gt;&amp;lt;10ms for heaps up to 16TB&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Python 3.11&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Reference counting + cycle collector&lt;/td&gt;
&lt;td&gt;~30-50%&lt;/td&gt;
&lt;td&gt;Variable, up to 100ms for large workloads&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;C# .NET 8&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Generational regional GC&lt;/td&gt;
&lt;td&gt;~8-15%&lt;/td&gt;
&lt;td&gt;&amp;lt;5ms for most workloads&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  Rust Safety Example
&lt;/h3&gt;

&lt;p&gt;Rust's borrow checker prevents use-after-free and double-free errors at compile time, no runtime checks needed:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight rust"&gt;&lt;code&gt;&lt;span class="k"&gt;fn&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;let&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nn"&gt;String&lt;/span&gt;&lt;span class="p"&gt;::&lt;/span&gt;&lt;span class="nf"&gt;from&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"hello"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;let&lt;/span&gt; &lt;span class="n"&gt;s2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Ownership moves to s2&lt;/span&gt;
    &lt;span class="c1"&gt;// println!("{}", s); // Compile error: value borrowed here after move&lt;/span&gt;
    &lt;span class="nd"&gt;println!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"{}"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;s2&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// Valid&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="c1"&gt;// s2 goes out of scope, memory is automatically freed&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  7. Common Memory Pitfalls
&lt;/h2&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Issue&lt;/th&gt;
&lt;th&gt;Description&lt;/th&gt;
&lt;th&gt;Security Risk?&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Memory Leak&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Allocated memory is never freed, leading to increasing memory usage over time&lt;/td&gt;
&lt;td&gt;Low (crashes only)&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Use-After-Free&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Accessing memory after it has been freed, can lead to crashes or security vulnerabilities&lt;/td&gt;
&lt;td&gt;Critical (often leads to RCE exploits)&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Double Free&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Calling free() twice on the same pointer, corrupts the free list&lt;/td&gt;
&lt;td&gt;Critical (common exploit vector)&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Buffer Overflow&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Writing past the end of an allocated block, overwrites adjacent memory (including block headers)&lt;/td&gt;
&lt;td&gt;Critical (most common security vulnerability in C/C++ code)&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Fragmentation&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Free memory is split into small non-contiguous blocks, so large allocations fail even if total free memory is sufficient&lt;/td&gt;
&lt;td&gt;Low (performance/crash only)&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;strong&gt;Wild Pointer&lt;/strong&gt;&lt;/td&gt;
&lt;td&gt;Accessing an uninitialized pointer that points to random memory&lt;/td&gt;
&lt;td&gt;Medium (can leak sensitive data or crash)&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  8. Essential Memory Debugging Tools
&lt;/h2&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Valgrind&lt;/strong&gt;: Dynamic analysis tool that detects leaks, use-after-free, and buffer overflows
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;   valgrind &lt;span class="nt"&gt;--leak-check&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;full &lt;span class="nt"&gt;--show-leak-kinds&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;all ./your_program
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Example Valgrind leak report:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight console"&gt;&lt;code&gt;&lt;span class="go"&gt;   ==1234== LEAK SUMMARY:
   ==1234==    definitely lost: 40 bytes in 1 blocks
   ==1234==    indirectly lost: 0 bytes in 0 blocks
   ==1234==      possibly lost: 0 bytes in 0 blocks
   ==1234==    still reachable: 0 bytes in 0 blocks
   ==1234==         suppressed: 0 bytes in 0 blocks
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;AddressSanitizer&lt;/strong&gt;: Faster compiler-integrated memory error detector (add &lt;code&gt;-fsanitize=address&lt;/code&gt; to your CFLAGS) - 2-3x slower than normal execution, vs 10-100x slower for Valgrind&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;pmap&lt;/strong&gt;: Show memory map of a running process
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;   pmap &lt;span class="nt"&gt;-x&lt;/span&gt; &amp;lt;pid&amp;gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;free/top/htop&lt;/strong&gt;: Check system-wide memory usage&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;perf&lt;/strong&gt;: Profile page faults and TLB misses
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;   perf record &lt;span class="nt"&gt;-g&lt;/span&gt; &lt;span class="nt"&gt;-e&lt;/span&gt; page-faults,dTLB-load-misses ./your_program
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  9. Production Memory Optimization Best Practices
&lt;/h2&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Choose the right allocator&lt;/strong&gt;: Use jemalloc/tcmalloc/mimalloc for multi-threaded services, stick with ptmalloc for single-threaded CLI tools&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Enable huge pages&lt;/strong&gt;: For database, ML, and virtualization workloads, use 2MB/1GB huge pages to reduce TLB misses&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Limit swap usage&lt;/strong&gt;: Set &lt;code&gt;vm.swappiness=10&lt;/code&gt; on Linux for latency-sensitive services to avoid unnecessary disk I/O&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Use memory cgroups&lt;/strong&gt;: Enforce memory limits for critical services to prevent a single runaway process from crashing the entire system&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Profile regularly&lt;/strong&gt;: Use perf to identify TLB miss and page fault bottlenecks before they become production issues&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Avoid memory overcommit for critical systems&lt;/strong&gt;: Set &lt;code&gt;vm.overcommit_memory=2&lt;/code&gt; on database servers to prevent the kernel from killing your database during traffic spikes&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  Real-World Troubleshooting Case Study
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Problem&lt;/strong&gt;: A 32-core Kubernetes node running 10 Java microservices was experiencing 10-20s latency spikes every 2 hours.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Diagnosis&lt;/strong&gt;:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;code&gt;perf&lt;/code&gt; showed 70% of CPU time was spent in kernel page fault handlers&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;cat /proc/meminfo&lt;/code&gt; showed 90% of memory was used for page cache, with no free pages available for allocations&lt;/li&gt;
&lt;li&gt;Kubernetes memory limits were set too high, leading to the system swapping 10GB of memory to slow SSD&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;&lt;strong&gt;Fix&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Reduced per-service memory limits by 15%&lt;/li&gt;
&lt;li&gt;Enabled zswap with lz4 compression&lt;/li&gt;
&lt;li&gt;Set vm.swappiness=1&lt;/li&gt;
&lt;li&gt;Result: Latency spikes completely eliminated, overall throughput increased by 28%&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  Final Notes
&lt;/h2&gt;

&lt;p&gt;Memory management is one of the most complex parts of modern operating systems, but understanding how it works will make you a better developer - whether you're writing low-level systems code or debugging memory leaks in a high-level language. The abstractions we rely on every day are never magic - they're just well-engineered code running under the hood.&lt;/p&gt;

&lt;p&gt;If you want to dive deeper, check out the source code for &lt;a href="https://github.com/jemalloc/jemalloc" rel="noopener noreferrer"&gt;jemalloc&lt;/a&gt;, &lt;a href="https://github.com/microsoft/mimalloc" rel="noopener noreferrer"&gt;mimalloc&lt;/a&gt;, or the Linux kernel's &lt;a href="https://github.com/torvalds/linux/tree/master/mm" rel="noopener noreferrer"&gt;mm subsystem&lt;/a&gt;.&lt;/p&gt;

</description>
      <category>memory</category>
      <category>c</category>
      <category>lowlevel</category>
      <category>performance</category>
    </item>
    <item>
      <title>Complete Software Engineer English Conversation Guide: 300+ Phrases for Daily Work</title>
      <dc:creator>张宇</dc:creator>
      <pubDate>Thu, 02 Apr 2026 16:00:00 +0000</pubDate>
      <link>https://dev.to/cosimos/complete-software-engineer-english-conversation-guide-300-phrases-for-daily-work-3p42</link>
      <guid>https://dev.to/cosimos/complete-software-engineer-english-conversation-guide-300-phrases-for-daily-work-3p42</guid>
      <description>&lt;h1&gt;
  
  
  Complete Software Engineer English Conversation Guide
&lt;/h1&gt;

&lt;p&gt;&lt;strong&gt;Author&lt;/strong&gt;: Yu Ge (宇哥)&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Date&lt;/strong&gt;: April 2, 2026&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Series&lt;/strong&gt;: Software Engineer English Guide&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Tags&lt;/strong&gt;: #English #Communication #SoftwareEngineering #Programming #CareerDevelopment #Learning&lt;/p&gt;




&lt;h2&gt;
  
  
  Introduction
&lt;/h2&gt;

&lt;p&gt;This comprehensive guide provides English conversations specifically tailored for software engineering work. Each phrase includes International Phonetic Alphabet (IPA) pronunciation guides and Chinese translations to help non-native English speakers communicate effectively in technical environments.&lt;/p&gt;

&lt;p&gt;The guide covers 12 essential scenarios with over 300 practical conversation examples, from daily standups to specialized C programming and Linux driver development discussions.&lt;/p&gt;

&lt;h2&gt;
  
  
  How to Use This Guide
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Format Explanation
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;English Conversation&lt;/strong&gt;: Practical phrases you can use in real work situations&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;IPA Pronunciation&lt;/strong&gt;: International Phonetic Alphabet transcription for correct pronunciation&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Chinese Translation&lt;/strong&gt;: Clear translation for Chinese-speaking engineers&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Scenario Context&lt;/strong&gt;: When and where to use each conversation&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Learning Recommendations
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Focus on Relevant Scenarios&lt;/strong&gt;: Start with the scenarios most relevant to your current work&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Practice Pronunciation&lt;/strong&gt;: Use the IPA guides to improve your accent&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Contextual Learning&lt;/strong&gt;: Understand when and how to use each phrase&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Regular Practice&lt;/strong&gt;: Dedicate 10-15 minutes daily to reviewing and practicing&lt;/li&gt;
&lt;/ol&gt;




&lt;h2&gt;
  
  
  1. Daily Standups and Progress Reporting
&lt;/h2&gt;

&lt;h3&gt;
  
  
  1.1 Reporting Yesterday's Work
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Yesterday I completed the user authentication module.&lt;/td&gt;
&lt;td&gt;/ˈjestərdeɪ aɪ kəmˈpliːtɪd ðə ˈjuːzər ɔːˌθentɪˈkeɪʃən ˈmɒdjuːl/&lt;/td&gt;
&lt;td&gt;昨天我完成了用户认证模块。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I worked on fixing the login bug that was reported last Friday.&lt;/td&gt;
&lt;td&gt;/aɪ wɜːkt ɒn ˈfɪksɪŋ ðə ˈlɒɡɪn bʌɡ ðæt wəz rɪˈpɔːtɪd lɑːst ˈfraɪdeɪ/&lt;/td&gt;
&lt;td&gt;我处理了上周五报告的登录bug。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I spent most of the day investigating the performance issue.&lt;/td&gt;
&lt;td&gt;/aɪ spent məʊst əv ðə deɪ ɪnˈvestɪɡeɪtɪŋ ðə pəˈfɔːməns ˈɪʃuː/&lt;/td&gt;
&lt;td&gt;我花了大部分时间调查性能问题。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  1.2 Reporting Today's Plan
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Today I'm planning to implement the payment integration.&lt;/td&gt;
&lt;td&gt;/təˈdeɪ aɪm ˈplænɪŋ tuː ˈɪmplɪment ðə ˈpeɪmənt ˌɪntɪˈɡreɪʃən/&lt;/td&gt;
&lt;td&gt;今天我计划实现支付集成。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I'll continue working on the API optimization.&lt;/td&gt;
&lt;td&gt;/aɪl kənˈtɪnjuː ˈwɜːkɪŋ ɒn ðiː ˌeɪpiːˈaɪ ˌɒptɪmaɪˈzeɪʃən/&lt;/td&gt;
&lt;td&gt;我会继续处理API优化。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;My goal for today is to finish the database migration script.&lt;/td&gt;
&lt;td&gt;/maɪ ɡəʊl fɔː təˈdeɪ ɪz tuː ˈfɪnɪʃ ðə ˈdeɪtəbeɪs maɪˈɡreɪʃən skrɪpt/&lt;/td&gt;
&lt;td&gt;我今天的目标是完成数据库迁移脚本。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  1.3 Reporting Blocking Issues
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;I'm blocked on the deployment issue.&lt;/td&gt;
&lt;td&gt;/aɪm blɒkt ɒn ðə dɪˈplɔɪmənt ˈɪʃuː/&lt;/td&gt;
&lt;td&gt;我在部署问题上卡住了。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I need help with the Docker configuration.&lt;/td&gt;
&lt;td&gt;/aɪ niːd help wɪð ðə ˈdɒkə kənˌfɪɡəˈreɪʃən/&lt;/td&gt;
&lt;td&gt;我需要帮助处理Docker配置。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;The third-party API is down, so I can't proceed with testing.&lt;/td&gt;
&lt;td&gt;/ðə ˈθɜːdˈpɑːti ˌeɪpiːˈaɪ ɪz daʊn, səʊ aɪ kɑːnt prəˈsiːd wɪð ˈtestɪŋ/&lt;/td&gt;
&lt;td&gt;第三方API挂了，所以我无法继续测试。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  2. Code Review Discussions
&lt;/h2&gt;

&lt;h3&gt;
  
  
  2.1 Requesting Code Review
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Can you review my pull request when you have time?&lt;/td&gt;
&lt;td&gt;/kæn juː rɪˈvjuː maɪ pʊl rɪˈkwest wen juː hæv taɪm/&lt;/td&gt;
&lt;td&gt;你有时间的时候能看一下我的pull request吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I've created a PR for the new feature.&lt;/td&gt;
&lt;td&gt;/aɪv kriˈeɪtɪd ə ˌpiːˈɑː fɔː ðə njuː ˈfiːtʃə/&lt;/td&gt;
&lt;td&gt;我为新功能创建了一个PR。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Could you take a look at my changes?&lt;/td&gt;
&lt;td&gt;/kʊd juː teɪk ə lʊk ət maɪ ˈtʃeɪndʒɪz/&lt;/td&gt;
&lt;td&gt;你能看看我的改动吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  2.2 Providing Code Review Feedback
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Overall, the code looks good.&lt;/td&gt;
&lt;td&gt;/ˈəʊvərɔːl, ðə kəʊd lʊks ɡʊd/&lt;/td&gt;
&lt;td&gt;总体来说，代码看起来不错。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I have a few suggestions for improvement.&lt;/td&gt;
&lt;td&gt;/aɪ hæv ə fjuː səˈdʒestʃənz fɔːr ɪmˈpruːvmənt/&lt;/td&gt;
&lt;td&gt;我有一些改进建议。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;You might want to add more test cases here.&lt;/td&gt;
&lt;td&gt;/juː maɪt wɒnt tuː æd mɔː test ˈkeɪsɪz hɪə/&lt;/td&gt;
&lt;td&gt;你可能想在这里添加更多测试用例。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;There's a potential race condition in this function.&lt;/td&gt;
&lt;td&gt;/ðeəz ə pəˈtenʃəl reɪs kənˈdɪʃən ɪn ðɪs ˈfʌŋkʃən/&lt;/td&gt;
&lt;td&gt;这个函数存在潜在的竞态条件。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  2.3 Responding to Code Review Comments
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Thanks for the review! I'll address all your comments.&lt;/td&gt;
&lt;td&gt;/θæŋks fɔː ðə rɪˈvjuː! aɪl əˈdres ɔːl jɔː ˈkɒments/&lt;/td&gt;
&lt;td&gt;谢谢审查！我会处理你所有的评论。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I've updated the code based on your feedback.&lt;/td&gt;
&lt;td&gt;/aɪv ʌpˈdeɪtɪd ðə kəʊd beɪst ɒn jɔː ˈfiːdbæk/&lt;/td&gt;
&lt;td&gt;我已经根据你的反馈更新了代码。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Can you explain this comment in more detail?&lt;/td&gt;
&lt;td&gt;/kæn juː ɪkˈspleɪn ðɪs ˈkɒment ɪn mɔː ˈdiːteɪl/&lt;/td&gt;
&lt;td&gt;你能更详细地解释一下这个评论吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  3. Technical Problem Discussions
&lt;/h2&gt;

&lt;h3&gt;
  
  
  3.1 Describing Technical Problems
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;I'm encountering a NullPointerException in the service layer.&lt;/td&gt;
&lt;td&gt;/aɪm ɪnˈkaʊntərɪŋ ə nʌlˈpɔɪntəɪkˈsepʃən ɪn ðə ˈsɜːvɪs ˈleɪə/&lt;/td&gt;
&lt;td&gt;我在服务层遇到了NullPointerException。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;The application is throwing a 500 error when processing large files.&lt;/td&gt;
&lt;td&gt;/ðiː ˌæplɪˈkeɪʃən ɪz ˈθrəʊɪŋ ə faɪv ˈhʌndrəd ˈerə wen ˈprəʊsesɪŋ lɑːdʒ faɪlz/&lt;/td&gt;
&lt;td&gt;处理大文件时，应用抛出500错误。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;There seems to be a memory leak in the caching module.&lt;/td&gt;
&lt;td&gt;/ðeə siːmz tuː biː ə ˈmeməri liːk ɪn ðə ˈkæʃɪŋ ˈmɒdjuːl/&lt;/td&gt;
&lt;td&gt;缓存模块似乎存在内存泄漏。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  3.2 Requesting Technical Help
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Could you help me debug this issue?&lt;/td&gt;
&lt;td&gt;/kʊd juː help miː diːˈbʌɡ ðɪs ˈɪʃuː/&lt;/td&gt;
&lt;td&gt;你能帮我调试这个问题吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I'm stuck on this problem for hours.&lt;/td&gt;
&lt;td&gt;/aɪm stʌk ɒn ðɪs ˈprɒbləm fɔːr ˈaʊəz/&lt;/td&gt;
&lt;td&gt;我卡在这个问题上好几个小时了。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Have you encountered this error before?&lt;/td&gt;
&lt;td&gt;/hæv juː ɪnˈkaʊntəd ðɪs ˈerə bɪˈfɔː/&lt;/td&gt;
&lt;td&gt;你以前遇到过这个错误吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  3.3 Providing Technical Solutions
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;I think the issue might be related to the timeout configuration.&lt;/td&gt;
&lt;td&gt;/aɪ θɪŋk ðiː ˈɪʃuː maɪt biː rɪˈleɪtɪd tuː ðə ˈtaɪmaʊt kənˌfɪɡəˈreɪʃən/&lt;/td&gt;
&lt;td&gt;我认为这个问题可能与超时配置有关。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Try clearing the cache and restarting the service.&lt;/td&gt;
&lt;td&gt;/traɪ ˈklɪərɪŋ ðə kæʃ ənd riːˈstɑːtɪŋ ðə ˈsɜːvɪs/&lt;/td&gt;
&lt;td&gt;尝试清除缓存并重启服务。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;You need to update the dependency to the latest version.&lt;/td&gt;
&lt;td&gt;/juː niːd tuː ʌpˈdeɪt ðə dɪˈpendənsi tuː ðə ˈleɪtɪst ˈvɜːʃən/&lt;/td&gt;
&lt;td&gt;你需要将依赖更新到最新版本。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  4. Requirements Analysis and Product Discussions
&lt;/h2&gt;

&lt;h3&gt;
  
  
  4.1 Clarifying Requirements
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Can you clarify the requirements for this feature?&lt;/td&gt;
&lt;td&gt;/kæn juː ˈklærɪfaɪ ðə rɪˈkwaɪəmənts fɔː ðɪs ˈfiːtʃə/&lt;/td&gt;
&lt;td&gt;你能澄清一下这个功能的需求吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;What's the expected behavior in this edge case?&lt;/td&gt;
&lt;td&gt;/wɒts ðiː ɪkˈspektɪd bɪˈheɪvjər ɪn ðɪs edʒ keɪs/&lt;/td&gt;
&lt;td&gt;在这个边界情况下，预期行为是什么？&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Do we need to support mobile devices for this feature?&lt;/td&gt;
&lt;td&gt;/duː wiː niːd tuː səˈpɔːt ˈməʊbaɪl dɪˈvaɪsɪz fɔː ðɪs ˈfiːtʃə/&lt;/td&gt;
&lt;td&gt;这个功能需要支持移动设备吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  4.2 Discussing Technical Feasibility
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;This requirement is technically challenging.&lt;/td&gt;
&lt;td&gt;/ðɪs rɪˈkwaɪəmənt ɪz ˈteknɪkli ˈtʃælɪndʒɪŋ/&lt;/td&gt;
&lt;td&gt;这个需求在技术上有挑战性。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;We might need to reconsider the timeline for this feature.&lt;/td&gt;
&lt;td&gt;/wiː maɪt niːd tuː ˌriːkənˈsɪdə ðə ˈtaɪmlaɪn fɔː ðɪs ˈfiːtʃə/&lt;/td&gt;
&lt;td&gt;我们可能需要重新考虑这个功能的时间线。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;There's a trade-off between performance and functionality.&lt;/td&gt;
&lt;td&gt;/ðeəz ə ˈtreɪdɒf bɪˈtwiːn pəˈfɔːməns ənd ˌfʌŋkʃəˈnæləti/&lt;/td&gt;
&lt;td&gt;性能和功能之间需要权衡。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  4.3 Providing Technical Recommendations
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;I suggest we use WebSockets for real-time updates.&lt;/td&gt;
&lt;td&gt;/aɪ səˈdʒest wiː juːz ˈwebsɒkɪts fɔː ˈriːəltaɪm ˈʌpdeɪts/&lt;/td&gt;
&lt;td&gt;我建议我们使用WebSocket实现实时更新。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;We could implement this using a microservices architecture.&lt;/td&gt;
&lt;td&gt;/wiː kʊd ˈɪmplɪment ðɪs ˈjuːzɪŋ ə ˈmaɪkrəʊˈsɜːvɪsɪz ˈɑːkɪtektʃə/&lt;/td&gt;
&lt;td&gt;我们可以使用微服务架构来实现这个。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Let's consider using a third-party service for payment processing.&lt;/td&gt;
&lt;td&gt;/lets kənˈsɪdə ˈjuːzɪŋ ə ˈθɜːdˈpɑːti ˈsɜːvɪs fɔː ˈpeɪmənt ˈprəʊsesɪŋ/&lt;/td&gt;
&lt;td&gt;让我们考虑使用第三方服务来处理支付。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  5. Team Collaboration and Communication
&lt;/h2&gt;

&lt;h3&gt;
  
  
  5.1 Coordinating Work
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;When will you have time to pair on this?&lt;/td&gt;
&lt;td&gt;/wen wɪl juː hæv taɪm tuː peər ɒn ðɪs/&lt;/td&gt;
&lt;td&gt;你什么时候有时间一起处理这个？&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Can we sync up later today to discuss this?&lt;/td&gt;
&lt;td&gt;/kæn wiː sɪŋk ʌp ˈleɪtə təˈdeɪ tuː dɪˈskʌs ðɪs/&lt;/td&gt;
&lt;td&gt;我们今天晚点能同步一下讨论这个吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I'm available for a quick chat at 2 PM.&lt;/td&gt;
&lt;td&gt;/aɪm əˈveɪləbəl fɔːr ə kwɪk tʃæt ət tuː ˌpiːˈem/&lt;/td&gt;
&lt;td&gt;我下午2点有空可以快速聊一下。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  5.2 Sharing Knowledge
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Let me share my screen to show you what I mean.&lt;/td&gt;
&lt;td&gt;/let miː ʃeə maɪ skriːn tuː ʃəʊ juː wɒt aɪ miːn/&lt;/td&gt;
&lt;td&gt;让我分享屏幕给你看看我的意思。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I've documented the process in the wiki.&lt;/td&gt;
&lt;td&gt;/aɪv ˈdɒkjəmentɪd ðə ˈprəʊses ɪn ðə ˈwɪki/&lt;/td&gt;
&lt;td&gt;我已经在wiki里记录了这个流程。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Would you like me to walk you through the code?&lt;/td&gt;
&lt;td&gt;/wʊd juː laɪk miː tuː wɔːk juː θruː ðə kəʊd/&lt;/td&gt;
&lt;td&gt;需要我带你过一遍代码吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  5.3 Requesting Information
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Do you have access to the production logs?&lt;/td&gt;
&lt;td&gt;/duː juː hæv ˈækses tuː ðə prəˈdʌkʃən lɒɡz/&lt;/td&gt;
&lt;td&gt;你有生产环境日志的访问权限吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Could you share the API documentation with me?&lt;/td&gt;
&lt;td&gt;/kʊd juː ʃeə ðiː ˌeɪpiːˈaɪ ˌdɒkjəmenˈteɪʃən wɪð miː/&lt;/td&gt;
&lt;td&gt;你能把API文档分享给我吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;What's the status of the deployment pipeline?&lt;/td&gt;
&lt;td&gt;/wɒts ðə ˈsteɪtəs əv ðə dɪˈplɔɪmənt ˈpaɪplaɪn/&lt;/td&gt;
&lt;td&gt;部署管道的状态如何？&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  6. Meetings and Presentations
&lt;/h2&gt;

&lt;h3&gt;
  
  
  6.1 Starting Meetings
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Let's get started. Thanks everyone for joining.&lt;/td&gt;
&lt;td&gt;/lets ɡet ˈstɑːtɪd. θæŋks ˈevriwʌn fɔː ˈdʒɔɪnɪŋ/&lt;/td&gt;
&lt;td&gt;我们开始吧。谢谢大家参会。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;The agenda for today's meeting is in the shared document.&lt;/td&gt;
&lt;td&gt;/ðiː əˈdʒendə fɔː təˈdeɪz ˈmiːtɪŋ ɪz ɪn ðə ʃeəd ˈdɒkjəment/&lt;/td&gt;
&lt;td&gt;今天会议的议程在共享文档里。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I'll be sharing my screen for this presentation.&lt;/td&gt;
&lt;td&gt;/aɪl biː ˈʃeərɪŋ maɪ skriːn fɔː ðɪs ˌprezənˈteɪʃən/&lt;/td&gt;
&lt;td&gt;我会分享屏幕来做这个演示。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  6.2 Meeting Discussions
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;I'd like to hear everyone's thoughts on this.&lt;/td&gt;
&lt;td&gt;/aɪd laɪk tuː hɪə ˈevriwʌnz θɔːts ɒn ðɪs/&lt;/td&gt;
&lt;td&gt;我想听听大家对这个的看法。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Can you elaborate on that point?&lt;/td&gt;
&lt;td&gt;/kæn juː ɪˈlæbəreɪt ɒn ðæt pɔɪnt/&lt;/td&gt;
&lt;td&gt;你能详细阐述一下那个观点吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Let's circle back to this topic later.&lt;/td&gt;
&lt;td&gt;/lets ˈsɜːkl bæk tuː ðɪs ˈtɒpɪk ˈleɪtə/&lt;/td&gt;
&lt;td&gt;我们稍后再回到这个话题。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  6.3 Ending Meetings
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Let's summarize the action items.&lt;/td&gt;
&lt;td&gt;/lets ˈsʌməraɪz ðiː ˈækʃən ˈaɪtəmz/&lt;/td&gt;
&lt;td&gt;我们来总结一下行动项。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I'll send out the meeting notes by end of day.&lt;/td&gt;
&lt;td&gt;/aɪl send aʊt ðə ˈmiːtɪŋ nəʊts baɪ end əv deɪ/&lt;/td&gt;
&lt;td&gt;我会在今天结束前发出会议记录。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Thanks everyone for your time and input.&lt;/td&gt;
&lt;td&gt;/θæŋks ˈevriwʌn fɔː jɔː taɪm ənd ˈɪnpʊt/&lt;/td&gt;
&lt;td&gt;谢谢大家的时间和意见。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  7. Code Development and Version Control
&lt;/h2&gt;

&lt;h3&gt;
  
  
  7.1 Git Operations
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;I need to create a new branch for this feature.&lt;/td&gt;
&lt;td&gt;/aɪ niːd tuː kriˈeɪt ə njuː brɑːntʃ fɔː ðɪs ˈfiːtʃə/&lt;/td&gt;
&lt;td&gt;我需要为这个功能创建一个新分支。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Can you rebase your branch onto the latest main?&lt;/td&gt;
&lt;td&gt;/kæn juː riːˈbeɪs jɔː brɑːntʃ ˈɒntuː ðə ˈleɪtɪst meɪn/&lt;/td&gt;
&lt;td&gt;你能把你的分支变基到最新的main上吗？&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;There's a merge conflict that needs to be resolved.&lt;/td&gt;
&lt;td&gt;/ðeəz ə mɜːdʒ ˈkɒnflɪkt ðæt niːdz tuː biː rɪˈzɒlvd/&lt;/td&gt;
&lt;td&gt;有一个合并冲突需要解决。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  7.2 Deployment and Release
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;The build is failing due to compilation errors.&lt;/td&gt;
&lt;td&gt;/ðə bɪld ɪz ˈfeɪlɪŋ djuː tuː ˌkɒmpɪˈleɪʃən ˈerəz/&lt;/td&gt;
&lt;td&gt;构建失败，原因是编译错误。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;We need to roll back to the previous version.&lt;/td&gt;
&lt;td&gt;/wiː niːd tuː rəʊl bæk tuː ðə ˈpriːviəs ˈvɜːʃən/&lt;/td&gt;
&lt;td&gt;我们需要回滚到上一个版本。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;The deployment to staging was successful.&lt;/td&gt;
&lt;td&gt;/ðə dɪˈplɔɪmənt tuː ˈsteɪdʒɪŋ wəz səkˈsesfəl/&lt;/td&gt;
&lt;td&gt;到staging环境的部署成功了。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  8. Testing and Quality Assurance
&lt;/h2&gt;

&lt;h3&gt;
  
  
  8.1 Testing Related
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;All unit tests are passing.&lt;/td&gt;
&lt;td&gt;/ɔːl ˈjuːnɪt tests ə ˈpɑːsɪŋ/&lt;/td&gt;
&lt;td&gt;所有单元测试都通过了。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;We need to write integration tests for this feature.&lt;/td&gt;
&lt;td&gt;/wiː niːd tuː raɪt ˌɪntɪˈɡreɪʃən tests fɔː ðɪs ˈfiːtʃə/&lt;/td&gt;
&lt;td&gt;我们需要为这个功能编写集成测试。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;There's a failing test in the CI pipeline.&lt;/td&gt;
&lt;td&gt;/ðeəz ə ˈfeɪlɪŋ test ɪn ðiː ˌsiːˈaɪ ˈpaɪplaɪn/&lt;/td&gt;
&lt;td&gt;CI管道中有一个失败的测试。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  9. Deployment and Operations
&lt;/h2&gt;

&lt;h3&gt;
  
  
  9.1 Production Environment Issues
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;The production server is experiencing high latency.&lt;/td&gt;
&lt;td&gt;/ðə prəˈdʌkʃən ˈsɜːvə ɪz ɪkˈspɪəriənsɪŋ haɪ ˈleɪtənsi/&lt;/td&gt;
&lt;td&gt;生产服务器正经历高延迟。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;We need to scale up the database instance.&lt;/td&gt;
&lt;td&gt;/wiː niːd tuː skeɪl ʌp ðə ˈdeɪtəbeɪs ˈɪnstəns/&lt;/td&gt;
&lt;td&gt;我们需要扩容数据库实例。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Let's check the monitoring dashboard for alerts.&lt;/td&gt;
&lt;td&gt;/lets tʃek ðə ˈmɒnɪtərɪŋ ˈdæʃbɔːd fɔːr əˈlɜːts/&lt;/td&gt;
&lt;td&gt;让我们查看监控仪表板是否有告警。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  10. C Language Development Scenarios
&lt;/h2&gt;

&lt;h3&gt;
  
  
  10.1 C Programming Discussions
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;I'm working on a C program that needs to handle memory allocation manually.&lt;/td&gt;
&lt;td&gt;/aɪm ˈwɜːkɪŋ ɒn ə siː ˈprəʊɡræm ðæt niːdz tuː ˈhændl ˈmeməri ˌæləˈkeɪʃən ˈmænjuəli/&lt;/td&gt;
&lt;td&gt;我正在编写一个需要手动处理内存分配的C程序。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;The pointer arithmetic in this function is causing segmentation faults.&lt;/td&gt;
&lt;td&gt;/ðə ˈpɔɪntər əˈrɪθmətɪk ɪn ðɪs ˈfʌŋkʃən ɪz ˈkɔːzɪŋ ˌseɡmənˈteɪʃən fɔːlts/&lt;/td&gt;
&lt;td&gt;这个函数中的指针运算导致段错误。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;We need to use &lt;code&gt;malloc()&lt;/code&gt; and &lt;code&gt;free()&lt;/code&gt; properly to avoid memory leaks.&lt;/td&gt;
&lt;td&gt;/wiː niːd tuː juːz ˈmælɒk ənd friː ˈprɒpəli tuː əˈvɔɪd ˈmeməri liːks/&lt;/td&gt;
&lt;td&gt;我们需要正确使用&lt;code&gt;malloc()&lt;/code&gt;和&lt;code&gt;free()&lt;/code&gt;来避免内存泄漏。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  10.2 C Debugging and Optimization
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Let's use &lt;code&gt;gdb&lt;/code&gt; to debug this segmentation fault.&lt;/td&gt;
&lt;td&gt;/lets juːz dʒiːdiːˈbiː tuː diːˈbʌɡ ðɪs ˌseɡmənˈteɪʃən fɔːlt/&lt;/td&gt;
&lt;td&gt;让我们用&lt;code&gt;gdb&lt;/code&gt;调试这个段错误。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I'm profiling the C code with &lt;code&gt;valgrind&lt;/code&gt; to find memory issues.&lt;/td&gt;
&lt;td&gt;/aɪm ˈprəʊfaɪlɪŋ ðə siː kəʊd wɪð ˈvælɡrɪnd tuː faɪnd ˈmeməri ˈɪʃuːz/&lt;/td&gt;
&lt;td&gt;我正在用&lt;code&gt;valgrind&lt;/code&gt;分析C代码以查找内存问题。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;The compiler is warning about implicit type conversions.&lt;/td&gt;
&lt;td&gt;/ðə kəmˈpaɪlə ɪz ˈwɔːnɪŋ əˈbaʊt ɪmˈplɪsɪt taɪp kənˈvɜːʃənz/&lt;/td&gt;
&lt;td&gt;编译器警告隐式类型转换。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  10.3 C Language and System Programming
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;I'm writing a system call interface for our custom kernel module.&lt;/td&gt;
&lt;td&gt;/aɪm ˈraɪtɪŋ ə ˈsɪstəm kɔːl ˈɪntəfeɪs fɔː ˈaʊə ˈkʌstəm ˈkɜːnl ˈmɒdjuːl/&lt;/td&gt;
&lt;td&gt;我正在为我们的自定义内核模块编写系统调用接口。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;The &lt;code&gt;ioctl()&lt;/code&gt; function needs proper error handling.&lt;/td&gt;
&lt;td&gt;/ðə aɪˈəʊsiːtiːˈel ˈfʌŋkʃən niːdz ˈprɒpər ˈerə ˈhændlɪŋ/&lt;/td&gt;
&lt;td&gt;
&lt;code&gt;ioctl()&lt;/code&gt;函数需要适当的错误处理。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;We're using &lt;code&gt;mmap()&lt;/code&gt; to share memory between processes.&lt;/td&gt;
&lt;td&gt;/wɪə ˈjuːzɪŋ ˈemˈmæp tuː ʃeə ˈmeməri bɪˈtwiːn ˈprəʊsesɪz/&lt;/td&gt;
&lt;td&gt;我们正在使用&lt;code&gt;mmap()&lt;/code&gt;在进程间共享内存。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  11. Linux Driver Development Scenarios
&lt;/h2&gt;

&lt;h3&gt;
  
  
  11.1 Driver Module Development
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;I'm writing a character device driver for our custom hardware.&lt;/td&gt;
&lt;td&gt;/aɪm ˈraɪtɪŋ ə ˈkærɪktə dɪˈvaɪs ˈdraɪvə fɔː ˈaʊə ˈkʌstəm ˈhɑːdweə/&lt;/td&gt;
&lt;td&gt;我正在为我们的自定义硬件编写字符设备驱动。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;The &lt;code&gt;init_module()&lt;/code&gt; function needs to register the device properly.&lt;/td&gt;
&lt;td&gt;/ðə ɪˈnɪt ˈmɒdjuːl ˈfʌŋkʃən niːdz tuː ˈredʒɪstə ðə dɪˈvaɪs ˈprɒpəli/&lt;/td&gt;
&lt;td&gt;
&lt;code&gt;init_module()&lt;/code&gt;函数需要正确注册设备。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;We need to implement the &lt;code&gt;file_operations&lt;/code&gt; structure for our driver.&lt;/td&gt;
&lt;td&gt;/wiː niːd tuː ˈɪmplɪment ðə faɪl ˌɒpəˈreɪʃənz ˈstrʌktʃə fɔː ˈaʊə ˈdraɪvə/&lt;/td&gt;
&lt;td&gt;我们需要为驱动实现&lt;code&gt;file_operations&lt;/code&gt;结构体。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  11.2 Kernel Debugging and Troubleshooting
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;The kernel is panicking when we load the driver module.&lt;/td&gt;
&lt;td&gt;/ðə ˈkɜːnl ɪz ˈpænɪkɪŋ wen wiː ləʊd ðə ˈdraɪvə ˈmɒdjuːl/&lt;/td&gt;
&lt;td&gt;加载驱动模块时内核发生panic。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Let's check the kernel logs with &lt;code&gt;dmesg&lt;/code&gt; to see the error messages.&lt;/td&gt;
&lt;td&gt;/lets tʃek ðə ˈkɜːnl lɒɡz wɪð ˈdiːmesɡ tuː siː ðiː ˈerə ˈmesɪdʒɪz/&lt;/td&gt;
&lt;td&gt;让我们用&lt;code&gt;dmesg&lt;/code&gt;检查内核日志查看错误信息。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;I'm using &lt;code&gt;printk()&lt;/code&gt; to add debug messages to the kernel log.&lt;/td&gt;
&lt;td&gt;/aɪm ˈjuːzɪŋ ˈprɪntkeɪ tuː æd diːˈbʌɡ ˈmesɪdʒɪz tuː ðə ˈkɜːnl lɒɡ/&lt;/td&gt;
&lt;td&gt;我正在用&lt;code&gt;printk()&lt;/code&gt;向内核日志添加调试信息。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  11.3 Device Tree and Hardware Interaction
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;We need to add the device node to the device tree blob.&lt;/td&gt;
&lt;td&gt;/wiː niːd tuː æd ðə dɪˈvaɪs nəʊd tuː ðə dɪˈvaɪs triː blɒb/&lt;/td&gt;
&lt;td&gt;我们需要将设备节点添加到设备树blob中。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;The driver reads the hardware registers through memory-mapped I/O.&lt;/td&gt;
&lt;td&gt;/ðə ˈdraɪvə riːdz ðə ˈhɑːdweə ˈredʒɪstəz θruː ˈmeməri ˈmæpt ˌaɪˈəʊ/&lt;/td&gt;
&lt;td&gt;驱动通过内存映射I/O读取硬件寄存器。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Let's check the interrupt request (IRQ) configuration in the device tree.&lt;/td&gt;
&lt;td&gt;/lets tʃek ðiː ˈɪntərʌpt rɪˈkwest aɪˈɑːˈkjuː kənˌfɪɡəˈreɪʃən ɪn ðə dɪˈvaɪs triː/&lt;/td&gt;
&lt;td&gt;让我们检查设备树中的中断请求(IRQ)配置。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  11.4 Driver Testing and Validation
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Conversation&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Translation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Let's write a userspace test program to verify the driver functionality.&lt;/td&gt;
&lt;td&gt;/lets raɪt ə ˈjuːzəspeɪs test ˈprəʊɡræm tuː ˈverɪfaɪ ðə ˈdraɪvə ˌfʌŋkʃəˈnæləti/&lt;/td&gt;
&lt;td&gt;让我们编写一个用户空间测试程序来验证驱动功能。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;We need to test the driver with different kernel versions.&lt;/td&gt;
&lt;td&gt;/wiː niːd tuː test ðə ˈdraɪvə wɪð ˈdɪfrənt ˈkɜːnl ˈvɜːʃənz/&lt;/td&gt;
&lt;td&gt;我们需要用不同的内核版本测试驱动。&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Let's measure the driver's performance with &lt;code&gt;perf&lt;/code&gt; tool.&lt;/td&gt;
&lt;td&gt;/lets ˈmeʒə ðə ˈdraɪvəz pəˈfɔːməns wɪð pɜːf tuːl/&lt;/td&gt;
&lt;td&gt;让我们用&lt;code&gt;perf&lt;/code&gt;工具测量驱动的性能。&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  12. Technical Terms Pronunciation Reference
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Common Technical Terms
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Term&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Explanation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;API&lt;/td&gt;
&lt;td&gt;/ˌeɪpiːˈaɪ/&lt;/td&gt;
&lt;td&gt;应用程序编程接口&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;CI/CD&lt;/td&gt;
&lt;td&gt;/ˌsiːˈaɪ ˌsiːˈdiː/&lt;/td&gt;
&lt;td&gt;持续集成/持续部署&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Docker&lt;/td&gt;
&lt;td&gt;/ˈdɒkə/&lt;/td&gt;
&lt;td&gt;容器化平台&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Kubernetes&lt;/td&gt;
&lt;td&gt;/ˌkuːbəˈnetɪs/&lt;/td&gt;
&lt;td&gt;容器编排系统&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Git&lt;/td&gt;
&lt;td&gt;/ɡɪt/&lt;/td&gt;
&lt;td&gt;版本控制系统&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;JavaScript&lt;/td&gt;
&lt;td&gt;/ˈdʒɑːvəskrɪpt/&lt;/td&gt;
&lt;td&gt;JavaScript编程语言&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Python&lt;/td&gt;
&lt;td&gt;/ˈpaɪθən/&lt;/td&gt;
&lt;td&gt;Python编程语言&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;React&lt;/td&gt;
&lt;td&gt;/riˈækt/&lt;/td&gt;
&lt;td&gt;React前端框架&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Node.js&lt;/td&gt;
&lt;td&gt;/nəʊd dʒeɪ ˈes/&lt;/td&gt;
&lt;td&gt;Node.js运行时环境&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  C Language Terms
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Term&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Explanation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;malloc()&lt;/td&gt;
&lt;td&gt;/ˈmælɒk/&lt;/td&gt;
&lt;td&gt;内存分配函数&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;free()&lt;/td&gt;
&lt;td&gt;/friː/&lt;/td&gt;
&lt;td&gt;内存释放函数&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;gdb&lt;/td&gt;
&lt;td&gt;/ˌdʒiːdiːˈbiː/&lt;/td&gt;
&lt;td&gt;GNU调试器&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;valgrind&lt;/td&gt;
&lt;td&gt;/ˈvælɡrɪnd/&lt;/td&gt;
&lt;td&gt;内存调试和分析工具&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;segmentation fault&lt;/td&gt;
&lt;td&gt;/ˌseɡmənˈteɪʃən fɔːlt/&lt;/td&gt;
&lt;td&gt;段错误&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;buffer overflow&lt;/td&gt;
&lt;td&gt;/ˈbʌfər ˈəʊvəfləʊ/&lt;/td&gt;
&lt;td&gt;缓冲区溢出&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  Linux Driver Terms
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;English Term&lt;/th&gt;
&lt;th&gt;IPA Pronunciation&lt;/th&gt;
&lt;th&gt;Chinese Explanation&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;dmesg&lt;/td&gt;
&lt;td&gt;/ˈdiːmesɡ/&lt;/td&gt;
&lt;td&gt;显示内核消息&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;printk()&lt;/td&gt;
&lt;td&gt;/ˈprɪntkeɪ/&lt;/td&gt;
&lt;td&gt;内核打印函数&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;ioctl()&lt;/td&gt;
&lt;td&gt;/aɪˈəʊsiːtiːˈel/&lt;/td&gt;
&lt;td&gt;设备控制函数&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;mmap()&lt;/td&gt;
&lt;td&gt;/ˈemˈmæp/&lt;/td&gt;
&lt;td&gt;内存映射函数&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;device tree&lt;/td&gt;
&lt;td&gt;/dɪˈvaɪs triː/&lt;/td&gt;
&lt;td&gt;设备树&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;interrupt&lt;/td&gt;
&lt;td&gt;/ˈɪntərʌpt/&lt;/td&gt;
&lt;td&gt;中断&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  Learning Strategies and Resources
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Daily Practice Methods
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Morning Reading&lt;/strong&gt;: Spend 10 minutes each morning reading conversations from one scenario&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Scenario Simulation&lt;/strong&gt;: Imagine actual work situations and try to express them in English&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Recording Comparison&lt;/strong&gt;: Record your pronunciation and compare with the IPA guide&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pair Practice&lt;/strong&gt;: Practice conversation scenarios with colleagues&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Pronunciation Techniques
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Stress Position&lt;/strong&gt;: Pay attention to stress positions in multi-syllable words&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Linking Sounds&lt;/strong&gt;: English words often link together in speech&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Intonation Changes&lt;/strong&gt;: Use rising intonation for questions, falling for statements&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Technical Terms&lt;/strong&gt;: Focus on memorizing correct pronunciation of common technical terms&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Recommended Resources
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Forvo&lt;/strong&gt; (&lt;a href="https://forvo.com/" rel="noopener noreferrer"&gt;https://forvo.com/&lt;/a&gt;) - Word pronunciation database&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Cambridge Dictionary&lt;/strong&gt; (&lt;a href="https://dictionary.cambridge.org/" rel="noopener noreferrer"&gt;https://dictionary.cambridge.org/&lt;/a&gt;) - Authoritative pronunciation reference&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;BBC Learning English&lt;/strong&gt; (&lt;a href="https://www.bbc.co.uk/learningenglish/" rel="noopener noreferrer"&gt;https://www.bbc.co.uk/learningenglish/&lt;/a&gt;) - Professional English learning&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;TechTerms.com&lt;/strong&gt; (&lt;a href="https://techterms.com/" rel="noopener noreferrer"&gt;https://techterms.com/&lt;/a&gt;) - Technical term explanations&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  Conclusion
&lt;/h2&gt;

&lt;p&gt;This comprehensive guide provides software engineers with practical English conversations for daily work scenarios. By practicing these phrases and paying attention to pronunciation, you can significantly improve your communication effectiveness in global software development teams.&lt;/p&gt;

&lt;p&gt;Remember that effective communication involves not just vocabulary and pronunciation, but also clarity, context, and cultural awareness. Start with the scenarios most relevant to your current work, practice regularly, and gradually expand your skills.&lt;/p&gt;

&lt;h3&gt;
  
  
  Key Takeaways
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Start with fundamentals&lt;/strong&gt;: Master daily standups and basic technical discussions first&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Focus on pronunciation&lt;/strong&gt;: Technical terminology pronunciation is crucial for clarity&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Practice in context&lt;/strong&gt;: Learn phrases that are directly applicable to your work&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Use available tools&lt;/strong&gt;: Leverage pronunciation guides and learning resources&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  Next Steps
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Identify priority areas&lt;/strong&gt;: Which scenarios are most relevant to your current work?&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Create practice schedule&lt;/strong&gt;: Dedicate regular time to English practice&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Apply immediately&lt;/strong&gt;: Start using these phrases in actual work communications&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Seek feedback&lt;/strong&gt;: Ask colleagues for feedback on your communication&lt;/li&gt;
&lt;/ol&gt;




&lt;p&gt;&lt;strong&gt;License&lt;/strong&gt;: This work is licensed under a &lt;a href="https://creativecommons.org/licenses/by-nc-sa/4.0/" rel="noopener noreferrer"&gt;CC BY-NC-SA 4.0&lt;/a&gt; International License.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Update History&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;2026-04-02: Initial version created with 12 scenarios and 300+ conversation examples&lt;/li&gt;
&lt;li&gt;2026-04-02: Added specialized sections for C programming and Linux driver development&lt;/li&gt;
&lt;/ul&gt;




&lt;p&gt;&lt;em&gt;Happy coding and communicating! Feel free to share your own favorite English phrases for software engineering work in the comments below.&lt;/em&gt;&lt;/p&gt;

</description>
      <category>english</category>
      <category>communication</category>
      <category>software</category>
      <category>programming</category>
    </item>
    <item>
      <title>The Complete Guide to Data Structures in C: From Arrays to Hash Tables</title>
      <dc:creator>张宇</dc:creator>
      <pubDate>Mon, 30 Mar 2026 10:46:49 +0000</pubDate>
      <link>https://dev.to/cosimos/the-complete-guide-to-data-structures-in-c-from-arrays-to-hash-tables-3gba</link>
      <guid>https://dev.to/cosimos/the-complete-guide-to-data-structures-in-c-from-arrays-to-hash-tables-3gba</guid>
      <description>&lt;h1&gt;
  
  
  The Complete Guide to Data Structures in C: From Arrays to Hash Tables
&lt;/h1&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;strong&gt;English Version&lt;/strong&gt; | &lt;a href="//./c-data-structures-complete-guide-zh.md"&gt;中文版&lt;/a&gt;&lt;/p&gt;
&lt;/blockquote&gt;

&lt;h2&gt;
  
  
  Introduction
&lt;/h2&gt;

&lt;p&gt;Data structures form the foundation of computer science, and understanding their implementation in C is crucial for system programming. As Niklaus Wirth stated in his book "Algorithms + Data Structures = Programs": "A program is a combination of algorithms and data structures." In C, this combination is even more intimate—you need to manage memory manually, understand data layout in memory, and make performance optimization decisions.&lt;/p&gt;

&lt;p&gt;This comprehensive guide will take you through the core data structures in C, from basic arrays to complex hash tables. Each section includes complete code implementations, performance analysis, and real-world use cases. Whether you're a beginner or an experienced developer, you'll gain practical knowledge and techniques.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;This article covers:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Fundamental data structures: arrays, strings, linked lists&lt;/li&gt;
&lt;li&gt;Linear structures: stacks, queues, deques&lt;/li&gt;
&lt;li&gt;Tree structures: binary trees, binary search trees, heaps&lt;/li&gt;
&lt;li&gt;Graph fundamentals: representation and traversal algorithms&lt;/li&gt;
&lt;li&gt;Efficient lookup: hash table design and implementation&lt;/li&gt;
&lt;li&gt;Advanced topics: memory management, cache optimization, practical applications&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  1. Fundamental Data Structures: Arrays and Strings
&lt;/h2&gt;

&lt;h3&gt;
  
  
  1.1 Static Arrays
&lt;/h3&gt;

&lt;p&gt;Arrays are the most fundamental data structure in C, allowing you to store elements of the same type in contiguous memory space. Static arrays have their size determined at compile time, making them highly efficient in terms of performance and memory usage.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Static array example&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;static_array_example&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;numbers&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;

    &lt;span class="c1"&gt;// Traverse array&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Static array elements: "&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;numbers&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// Calculate array size&lt;/span&gt;
    &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;numbers&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;numbers&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Array size: %zu&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;static_array_example&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;Key characteristics:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Contiguous memory, fast access (O(1) time complexity)&lt;/li&gt;
&lt;li&gt;Fixed size, cannot be dynamically expanded&lt;/li&gt;
&lt;li&gt;Decay to pointers when passed as function arguments&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  1.2 Dynamic Array Implementation
&lt;/h3&gt;

&lt;p&gt;Dynamic arrays (also known as resizable arrays) allow changing their size at runtime. This is achieved using &lt;code&gt;malloc&lt;/code&gt;, &lt;code&gt;realloc&lt;/code&gt;, and &lt;code&gt;free&lt;/code&gt; functions.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Dynamic array structure&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;      &lt;span class="c1"&gt;// Data pointer&lt;/span&gt;
    &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;    &lt;span class="c1"&gt;// Current number of elements&lt;/span&gt;
    &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Capacity&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;DynamicArray&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Create dynamic array&lt;/span&gt;
&lt;span class="n"&gt;DynamicArray&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;create_dynamic_array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;initial_capacity&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;DynamicArray&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;DynamicArray&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;DynamicArray&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;initial_capacity&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;initial_capacity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Append element to dynamic array&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;dynamic_array_append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;DynamicArray&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="c1"&gt;// Capacity expansion: typically expand to 1.5-2 times current capacity&lt;/span&gt;
        &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;new_capacity&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;realloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;new_capacity&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Failure&lt;/span&gt;

        &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_capacity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Free dynamic array&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;free_dynamic_array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;DynamicArray&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;DynamicArray&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;create_dynamic_array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Failed to create dynamic array&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// Add elements&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;dynamic_array_append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Dynamic array elements: "&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;Size: %zu, Capacity: %zu&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="n"&gt;free_dynamic_array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  1.3 String Manipulation and Common Algorithms
&lt;/h3&gt;

&lt;p&gt;Strings in C are character arrays terminated with a null character ('\0'). Understanding string operations is essential for data processing.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;string.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;ctype.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Custom string copy function&lt;/span&gt;
&lt;span class="kt"&gt;char&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;my_strcpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="sc"&gt;'\0'&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// String reversal algorithm&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;reverse_string&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;tmp&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// Find string end&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Point to last character (skip '\0')&lt;/span&gt;

    &lt;span class="c1"&gt;// Two-pointer reversal&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;tmp&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;tmp&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Check if string is palindrome&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;is_palindrome&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;tolower&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;tolower&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;text&lt;/span&gt;&lt;span class="p"&gt;[]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"Hello, World!"&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;buffer&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;50&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

    &lt;span class="n"&gt;my_strcpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;buffer&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;text&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Original string: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;text&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Copied string: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;buffer&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="n"&gt;reverse_string&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;text&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Reversed: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;text&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;palindrome&lt;/span&gt;&lt;span class="p"&gt;[]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"A man a plan a canal Panama"&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Is '%s' a palindrome? %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; 
           &lt;span class="n"&gt;palindrome&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; 
           &lt;span class="n"&gt;is_palindrome&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;palindrome&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="s"&gt;"Yes"&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"No"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  2. Linked Lists: Flexible Data Organization
&lt;/h2&gt;

&lt;h3&gt;
  
  
  2.1 Singly Linked List Implementation
&lt;/h3&gt;

&lt;p&gt;Linked lists organize data through links between nodes, where each node contains data and a pointer to the next node. Linked lists provide dynamic sizing and efficient insertion/deletion operations.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Linked list node structure&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Create new node&lt;/span&gt;
&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;create_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Insert node at head of list&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;insert_at_head&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;create_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Insert node at tail of list&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;insert_at_tail&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;create_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Traverse linked list&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;print_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Linked list: "&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d -&amp;gt; "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"NULL&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Reverse linked list&lt;/span&gt;
&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;reverse_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Free linked list memory&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;free_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// Insert elements&lt;/span&gt;
    &lt;span class="n"&gt;insert_at_tail&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;insert_at_tail&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;20&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;insert_at_head&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;insert_at_tail&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;30&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="n"&gt;print_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// Reverse list&lt;/span&gt;
    &lt;span class="n"&gt;list&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;reverse_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"After reversal: "&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;print_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="n"&gt;free_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;list&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  2.2 Linked List Operation Algorithms
&lt;/h3&gt;

&lt;p&gt;Linked lists support various efficient algorithms. Here are a few classic examples:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Detect cycle in linked list (Floyd's Cycle Detection Algorithm)&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;has_cycle&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Cycle detected&lt;/span&gt;
        &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// No cycle&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Find middle node of linked list&lt;/span&gt;
&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;find_middle&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Merge two sorted linked lists&lt;/span&gt;
&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;merge_sorted_lists&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;list1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;list2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="c1"&gt;// Create a dummy node to simplify operations&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="n"&gt;dummy&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;dummy&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;dummy&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;list1&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;list2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;list1&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;list2&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;list1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;list1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;list1&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;list2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;list2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;list2&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;tail&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// Attach remaining portion&lt;/span&gt;
    &lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;list1&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;list1&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;list2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;dummy&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;(Due to length constraints, the following sections will be outlined in detail, with complete code provided in subsequent versions)&lt;/p&gt;




&lt;h2&gt;
  
  
  3. Stacks and Queues: LIFO and FIFO
&lt;/h2&gt;

&lt;h3&gt;
  
  
  3.1 Stack Implementation and Applications
&lt;/h3&gt;

&lt;p&gt;A stack is a Last-In-First-Out (LIFO) data structure. The last element pushed is the first one popped—like a stack of plates.&lt;/p&gt;

&lt;h4&gt;
  
  
  Array Implementation
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_SIZE 100
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;ArrayStack&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;stack_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ArrayStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;stack_is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ArrayStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;stack_is_full&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ArrayStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;MAX_SIZE&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;stack_push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ArrayStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stack_is_full&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;stack_pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ArrayStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stack_is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;stack_peek&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ArrayStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stack_is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;stack_size&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ArrayStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Linked List Implementation
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;StackNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;StackNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;StackNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;StackNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;LinkedStack&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;linked_stack_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LinkedStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;linked_stack_push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LinkedStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;StackNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;StackNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;StackNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;linked_stack_pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LinkedStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;StackNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;temp&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Application: Parentheses Matching
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;string.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_SIZE 1000
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;CharStack&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;char_stack_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;char_stack_is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;char_stack_push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="nf"&gt;char_stack_pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="nf"&gt;char_stack_peek&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;char_stack_is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="sc"&gt;'\0'&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;is_valid_parentheses&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;char_stack_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="sc"&gt;'\0'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'('&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'['&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'{'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;char_stack_push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;')'&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;']'&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'}'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;char_stack_is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

            &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;char_stack_pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;')'&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="sc"&gt;'('&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt;
                &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;']'&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="sc"&gt;'['&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt;
                &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'}'&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="sc"&gt;'{'&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;char_stack_is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;tests&lt;/span&gt;&lt;span class="p"&gt;[]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s"&gt;"()"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"([])"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"{[()]}"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"([)]"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"((("&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"())"&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"'%s' -&amp;gt; %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;tests&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;is_valid_parentheses&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;tests&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="s"&gt;"Valid"&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"Invalid"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Application: Expression Evaluation (Infix to Postfix)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;ctype.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_SIZE 100
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;CharStack&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;init_stack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="nf"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="nf"&gt;peek&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="sc"&gt;'\0'&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;precedence&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;op&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;switch&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;op&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;case&lt;/span&gt; &lt;span class="sc"&gt;'+'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="k"&gt;case&lt;/span&gt; &lt;span class="sc"&gt;'-'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;case&lt;/span&gt; &lt;span class="sc"&gt;'*'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="k"&gt;case&lt;/span&gt; &lt;span class="sc"&gt;'/'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="nl"&gt;default:&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;is_operator&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'+'&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'-'&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'*'&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'/'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;infix_to_postfix&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;infix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;CharStack&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;init_stack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;infix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="sc"&gt;'\0'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;infix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;isspace&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;continue&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;isdigit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sc"&gt;' '&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;'('&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="sc"&gt;')'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;peek&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="sc"&gt;'('&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
                &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sc"&gt;' '&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
            &lt;span class="n"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;is_operator&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;precedence&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;peek&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;precedence&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
                &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sc"&gt;' '&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
            &lt;span class="n"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sc"&gt;' '&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sc"&gt;'\0'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;infix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"3 + 4 * 2 - 1"&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

    &lt;span class="n"&gt;infix_to_postfix&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;infix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Infix: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;infix&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Postfix: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;postfix&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  3.2 Queue Implementation and Variants
&lt;/h3&gt;

&lt;p&gt;A queue is a First-In-First-Out (FIFO) data structure. Like a line at a store—first come, first served.&lt;/p&gt;

&lt;h4&gt;
  
  
  Circular Queue Implementation
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_SIZE 100
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;CircularQueue&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;queue_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CircularQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;queue_is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CircularQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;queue_is_full&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CircularQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;queue_enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CircularQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;queue_is_full&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;queue_dequeue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CircularQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;queue_is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;queue_peek&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CircularQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;queue_is_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Linked Queue Implementation
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;QueueNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;QueueNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;QueueNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;QueueNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;QueueNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;LinkedQueue&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;linked_queue_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LinkedQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;linked_queue_enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LinkedQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;QueueNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;QueueNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;QueueNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;linked_queue_dequeue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LinkedQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;QueueNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;temp&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Deque (Double-Ended Queue)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;DequeNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;DequeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;DequeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;DequeNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;DequeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;DequeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;Deque&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;deque_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Deque&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;deque_push_front&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Deque&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;DequeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;DequeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;DequeNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;deque_push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Deque&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;DequeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;DequeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;DequeNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;deque_pop_front&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Deque&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;DequeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;temp&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;deque_pop_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Deque&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;DequeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;temp&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  3.3 Real-World Use Cases
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Browser Forward/Back Navigation
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;string.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_URL 256
#define MAX_HISTORY 50
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_URL&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;Page&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;Page&lt;/span&gt; &lt;span class="n"&gt;pages&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_HISTORY&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;PageStack&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;page_stack_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;PageStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;page_stack_push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;PageStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;MAX_HISTORY&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;strncpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;pages&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;MAX_URL&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;page_stack_pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;PageStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;strncpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;pages&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;MAX_URL&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;PageStack&lt;/span&gt; &lt;span class="n"&gt;back_stack&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;PageStack&lt;/span&gt; &lt;span class="n"&gt;forward_stack&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;current_url&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_URL&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;BrowserHistory&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;browser_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BrowserHistory&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;homepage&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;page_stack_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;back_stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;page_stack_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;forward_stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;strncpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;current_url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;homepage&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;MAX_URL&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;browser_visit&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BrowserHistory&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;page_stack_push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;back_stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;current_url&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;page_stack_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;forward_stack&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;strncpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;current_url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;MAX_URL&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Visit: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;browser_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BrowserHistory&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;prev_url&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_URL&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;page_stack_pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;back_stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;prev_url&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;page_stack_push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;forward_stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;current_url&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;strncpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;current_url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;prev_url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;MAX_URL&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Back to: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;current_url&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Cannot go back&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;browser_forward&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BrowserHistory&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;next_url&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_URL&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;page_stack_pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;forward_stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;next_url&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;page_stack_push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;back_stack&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;current_url&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;strncpy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;current_url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;next_url&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;MAX_URL&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Forward to: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bh&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;current_url&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Cannot go forward&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Stack vs Queue Comparison
&lt;/h4&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Feature&lt;/th&gt;
&lt;th&gt;Stack&lt;/th&gt;
&lt;th&gt;Queue&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Access Principle&lt;/td&gt;
&lt;td&gt;LIFO (Last-In-First-Out)&lt;/td&gt;
&lt;td&gt;FIFO (First-In-First-Out)&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Insert Position&lt;/td&gt;
&lt;td&gt;Top&lt;/td&gt;
&lt;td&gt;Rear&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Delete Position&lt;/td&gt;
&lt;td&gt;Top&lt;/td&gt;
&lt;td&gt;Front&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Main Operations&lt;/td&gt;
&lt;td&gt;push, pop, peek&lt;/td&gt;
&lt;td&gt;enqueue, dequeue, peek&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Typical Uses&lt;/td&gt;
&lt;td&gt;Function calls, undo, parentheses&lt;/td&gt;
&lt;td&gt;Task scheduling, BFS, buffers&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Array Implementation&lt;/td&gt;
&lt;td&gt;Simple, top pointer&lt;/td&gt;
&lt;td&gt;Circular array, front/rear&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Linked Implementation&lt;/td&gt;
&lt;td&gt;Head insert/delete&lt;/td&gt;
&lt;td&gt;Tail insert, head delete&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  4. Tree Structures: Hierarchical Data Organization
&lt;/h2&gt;

&lt;h3&gt;
  
  
  4.1 Binary Trees and Binary Search Trees
&lt;/h3&gt;

&lt;p&gt;A binary tree has at most two children per node. A Binary Search Tree (BST) is a special binary tree where: left subtree values &amp;lt; root value &amp;lt; right subtree values.&lt;/p&gt;

&lt;h4&gt;
  
  
  Binary Tree Implementation
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;create_tree_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Preorder: Root -&amp;gt; Left -&amp;gt; Right&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;preorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;preorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;preorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Inorder: Left -&amp;gt; Root -&amp;gt; Right&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;inorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;inorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;inorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Postorder: Left -&amp;gt; Right -&amp;gt; Root&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;postorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;postorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;postorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Level Order (BFS)&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_QUEUE 100
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_QUEUE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;TreeQueue&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;tree_queue_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;tree_queue_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;tree_queue_enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;tree_queue_dequeue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;level_order_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;TreeQueue&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;tree_queue_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;tree_queue_enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;tree_queue_empty&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;tree_queue_dequeue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;tree_queue_enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;tree_queue_enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;tree_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;tree_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;tree_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;tree_count_nodes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;tree_count_nodes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;tree_count_nodes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;free_tree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;free_tree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;free_tree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Binary Search Tree (BST)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;BSTNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="n"&gt;BSTNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;bst_create_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BSTNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BSTNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;BSTNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;bst_insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;bst_create_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;bst_insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;bst_insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;BSTNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;bst_search&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;bst_search&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;bst_search&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;BSTNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;bst_find_min&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;BSTNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;bst_find_max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;BSTNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;bst_delete&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;bst_delete&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;bst_delete&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="c1"&gt;// Found node to delete&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;temp&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;temp&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;temp&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;

        &lt;span class="c1"&gt;// Two children: replace with inorder successor&lt;/span&gt;
        &lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;successor&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;bst_find_min&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;successor&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;bst_delete&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;successor&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;bst_inorder&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;BSTNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;bst_inorder&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;bst_inorder&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  4.2 Balanced Trees Introduction
&lt;/h3&gt;

&lt;p&gt;Regular BSTs can degenerate into linked lists (O(n) worst case). Balanced trees maintain height through rotations.&lt;/p&gt;

&lt;h4&gt;
  
  
  AVL Tree Basics
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;height&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;AVLNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;avl_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;height&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;avl_balance_factor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;avl_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;avl_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;avl_update_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;avl_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;avl_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;height&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;AVLNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;avl_create_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AVLNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AVLNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;height&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Right rotation (LL case)&lt;/span&gt;
&lt;span class="n"&gt;AVLNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;avl_rotate_right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;T2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;T2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;avl_update_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;avl_update_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Left rotation (RR case)&lt;/span&gt;
&lt;span class="n"&gt;AVLNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;avl_rotate_left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;T2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;T2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;avl_update_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;avl_update_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;AVLNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;avl_insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AVLNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;avl_create_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;avl_insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;avl_insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// No duplicates&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;avl_update_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;balance&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;avl_balance_factor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// LL case&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;balance&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;avl_rotate_right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// RR case&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;balance&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;avl_rotate_left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// LR case&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;balance&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;avl_rotate_left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;avl_rotate_right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// RL case&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;balance&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;avl_rotate_right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;avl_rotate_left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  4.3 Heaps and Priority Queues
&lt;/h3&gt;

&lt;p&gt;A heap is a complete binary tree where parent &amp;gt;= children (max heap) or parent &amp;lt;= children (min heap).&lt;/p&gt;

&lt;h4&gt;
  
  
  Max Heap Implementation
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_HEAP_SIZE 100
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_HEAP_SIZE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;MaxHeap&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;heap_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MaxHeap&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;heap_parent&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;heap_left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;heap_right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;heap_swap&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;heap_sift_up&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MaxHeap&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;heap_parent&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;heap_swap&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;heap_parent&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)],&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
        &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;heap_parent&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;heap_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MaxHeap&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;max_index&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;heap_left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;heap_right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;max_index&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
        &lt;span class="n"&gt;max_index&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;max_index&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
        &lt;span class="n"&gt;max_index&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;max_index&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;heap_swap&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;max_index&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
        &lt;span class="n"&gt;heap_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;max_index&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;heap_insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MaxHeap&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;MAX_HEAP_SIZE&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;heap_sift_up&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;heap_extract_max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MaxHeap&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;max&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;heap_sift_down&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  5. Graph Fundamentals: Relationships and Connections
&lt;/h2&gt;

&lt;h3&gt;
  
  
  5.1 Graph Representation Methods
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Adjacency Matrix
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_VERTICES 100
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;num_vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;is_directed&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;GraphMatrix&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;graph_matrix_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GraphMatrix&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;vertices&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;directed&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;num_vertices&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;is_directed&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;directed&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;graph_matrix_add_edge&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GraphMatrix&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;weight&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;weight&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;is_directed&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;weight&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Adjacency List
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_VERTICES 100
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;AdjNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;weight&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;AdjNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;AdjNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;AdjNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;AdjList&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;AdjList&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;num_vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;is_directed&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;GraphList&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;graph_list_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GraphList&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;vertices&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;directed&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;num_vertices&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;is_directed&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;directed&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;graph_list_add_edge&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GraphList&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;weight&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;AdjNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AdjNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AdjNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;weight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;weight&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;is_directed&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AdjNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AdjNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
        &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;weight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;weight&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  5.2 Traversal Algorithms
&lt;/h3&gt;

&lt;h4&gt;
  
  
  DFS and BFS
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_VERTICES 100
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;AdjNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;AdjNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;AdjNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;AdjNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;AdjList&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;AdjList&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;num_vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;Graph&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;graph_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Graph&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;vertices&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;num_vertices&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;graph_add_edge&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Graph&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;AdjNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AdjNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AdjNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AdjNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;AdjNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;from&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;to&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// DFS Recursive&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;dfs_recursive&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Graph&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="n"&gt;AdjNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
            &lt;span class="n"&gt;dfs_recursive&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// BFS Iterative&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;bfs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Graph&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;v&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

        &lt;span class="n"&gt;AdjNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;g&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
                &lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
            &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  5.3 Classic Graph Algorithms
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Dijkstra's Shortest Path
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;limits.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdbool.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_VERTICES 100
&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;num_vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;min_distance&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[],&lt;/span&gt; &lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;min&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;INT_MAX&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;min_index&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;v&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;v&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;num_vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;min&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;min&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
            &lt;span class="n"&gt;min_index&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;min_index&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;print_path&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;parent&lt;/span&gt;&lt;span class="p"&gt;[],&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;parent&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;print_path&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;parent&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;parent&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;" -&amp;gt; %d"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;dijkstra&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="n"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;parent&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_VERTICES&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;num_vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;INT_MAX&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;parent&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;start&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;count&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;count&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;num_vertices&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;count&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;u&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;min_distance&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;u&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;v&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;v&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;num_vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;u&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;u&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;INT_MAX&lt;/span&gt;
                &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;u&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;u&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;u&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;graph&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;u&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
                &lt;span class="n"&gt;parent&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;v&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;u&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Vertex&lt;/span&gt;&lt;span class="se"&gt;\t&lt;/span&gt;&lt;span class="s"&gt;Distance&lt;/span&gt;&lt;span class="se"&gt;\t&lt;/span&gt;&lt;span class="s"&gt;Path&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;num_vertices&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d&lt;/span&gt;&lt;span class="se"&gt;\t&lt;/span&gt;&lt;span class="s"&gt;%d&lt;/span&gt;&lt;span class="se"&gt;\t\t&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dist&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
        &lt;span class="n"&gt;print_path&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;parent&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  6. Hash Tables: The Power of Efficient Lookup
&lt;/h2&gt;

&lt;h3&gt;
  
  
  6.1 Hash Function Design
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;string.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Integer hash&lt;/span&gt;
&lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;hash_int&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;table_size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;table_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// String hash (djb2 algorithm)&lt;/span&gt;
&lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;hash_string&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;table_size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;long&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;5381&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
        &lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;table_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// FNV-1a hash&lt;/span&gt;
&lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;hash_fnv1a&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;table_size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2166136261u&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;^=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;str&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;*=&lt;/span&gt; &lt;span class="mi"&gt;16777619&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;table_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  6.2 Collision Resolution Methods
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Separate Chaining
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;string.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define TABLE_SIZE 100
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;HashNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;HashNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;HashNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;HashNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;buckets&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;TABLE_SIZE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;HashTable&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;hash&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;long&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;5381&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
        &lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;TABLE_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;hash_table_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;HashTable&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;TABLE_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;buckets&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;hash_table_put&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;HashTable&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;HashNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;buckets&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;strcmp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;HashNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;HashNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;HashNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;strdup&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;buckets&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;buckets&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;hash_table_get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;HashTable&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;HashNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;buckets&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;strcmp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Open Addressing (Linear Probing)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;string.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define TABLE_SIZE 10
#define DELETED_NODE ((char*)-1)
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;HashEntry&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;HashEntry&lt;/span&gt; &lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;TABLE_SIZE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;OpenHashTable&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;open_hash_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;OpenHashTable&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;TABLE_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;open_hash_put&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;OpenHashTable&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;TABLE_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;TABLE_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pos&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pos&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;DELETED_NODE&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pos&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;strdup&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pos&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;strcmp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pos&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pos&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;open_hash_get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;OpenHashTable&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;unsigned&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hash&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;TABLE_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;pos&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;TABLE_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pos&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pos&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;DELETED_NODE&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;strcmp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pos&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;ht&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;table&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;pos&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Collision Resolution Comparison
&lt;/h4&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Method&lt;/th&gt;
&lt;th&gt;Pros&lt;/th&gt;
&lt;th&gt;Cons&lt;/th&gt;
&lt;th&gt;Best For&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Separate Chaining&lt;/td&gt;
&lt;td&gt;Simple, handles high load&lt;/td&gt;
&lt;td&gt;Extra pointer space&lt;/td&gt;
&lt;td&gt;General use, high collision&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Linear Probing&lt;/td&gt;
&lt;td&gt;Cache-friendly, no pointers&lt;/td&gt;
&lt;td&gt;Clustering, complex delete&lt;/td&gt;
&lt;td&gt;Small tables, low collision&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Quadratic Probing&lt;/td&gt;
&lt;td&gt;Less clustering&lt;/td&gt;
&lt;td&gt;Complex delete&lt;/td&gt;
&lt;td&gt;Medium tables&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Double Hashing&lt;/td&gt;
&lt;td&gt;Best distribution&lt;/td&gt;
&lt;td&gt;Computation overhead&lt;/td&gt;
&lt;td&gt;High performance needs&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  7. Advanced Topics and Performance Analysis
&lt;/h2&gt;

&lt;h3&gt;
  
  
  7.1 Data Structure Selection Strategies
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Frequent random access&lt;/strong&gt; → Array&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Frequent insert/delete&lt;/strong&gt; → Linked List&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;LIFO access pattern&lt;/strong&gt; → Stack&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;FIFO access pattern&lt;/strong&gt; → Queue&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Ordered data with fast lookup&lt;/strong&gt; → BST or Hash Table&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Priority-based access&lt;/strong&gt; → Heap&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Relationship modeling&lt;/strong&gt; → Graph&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  7.2 Memory Management and Cache Optimization
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Cache Optimization Tips:
1. Use contiguous memory (arrays vs linked lists)
2. Align data to cache lines (typically 64 bytes)
3. Access memory sequentially (spatial locality)
4. Reuse recently accessed data (temporal locality)
5. Consider cache-aware data structures (B-trees, cache-oblivious)
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  7.3 Applications in Real Projects
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Database Systems&lt;/strong&gt;: B-trees for indexing, hash tables for caching&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Network Protocol Stacks&lt;/strong&gt;: Ring buffers, priority queues&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Game Development&lt;/strong&gt;: Spatial partitioning (quadtrees, octrees)&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Compilers&lt;/strong&gt;: Symbol tables (hash tables), AST (trees)&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  8. Common Interview Questions and Answers
&lt;/h2&gt;

&lt;h3&gt;
  
  
  8.1 Fundamental Concept Questions
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Q1: Array vs Linked List - Differences and Use Cases?
&lt;/h4&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Feature&lt;/th&gt;
&lt;th&gt;Array&lt;/th&gt;
&lt;th&gt;Linked List&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Memory Layout&lt;/td&gt;
&lt;td&gt;Contiguous&lt;/td&gt;
&lt;td&gt;Discrete&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Access Time&lt;/td&gt;
&lt;td&gt;O(1) random&lt;/td&gt;
&lt;td&gt;O(n) sequential&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Insert/Delete&lt;/td&gt;
&lt;td&gt;O(n) shift elements&lt;/td&gt;
&lt;td&gt;O(1) modify pointers&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Memory Overhead&lt;/td&gt;
&lt;td&gt;Data only&lt;/td&gt;
&lt;td&gt;Extra pointers&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Cache Friendliness&lt;/td&gt;
&lt;td&gt;High&lt;/td&gt;
&lt;td&gt;Low&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Size Adjustment&lt;/td&gt;
&lt;td&gt;Reallocate&lt;/td&gt;
&lt;td&gt;Dynamic&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;&lt;strong&gt;Selection Guide:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Frequent random access → Array&lt;/li&gt;
&lt;li&gt;Frequent insert/delete → Linked List&lt;/li&gt;
&lt;li&gt;Fixed data size → Array&lt;/li&gt;
&lt;li&gt;Variable data size → Linked List or dynamic array&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Q2: Stack vs Queue Applications?
&lt;/h4&gt;

&lt;p&gt;&lt;strong&gt;Stack Applications:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Function call stack (recursion)&lt;/li&gt;
&lt;li&gt;Expression evaluation&lt;/li&gt;
&lt;li&gt;Parentheses matching&lt;/li&gt;
&lt;li&gt;Browser back/forward&lt;/li&gt;
&lt;li&gt;Undo/redo operations&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Queue Applications:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Task scheduling&lt;/li&gt;
&lt;li&gt;BFS traversal&lt;/li&gt;
&lt;li&gt;Message queues&lt;/li&gt;
&lt;li&gt;Buffer management&lt;/li&gt;
&lt;li&gt;Print job queue&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Q3: Tree Structure Advantages?
&lt;/h4&gt;

&lt;p&gt;&lt;strong&gt;Characteristics:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Hierarchical data organization&lt;/li&gt;
&lt;li&gt;Recursive definition, natural for recursive algorithms&lt;/li&gt;
&lt;li&gt;One-to-many relationships&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Advantages:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;BST provides O(log n) search efficiency&lt;/li&gt;
&lt;li&gt;Heaps enable efficient min/max retrieval&lt;/li&gt;
&lt;li&gt;Foundation for sorting and searching algorithms&lt;/li&gt;
&lt;li&gt;Core structure in file systems and database indices&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  8.2 Coding Implementation Challenges
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Implement: LRU Cache
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define CACHE_SIZE 3
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;CacheNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;CacheNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;CacheNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;CacheNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;CacheNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;CacheNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;LRUCache&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="n"&gt;LRUCache&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;lru_create&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;LRUCache&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LRUCache&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LRUCache&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;move_to_head&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LRUCache&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;CacheNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;lru_get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LRUCache&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;CacheNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;move_to_head&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;lru_put&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LRUCache&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;CacheNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;move_to_head&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;CacheNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CacheNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;CacheNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;CacheNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;to_remove&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;to_remove&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Evicted: key=%d, value=%d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;to_remove&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;to_remove&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;to_remove&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;cache&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Implement: Detect Cycle in Linked List
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;ListNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Floyd's Cycle Detection&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;has_cycle&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Find cycle entry&lt;/span&gt;
&lt;span class="n"&gt;ListNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;find_cycle_entry&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;entry&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;entry&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;entry&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
                &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;cycle_length&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;has_cycle&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;entry&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;find_cycle_entry&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;length&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;entry&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;length&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;length&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Implement: Reverse Linked List
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Iterative&lt;/span&gt;
&lt;span class="n"&gt;ListNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;reverse_list_iterative&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Recursive&lt;/span&gt;
&lt;span class="n"&gt;ListNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;reverse_list_recursive&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;reverse_list_recursive&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;new_head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Implement: Find Kth from End
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="n"&gt;ListNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;find_kth_from_end&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Implement: Merge Two Sorted Lists
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Iterative&lt;/span&gt;
&lt;span class="n"&gt;ListNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;merge_two_lists_iterative&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="n"&gt;dummy&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;tail&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;dummy&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;l1&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;l1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;l2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;tail&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;tail&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;l1&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;l1&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;dummy&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Recursive&lt;/span&gt;
&lt;span class="n"&gt;ListNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;merge_two_lists_recursive&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;merge_two_lists_recursive&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;merge_two_lists_recursive&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;l1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;l2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Implement: Is Balanced Binary Tree
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;check_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;check_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;check_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;is_balanced&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;check_height&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Implement: Level Order Traversal by Level
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;level_order_by_level&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_QUEUE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;level_size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Level: "&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;level_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
            &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Implement: Lowest Common Ancestor (LCA)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;lowest_common_ancestor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;p&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;lowest_common_ancestor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;lowest_common_ancestor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// For BST&lt;/span&gt;
&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;bst_lca&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;bst_lca&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;bst_lca&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  8.3 Performance Analysis Questions
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Q1: Hash Table Performance Under Different Load Factors
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Load Factor α = elements / buckets

Separate Chaining:
- Successful search: 1 + α/2 comparisons average
- Unsuccessful search: α comparisons average
- Recommended load factor: 0.7 - 0.8

Open Addressing (Linear Probing):
- Successful search: (1 + 1/(1-α)) / 2
- Unsuccessful search: (1 + 1/(1-α)²) / 2
- Recommended load factor: &amp;lt; 0.7

Examples:
α = 0.5: ~1.5 comparisons for successful search
α = 0.75: ~2.0 comparisons for successful search
α = 0.9: ~5.5 comparisons (performance drops sharply)
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Q2: Sorting Algorithm Comparison
&lt;/h4&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Algorithm&lt;/th&gt;
&lt;th&gt;Best&lt;/th&gt;
&lt;th&gt;Average&lt;/th&gt;
&lt;th&gt;Worst&lt;/th&gt;
&lt;th&gt;Space&lt;/th&gt;
&lt;th&gt;Stable&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Bubble Sort&lt;/td&gt;
&lt;td&gt;O(n)&lt;/td&gt;
&lt;td&gt;O(n²)&lt;/td&gt;
&lt;td&gt;O(n²)&lt;/td&gt;
&lt;td&gt;O(1)&lt;/td&gt;
&lt;td&gt;Yes&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Selection Sort&lt;/td&gt;
&lt;td&gt;O(n²)&lt;/td&gt;
&lt;td&gt;O(n²)&lt;/td&gt;
&lt;td&gt;O(n²)&lt;/td&gt;
&lt;td&gt;O(1)&lt;/td&gt;
&lt;td&gt;No&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Insertion Sort&lt;/td&gt;
&lt;td&gt;O(n)&lt;/td&gt;
&lt;td&gt;O(n²)&lt;/td&gt;
&lt;td&gt;O(n²)&lt;/td&gt;
&lt;td&gt;O(1)&lt;/td&gt;
&lt;td&gt;Yes&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Quick Sort&lt;/td&gt;
&lt;td&gt;O(n log n)&lt;/td&gt;
&lt;td&gt;O(n log n)&lt;/td&gt;
&lt;td&gt;O(n²)&lt;/td&gt;
&lt;td&gt;O(log n)&lt;/td&gt;
&lt;td&gt;No&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Merge Sort&lt;/td&gt;
&lt;td&gt;O(n log n)&lt;/td&gt;
&lt;td&gt;O(n log n)&lt;/td&gt;
&lt;td&gt;O(n log n)&lt;/td&gt;
&lt;td&gt;O(n)&lt;/td&gt;
&lt;td&gt;Yes&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Heap Sort&lt;/td&gt;
&lt;td&gt;O(n log n)&lt;/td&gt;
&lt;td&gt;O(n log n)&lt;/td&gt;
&lt;td&gt;O(n log n)&lt;/td&gt;
&lt;td&gt;O(1)&lt;/td&gt;
&lt;td&gt;No&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;p&gt;&lt;strong&gt;Selection Guide:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Small data → Insertion sort&lt;/li&gt;
&lt;li&gt;Large data, stable → Merge sort&lt;/li&gt;
&lt;li&gt;Large data, in-place → Quick sort or Heap sort&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  8.4 Advanced Interview Questions
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Implement: Thread-Safe Queue
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;pthread.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="cp"&gt;#define MAX_SIZE 100
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;pthread_mutex_t&lt;/span&gt; &lt;span class="n"&gt;mutex&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;pthread_cond_t&lt;/span&gt; &lt;span class="n"&gt;not_empty&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;pthread_cond_t&lt;/span&gt; &lt;span class="n"&gt;not_full&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;ThreadSafeQueue&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;ts_queue_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ThreadSafeQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;pthread_mutex_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;mutex&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;pthread_cond_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;not_empty&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;pthread_cond_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;not_full&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;ts_queue_enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ThreadSafeQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;pthread_mutex_lock&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;mutex&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="n"&gt;pthread_cond_wait&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;not_full&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;mutex&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;rear&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;pthread_cond_signal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;not_empty&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;pthread_mutex_unlock&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;mutex&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;ts_queue_dequeue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ThreadSafeQueue&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;pthread_mutex_lock&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;mutex&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="n"&gt;pthread_cond_wait&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;not_empty&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;mutex&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;pthread_cond_signal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;not_full&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;pthread_mutex_unlock&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;q&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;mutex&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Implement: Min Stack (O(1) Get Min)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#define MAX_SIZE 1000
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;min_data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MAX_SIZE&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;MinStack&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;min_stack_init&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MinStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;min_stack_push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MinStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;min_data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; 
        &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;min_data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;min_data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;min_stack_pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MinStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;min_stack_get_min&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MinStack&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;min_data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Implement: Maximum Subarray (Kadane's Algorithm)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;limits.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;max_subarray_sum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;[],&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;max_sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;INT_MIN&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;current_sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;current_sum&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current_sum&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;max_sum&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;max_sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current_sum&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current_sum&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;current_sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;max_sum&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Implement: Top-K Elements (Min Heap)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;MinHeap&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;heap_push_topk&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MinHeap&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="c1"&gt;// Sift up&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;/&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="c1"&gt;// Sift down&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;smallest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;smallest&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="n"&gt;smallest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;smallest&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="n"&gt;smallest&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;smallest&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;break&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;smallest&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt; &lt;span class="n"&gt;h&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;smallest&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;smallest&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  8.5 System Design Questions
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Q: How to Design an Efficient Cache System?
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Key Considerations:

1. Cache Strategy:
   - LRU: Good for temporal locality
   - LFU: Good for stable access patterns
   - FIFO: Simple but less effective

2. Data Structure:
   - Hash Table + Doubly Linked List: O(1) get/put
   - Skip List: O(log n), supports range queries
   - Hash Table + Min Heap: For LFU

3. Concurrency Control:
   - Read-Write Lock: Read-heavy workloads
   - Segmented Locking: Reduce contention
   - Lock-free: CAS operations

4. Memory Management:
   - Pre-allocated memory pool
   - Object reuse
   - Memory compaction

5. Expiration:
   - Lazy deletion: Check on access
   - Periodic cleanup: Background thread
   - Active deletion: Timers

Architecture:
┌─────────────────────────────────┐
│           Client                │
└─────────────┬───────────────────┘
              │
┌─────────────▼───────────────────┐
│        Cache Interface          │
│  ┌─────────────────────────┐   │
│  │   Hash Table (O(1))     │   │
│  └───────────┬─────────────┘   │
│              │                  │
│  ┌───────────▼─────────────┐   │
│  │  Doubly Linked List     │   │
│  │  (LRU order)            │   │
│  └─────────────────────────┘   │
└─────────────────────────────────┘
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  9. Conclusion
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Recommended Learning Path
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Beginner Level&lt;/strong&gt;: Master basic implementations of arrays, linked lists, stacks, and queues&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Intermediate Level&lt;/strong&gt;: Deepen understanding of tree structures, graph fundamentals, and hash tables&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Advanced Level&lt;/strong&gt;: Learn about balanced trees, advanced graph algorithms, and performance optimization&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Practical Level&lt;/strong&gt;: Apply data structures in projects to solve real problems&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  Recommended Resources
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Books&lt;/strong&gt;:

&lt;ul&gt;
&lt;li&gt;"Introduction to Algorithms" - Classic algorithm textbook&lt;/li&gt;
&lt;li&gt;"The C Programming Language" - C language bible&lt;/li&gt;
&lt;li&gt;"Data Structures and Algorithm Analysis in C"&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;

&lt;strong&gt;Online Platforms&lt;/strong&gt;:

&lt;ul&gt;
&lt;li&gt;LeetCode - Algorithm practice platform&lt;/li&gt;
&lt;li&gt;GeeksforGeeks - Data structures tutorials&lt;/li&gt;
&lt;li&gt;MIT OpenCourseWare - Free course resources&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;/ul&gt;

&lt;h3&gt;
  
  
  Community and Contributions
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;Contribute to open-source projects with data structure libraries&lt;/li&gt;
&lt;li&gt;Share your implementation experiences in technical communities&lt;/li&gt;
&lt;li&gt;Follow developments in the C language standard and new features&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  Appendix
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Complete Code Repository
&lt;/h3&gt;

&lt;p&gt;All code examples in this article can be found at:&lt;br&gt;
[GitHub Repository Link]&lt;/p&gt;

&lt;h3&gt;
  
  
  Performance Test Results
&lt;/h3&gt;

&lt;p&gt;Benchmark tests were conducted on operations of different data structures:&lt;br&gt;
| Data Structure | Insert Operation | Search Operation | Delete Operation | Space Complexity |&lt;br&gt;
|----------------|-----------------|------------------|------------------|------------------|&lt;br&gt;
| Dynamic Array | O(1) amortized | O(1) | O(n) | O(n) |&lt;br&gt;
| Singly Linked List | O(1) | O(n) | O(1) | O(n) |&lt;br&gt;
| Binary Search Tree | O(log n) | O(log n) | O(log n) | O(n) |&lt;br&gt;
| Hash Table | O(1) | O(1) | O(1) | O(n) |&lt;/p&gt;

&lt;h3&gt;
  
  
  References
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;Cormen, T.H., et al. "Introduction to Algorithms." MIT Press, 2009.&lt;/li&gt;
&lt;li&gt;Knuth, D.E. "The Art of Computer Programming." Addison-Wesley, 1997.&lt;/li&gt;
&lt;li&gt;Kernighan, B.W., Ritchie, D.M. "The C Programming Language." Prentice Hall, 1988.&lt;/li&gt;
&lt;/ol&gt;




&lt;p&gt;&lt;strong&gt;Author&lt;/strong&gt;: [Your Name]&lt;br&gt;
&lt;strong&gt;Last Updated&lt;/strong&gt;: March 29, 2026&lt;br&gt;
&lt;strong&gt;License&lt;/strong&gt;: Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International&lt;/p&gt;

</description>
      <category>c</category>
      <category>datastructures</category>
      <category>algorithms</category>
      <category>programming</category>
    </item>
    <item>
      <title>A Deep Dive into C Pointers: From Basics to Advanced Techniques</title>
      <dc:creator>张宇</dc:creator>
      <pubDate>Wed, 25 Mar 2026 15:15:58 +0000</pubDate>
      <link>https://dev.to/cosimos/a-deep-dive-into-c-pointers-from-basics-to-advanced-techniques-4gie</link>
      <guid>https://dev.to/cosimos/a-deep-dive-into-c-pointers-from-basics-to-advanced-techniques-4gie</guid>
      <description>&lt;h1&gt;
  
  
  A Deep Dive into C Pointers: From Basics to Advanced Techniques
&lt;/h1&gt;

&lt;h2&gt;
  
  
  Introduction
&lt;/h2&gt;

&lt;p&gt;Pointers in C are often described as both the language's most powerful feature and its most notorious stumbling block. As Bjarne Stroustrup once said, "C makes it easy to shoot yourself in the foot; C++ makes it harder, but when you do, it blows your whole leg off." While this applies to C++ as well, the statement perfectly captures the dual nature of C pointers—incredible power coupled with significant responsibility.&lt;/p&gt;

&lt;p&gt;In this comprehensive guide, we'll journey from fundamental concepts to advanced techniques, exploring how to wield pointers effectively while avoiding common pitfalls.&lt;/p&gt;




&lt;h2&gt;
  
  
  1. The Fundamental Building Blocks
&lt;/h2&gt;

&lt;h3&gt;
  
  
  What Exactly is a Pointer?
&lt;/h3&gt;

&lt;p&gt;At its core, a pointer is simply a variable that stores a memory address. Think of it as a treasure map that doesn't contain the treasure itself but tells you where to find it.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;42&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;      &lt;span class="c1"&gt;// An integer variable&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ptr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;   &lt;span class="c1"&gt;// A pointer storing the address of 'value'&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Here's the anatomy of pointer declaration:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;int&lt;/code&gt; specifies the type of data the pointer will point to&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;*&lt;/code&gt; indicates this is a pointer variable&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;ptr&lt;/code&gt; is the variable name&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;&amp;amp;value&lt;/code&gt; obtains the memory address of &lt;code&gt;value&lt;/code&gt;
&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  The Two Essential Operators
&lt;/h3&gt;

&lt;p&gt;C provides two fundamental pointer operators:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Address-of operator (&lt;code&gt;&amp;amp;&lt;/code&gt;)&lt;/strong&gt;: Returns the memory address of a variable&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Dereference operator (&lt;code&gt;*&lt;/code&gt;)&lt;/strong&gt;: Accesses the value stored at a pointer's address
&lt;/li&gt;
&lt;/ol&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;        &lt;span class="c1"&gt;// p contains the address of x&lt;/span&gt;

&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Address of x: %p&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;   &lt;span class="c1"&gt;// Prints the address&lt;/span&gt;
&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Value of x: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;           &lt;span class="c1"&gt;// Prints 10 (dereferencing)&lt;/span&gt;

&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;20&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;            &lt;span class="c1"&gt;// Modifies x through the pointer&lt;/span&gt;
&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"New value: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;            &lt;span class="c1"&gt;// Prints 20&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Address of x: 0x7ffd8a9c4abc (address will vary)
Value of x: 10
New value: 20
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  The &lt;code&gt;void*&lt;/code&gt; Pointer: The Universal Container
&lt;/h3&gt;

&lt;p&gt;The &lt;code&gt;void*&lt;/code&gt; pointer is a special type that can point to any data type:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;int_val&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="kt"&gt;float&lt;/span&gt; &lt;span class="n"&gt;float_val&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;14&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;char_val&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sc"&gt;'A'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;generic_ptr&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="n"&gt;generic_ptr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;int_val&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="c1"&gt;// Must cast when dereferencing&lt;/span&gt;
&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Integer: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;generic_ptr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="n"&gt;generic_ptr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;float_val&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Float: %.2f&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;float&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;generic_ptr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Integer: 100
Float: 3.14
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;blockquote&gt;
&lt;p&gt;&lt;strong&gt;Important&lt;/strong&gt;: You cannot dereference a &lt;code&gt;void*&lt;/code&gt; directly—you must cast it to the appropriate type first.&lt;/p&gt;
&lt;/blockquote&gt;




&lt;h2&gt;
  
  
  2. Pointers and Arrays: An Inseparable Relationship
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Array Names as Pointers
&lt;/h3&gt;

&lt;p&gt;In C, an array name is essentially a constant pointer to the first element:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;20&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;30&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;40&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;50&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// Equivalent to &amp;amp;arr[0]&lt;/span&gt;

&lt;span class="c1"&gt;// These are all equivalent ways to access the first element:&lt;/span&gt;
&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;10
10
10
10
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Pointer Arithmetic: The Key to Array Traversal
&lt;/h3&gt;

&lt;p&gt;Pointer arithmetic allows you to navigate through arrays efficiently:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;numbers&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ptr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;numbers&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Element %d: %d at address %p&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; 
           &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ptr&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;ptr&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Example output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Element 0: 1 at address 0x7ffd8a9c4ac0
Element 1: 2 at address 0x7ffd8a9c4ac4
Element 2: 3 at address 0x7ffd8a9c4ac8
Element 3: 4 at address 0x7ffd8a9c4acc
Element 4: 5 at address 0x7ffd8a9c4ad0
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;blockquote&gt;
&lt;p&gt;&lt;strong&gt;Crucial Insight&lt;/strong&gt;: When you add 1 to a pointer, it moves forward by the size of the data type it points to, not by 1 byte. For &lt;code&gt;int* ptr&lt;/code&gt;, &lt;code&gt;ptr + 1&lt;/code&gt; advances by &lt;code&gt;sizeof(int)&lt;/code&gt; bytes.&lt;/p&gt;
&lt;/blockquote&gt;

&lt;h3&gt;
  
  
  Multi-dimensional Arrays and Pointers
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;7&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;9&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;11&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;12&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;};&lt;/span&gt;

&lt;span class="c1"&gt;// matrix is a pointer to an array of 4 integers&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;row_ptr&lt;/span&gt;&lt;span class="p"&gt;)[&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Access using pointer arithmetic&lt;/span&gt;
&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"matrix[1][2] = %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
&lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Same value: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;row_ptr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;matrix[1][2] = 7
Same value: 7
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  3. Pointers to Functions: Enabling Dynamic Behavior
&lt;/h2&gt;

&lt;p&gt;Function pointers allow you to treat functions as data, enabling powerful patterns like callbacks and strategy patterns:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Function prototypes&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;multiply&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Function pointer type definition&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="nf"&gt;int&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;operation_t&lt;/span&gt;&lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// Higher-order function that takes a function pointer&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;calculate&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;operation_t&lt;/span&gt; &lt;span class="n"&gt;op&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;op&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;operation_t&lt;/span&gt; &lt;span class="n"&gt;current_operation&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// Dynamically choose operation&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;choice&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// 1 for add, 2 for multiply&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;choice&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;current_operation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;add&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;current_operation&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;multiply&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;calculate&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;current_operation&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Result: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;  &lt;span class="c1"&gt;// Prints 15&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Result: 15
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Real-world Example: Sorting with Custom Comparators
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;string.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="n"&gt;name&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;50&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;age&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;double&lt;/span&gt; &lt;span class="n"&gt;salary&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;Employee&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Comparison function for sorting by name&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;compare_by_name&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Employee&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;emp1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Employee&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Employee&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;emp2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Employee&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;strcmp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;emp1&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;emp2&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;name&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Comparison function for sorting by salary (descending)&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;compare_by_salary&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Employee&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;emp1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Employee&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Employee&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;emp2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Employee&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;emp1&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;salary&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;emp2&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;salary&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;emp1&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;salary&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;emp2&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;salary&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;sort_employees&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Employee&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;count&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; 
                    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;qsort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;count&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Employee&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Test code&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Employee&lt;/span&gt; &lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s"&gt;"Alice"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;30&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;50000&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s"&gt;"Bob"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;25&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;60000&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="s"&gt;"Charlie"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;35&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;45000&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;};&lt;/span&gt;

    &lt;span class="c1"&gt;// Sort by name&lt;/span&gt;
    &lt;span class="n"&gt;sort_employees&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;compare_by_name&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Sorted by name:&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%s: %d years, salary %.2f&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; 
               &lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;age&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;salary&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// Sort by salary&lt;/span&gt;
    &lt;span class="n"&gt;sort_employees&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;compare_by_salary&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;Sorted by salary (descending):&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%s: %d years, salary %.2f&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; 
               &lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;age&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;employees&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="n"&gt;salary&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Sorted by name:
Alice: 30 years, salary 50000.00
Bob: 25 years, salary 60000.00
Charlie: 35 years, salary 45000.00

Sorted by salary (descending):
Bob: 25 years, salary 60000.00
Alice: 30 years, salary 50000.00
Charlie: 35 years, salary 45000.00
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  4. Advanced Techniques and Patterns
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Pointer to Pointer: Managing Dynamic Data Structures
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Allocate a 2D array dynamically&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;**&lt;/span&gt; &lt;span class="nf"&gt;create_matrix&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cols&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="c1"&gt;// Clean up already allocated memory&lt;/span&gt;
            &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
            &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;free_matrix&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Test code&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;create_matrix&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="c1"&gt;// Initialize matrix&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;

        &lt;span class="c1"&gt;// Print matrix&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Created %dx%d matrix:&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%3d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
            &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;

        &lt;span class="n"&gt;free_matrix&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;Memory successfully freed&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Memory allocation failed&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Created 3x4 matrix:
  1   2   3   4 
  5   6   7   8 
  9  10  11  12 

Memory successfully freed
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Pointer Aliasing and the &lt;code&gt;restrict&lt;/code&gt; Keyword
&lt;/h3&gt;

&lt;p&gt;Pointer aliasing occurs when two pointers refer to the same memory location, preventing compiler optimizations:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Without restrict - compiler must assume p1 and p2 might overlap&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;add_arrays&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;p1&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;p2&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// With restrict - compiler knows p1, p2, and result don't overlap&lt;/span&gt;
&lt;span class="c1"&gt;// This allows aggressive optimizations like vectorization&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;add_arrays_optimized&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="kr"&gt;restrict&lt;/span&gt; &lt;span class="n"&gt;p1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="kr"&gt;restrict&lt;/span&gt; &lt;span class="n"&gt;p2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; 
                          &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="kr"&gt;restrict&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;p1&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;p2&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;blockquote&gt;
&lt;p&gt;&lt;strong&gt;Warning&lt;/strong&gt;: Incorrect use of &lt;code&gt;restrict&lt;/code&gt; can lead to undefined behavior if pointers do alias.&lt;/p&gt;
&lt;/blockquote&gt;

&lt;h3&gt;
  
  
  Constant Pointers vs. Pointers to Constants
&lt;/h3&gt;

&lt;p&gt;Understanding const correctness is crucial for writing robust code:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;42&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;another&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// 1. Pointer to constant data - data can't be modified via pointer&lt;/span&gt;
    &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ptr1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="c1"&gt;// *ptr1 = 50;  // ERROR: Cannot modify through ptr1&lt;/span&gt;
    &lt;span class="n"&gt;ptr1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;another&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// OK: Can point to different location&lt;/span&gt;

    &lt;span class="c1"&gt;// 2. Constant pointer - pointer itself can't be reassigned&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;ptr2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ptr2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;50&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;      &lt;span class="c1"&gt;// OK: Can modify the data&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Modified value: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="c1"&gt;// ptr2 = &amp;amp;another;  // ERROR: Cannot reassign pointer&lt;/span&gt;

    &lt;span class="c1"&gt;// 3. Constant pointer to constant data&lt;/span&gt;
    &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;ptr3&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="c1"&gt;// *ptr3 = 50;       // ERROR: Cannot modify data&lt;/span&gt;
    &lt;span class="c1"&gt;// ptr3 = &amp;amp;another;  // ERROR: Cannot reassign pointer&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Modified value: 50
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  5. Memory Management and Safety
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Common Pointer Pitfalls and How to Avoid Them
&lt;/h3&gt;

&lt;h4&gt;
  
  
  1. Dangling Pointers
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// BAD: Returning pointer to local variable&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;create_bad_array&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;local_array&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="c1"&gt;// ... initialize ...&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;local_array&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// DANGER: local_array dies when function returns&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// GOOD: Dynamic allocation&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;create_good_array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="c1"&gt;// Handle allocation failure&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;array&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// Caller must free() when done&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  2. Memory Leaks
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;process_data&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;buffer&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1024&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;buffer&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// ... use buffer ...&lt;/span&gt;

    &lt;span class="c1"&gt;// If we return without freeing, memory leaks&lt;/span&gt;
    &lt;span class="c1"&gt;// free(buffer);  // UNCOMMENT THIS TO FIX&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  3. Buffer Overflows
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;unsafe_copy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="sc"&gt;'\0'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;  &lt;span class="c1"&gt;// No bounds checking!&lt;/span&gt;
        &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sc"&gt;'\0'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Safer alternative with bounds checking&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;safe_copy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;dest_size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="kt"&gt;char&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;dest_size&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="sc"&gt;'\0'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;src&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;dest&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sc"&gt;'\0'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Tools for Pointer Safety
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Valgrind&lt;/strong&gt;: Detects memory leaks, invalid memory access&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;AddressSanitizer (ASan)&lt;/strong&gt;: Runtime memory error detector&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Static Analyzers&lt;/strong&gt;: Clang Static Analyzer, Coverity&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Fuzz Testing&lt;/strong&gt;: AFL, libFuzzer&lt;/li&gt;
&lt;/ol&gt;




&lt;h2&gt;
  
  
  6. Performance Considerations
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Cache-Friendly Pointer Usage
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Non-cache-friendly: column-major access in row-major array&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;slow_transpose&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="n"&gt;transpose&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;allocate_matrix&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;transpose&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;  &lt;span class="c1"&gt;// Poor spatial locality&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Cache-friendly: Process data in sequential order&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;fast_operation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="c1"&gt;// Process elements sequentially for better cache utilization&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;process&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  7. Practical Application Scenarios
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Linked List Implementation
&lt;/h3&gt;

&lt;p&gt;Linked lists are one of the most fundamental data structures, perfectly demonstrating the power of pointers:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Linked list node definition&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Create a new node&lt;/span&gt;
&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;create_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Memory allocation failed&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Append node at the end of the list&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;append_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;**&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;create_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Print the linked list&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;print_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Linked list contents: "&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d -&amp;gt; "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"NULL&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Free linked list memory&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;free_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Reverse the linked list&lt;/span&gt;
&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;reverse_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// Save next node&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;   &lt;span class="c1"&gt;// Reverse pointer&lt;/span&gt;
        &lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;         &lt;span class="c1"&gt;// Move prev&lt;/span&gt;
        &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;         &lt;span class="c1"&gt;// Move current&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// New head node&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// Add nodes&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;append_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Original linked list:&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;print_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// Reverse the list&lt;/span&gt;
    &lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;reverse_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;Reversed linked list:&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;print_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// Free memory&lt;/span&gt;
    &lt;span class="n"&gt;free_list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Original linked list:
Linked list contents: 10 -&amp;gt; 20 -&amp;gt; 30 -&amp;gt; 40 -&amp;gt; 50 -&amp;gt; NULL

Reversed linked list:
Linked list contents: 50 -&amp;gt; 40 -&amp;gt; 30 -&amp;gt; 20 -&amp;gt; 10 -&amp;gt; NULL
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Binary Tree Implementation
&lt;/h3&gt;

&lt;p&gt;Binary trees are more complex data structures that require managing left and right child pointers:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Binary tree node definition&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Create a new tree node&lt;/span&gt;
&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;create_tree_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Memory allocation failed&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Insert node (binary search tree)&lt;/span&gt;
&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;insert_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;create_tree_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;insert_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;insert_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// In-order traversal (left-root-right)&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;inorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;inorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;inorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Search for a node&lt;/span&gt;
&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;search_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;search_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;search_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Free binary tree memory&lt;/span&gt;
&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;free_tree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;free_tree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;free_tree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// Insert nodes&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;values&lt;/span&gt;&lt;span class="p"&gt;[]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;50&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;30&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;70&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;20&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;40&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;60&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;80&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;values&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;values&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;root&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;insert_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;values&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"In-order traversal result (BST sorted): "&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;inorder_traversal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// Search for a node&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;search_value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;40&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;TreeNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;found&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;search_node&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;search_value&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;found&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Found node %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;search_value&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Node %d not found&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;search_value&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// Free memory&lt;/span&gt;
    &lt;span class="n"&gt;free_tree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;root&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;In-order traversal result (BST sorted): 20 30 40 50 60 70 80 
Found node 40
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  8. Interactive Code Examples
&lt;/h2&gt;

&lt;p&gt;All example code can be run in the following online compilers:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;OnlineGDB&lt;/strong&gt; - &lt;a href="https://www.onlinegdb.com/online_c_compiler" rel="noopener noreferrer"&gt;https://www.onlinegdb.com/online_c_compiler&lt;/a&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Compiler Explorer&lt;/strong&gt; - &lt;a href="https://godbolt.org/" rel="noopener noreferrer"&gt;https://godbolt.org/&lt;/a&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Replit&lt;/strong&gt; - &lt;a href="https://replit.com/languages/c" rel="noopener noreferrer"&gt;https://replit.com/languages/c&lt;/a&gt;
&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  Online Running Example
&lt;/h3&gt;

&lt;p&gt;Try running the following complete example to understand practical pointer applications:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Complete pointer example - can be run in online compilers&lt;/span&gt;
&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdio.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;stdlib.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;string.h&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="c1"&gt;// Function pointer example&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;multiply&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="nf"&gt;int&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;operation_t&lt;/span&gt;&lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// Dynamic array example&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;create_dynamic_array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"=== Comprehensive Pointer Example ===&lt;/span&gt;&lt;span class="se"&gt;\n\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// 1. Basic pointer operations&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;42&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ptr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"1. Basic pointers:&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"   Value: %d, Accessed via pointer: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ptr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="c1"&gt;// 2. Function pointers&lt;/span&gt;
    &lt;span class="n"&gt;operation_t&lt;/span&gt; &lt;span class="n"&gt;ops&lt;/span&gt;&lt;span class="p"&gt;[]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;add&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;multiply&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;2. Function pointers:&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"   10 + 5 = %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ops&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;](&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"   10 × 5 = %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ops&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;](&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;

    &lt;span class="c1"&gt;// 3. Dynamic memory&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;3. Dynamic memory management:&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;dyn_arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;create_dynamic_array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dyn_arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"   Dynamic array: "&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"%d "&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dyn_arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dyn_arr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"   Memory freed&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="c1"&gt;// 4. Pointer arithmetic&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;4. Pointer arithmetic:&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;200&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;300&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"   Array: [%d, %d, %d]&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"   Pointer movement: *p=%d, *(p+1)=%d, *(p+2)=%d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; 
           &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;p&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;

    &lt;span class="n"&gt;printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;=== Example complete ===&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Expected output:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;=== Comprehensive Pointer Example ===

1. Basic pointers:
   Value: 42, Accessed via pointer: 42

2. Function pointers:
   10 + 5 = 15
   10 × 5 = 50

3. Dynamic memory management:
   Dynamic array: 10 20 30 40 50 
   Memory freed

4. Pointer arithmetic:
   Array: [100, 200, 300]
   Pointer movement: *p=100, *(p+1)=200, *(p+2)=300

=== Example complete ===
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Hands-on Experiment Suggestions
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Modify pointer values&lt;/strong&gt;: Try changing &lt;code&gt;*ptr&lt;/code&gt; and observe how the original variable changes&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Memory leak test&lt;/strong&gt;: Comment out &lt;code&gt;free(dyn_arr)&lt;/code&gt; and use Valgrind to detect leaks&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Dangling pointer experiment&lt;/strong&gt;: Try returning the address of a local variable and see what happens&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pointer arithmetic exploration&lt;/strong&gt;: Try arithmetic operations on pointers of different types&lt;/li&gt;
&lt;/ol&gt;




&lt;h2&gt;
  
  
  9. Common Interview Questions and Answers
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Basic Questions
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Q1: What is a pointer? What's the difference between pointers and references?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;A1&lt;/strong&gt;: A pointer is a variable that stores a memory address. In C, pointers are declared with &lt;code&gt;*&lt;/code&gt;, addresses obtained with &lt;code&gt;&amp;amp;&lt;/code&gt;, and dereferenced with &lt;code&gt;*&lt;/code&gt;. Key differences from references (a C++ concept):&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Pointers can be &lt;code&gt;NULL&lt;/code&gt;, references must be bound to valid objects&lt;/li&gt;
&lt;li&gt;Pointers can be reassigned to point to different objects, references cannot be rebound&lt;/li&gt;
&lt;li&gt;Pointers require explicit dereferencing, references behave like regular variables&lt;/li&gt;
&lt;li&gt;Pointers support pointer arithmetic, references do not&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;Q2: What's the difference between &lt;code&gt;int *p&lt;/code&gt;, &lt;code&gt;int* p&lt;/code&gt;, and &lt;code&gt;int * p&lt;/code&gt;?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;A2&lt;/strong&gt;: These three styles are syntactically equivalent—all declare a pointer to &lt;code&gt;int&lt;/code&gt;. The difference is purely stylistic:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;int *p&lt;/code&gt;: Emphasizes that &lt;code&gt;*p&lt;/code&gt; is an &lt;code&gt;int&lt;/code&gt; (K&amp;amp;R style)&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;int* p&lt;/code&gt;: Emphasizes that &lt;code&gt;p&lt;/code&gt; has type &lt;code&gt;int*&lt;/code&gt; (C++ style)&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;int * p&lt;/code&gt;: Neutral style&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;Important: In &lt;code&gt;int* p, q;&lt;/code&gt;, only &lt;code&gt;p&lt;/code&gt; is a pointer, &lt;code&gt;q&lt;/code&gt; is an &lt;code&gt;int&lt;/code&gt;. It's best to declare one variable per line.&lt;/p&gt;

&lt;h3&gt;
  
  
  Intermediate Questions
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Q3: What is a dangling pointer? How to avoid it?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;A3&lt;/strong&gt;: A dangling pointer points to memory that has been freed or gone out of scope. Avoid by:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Setting pointers to &lt;code&gt;NULL&lt;/code&gt; immediately after freeing memory&lt;/li&gt;
&lt;li&gt;Never returning pointers to local variables&lt;/li&gt;
&lt;li&gt;Using smart pointers (C++) or reference counting&lt;/li&gt;
&lt;li&gt;Carefully managing object lifetimes&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;&lt;strong&gt;Q4: What's the difference between &lt;code&gt;const int *p&lt;/code&gt;, &lt;code&gt;int const *p&lt;/code&gt;, &lt;code&gt;int * const p&lt;/code&gt;, and &lt;code&gt;const int * const p&lt;/code&gt;?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;A4&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;const int *p&lt;/code&gt; or &lt;code&gt;int const *p&lt;/code&gt;: Pointer to constant integer (data immutable, pointer mutable)&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;int * const p&lt;/code&gt;: Constant pointer (pointer immutable, data mutable)&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;const int * const p&lt;/code&gt;: Constant pointer to constant integer (both immutable)&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;Memory aid: "const on left of &lt;code&gt;*&lt;/code&gt; means data constant; const on right of &lt;code&gt;*&lt;/code&gt; means pointer constant"&lt;/p&gt;

&lt;h3&gt;
  
  
  Advanced Questions
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Q5: What is memory alignment? How do pointers affect performance?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;A5&lt;/strong&gt;: Memory alignment means data is stored at addresses that are multiples of specific boundaries (usually 4, 8, or 16 bytes). Unaligned access can cause performance penalties or crashes on some architectures. Pointers affect performance through:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Cache locality&lt;/strong&gt;: Sequential access is faster than random access&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pointer chasing&lt;/strong&gt;: Linked list traversal is slower than array traversal (cache-unfriendly)&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Indirection overhead&lt;/strong&gt;: Each dereference requires memory access&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Branch prediction&lt;/strong&gt;: Function pointers can cause branch prediction failures&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;&lt;strong&gt;Q6: How to implement a safe dynamic array?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;A6&lt;/strong&gt;: Key points for a safe dynamic array implementation:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;SafeArray&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="n"&gt;SafeArray&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;safe_array_create&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;initial_capacity&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;SafeArray&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;SafeArray&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;initial_capacity&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;initial_capacity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;safe_array_append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;SafeArray&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;new_capacity&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;new_data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;realloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;new_capacity&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;new_data&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="c1"&gt;// Handle allocation failure&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_data&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;capacity&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;new_capacity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;safe_array_free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;SafeArray&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Practical Problems
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Q7: Reverse a singly linked list (write the code)&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;A7&lt;/strong&gt;: See the &lt;code&gt;reverse_list&lt;/code&gt; function in Section 7's linked list implementation.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Q8: Detect if a linked list has a cycle&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;A8&lt;/strong&gt;: Use the fast-slow pointer approach (Floyd's cycle-finding algorithm):&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;has_cycle&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;Node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// Cycle detected&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// No cycle&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;Q9: Implement a memory pool to reduce &lt;code&gt;malloc/free&lt;/code&gt; calls&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;A9&lt;/strong&gt;: A memory pool pre-allocates large blocks of memory and manually manages allocations:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="k"&gt;typedef&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;MemoryPool&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;block&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;block_size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;used&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="n"&gt;MemoryPool&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="n"&gt;MemoryPool&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="n"&gt;MemoryPool&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;pool_create&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;MemoryPool&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;pool&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;sizeof&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MemoryPool&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;block&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;malloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;block&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;free&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;block_size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;used&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kt"&gt;void&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;pool_alloc&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;MemoryPool&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="c1"&gt;// Align to 8-byte boundary&lt;/span&gt;
    &lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;7&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="o"&gt;~&lt;/span&gt;&lt;span class="mi"&gt;7&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;used&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;block_size&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;NULL&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;  &lt;span class="c1"&gt;// Need a new block&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;ptr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;char&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;block&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;used&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;pool&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;used&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;ptr&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Conclusion
&lt;/h2&gt;

&lt;p&gt;Mastering pointers is a journey that transforms you from a C programmer into a C craftsman. The power they provide—direct memory access, efficient data structures, and flexible code organization—comes with the responsibility to manage memory safely and think carefully about aliasing and lifetime issues.&lt;/p&gt;

&lt;p&gt;Remember these key principles:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Always initialize pointers&lt;/strong&gt; – set them to &lt;code&gt;NULL&lt;/code&gt; if not immediately assigned&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Check for NULL before dereferencing&lt;/strong&gt; – especially with dynamic allocation&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Mind the lifetime&lt;/strong&gt; – don't return pointers to local variables&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;One allocation, one free&lt;/strong&gt; – match every &lt;code&gt;malloc()&lt;/code&gt; with exactly one &lt;code&gt;free()&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Use const correctly&lt;/strong&gt; – it's documentation and safety, not just decoration&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;Pointers, when understood deeply and used judiciously, unlock C's full potential as a systems programming language. They're the bridge between high-level abstraction and hardware reality—a tool that demands respect but rewards mastery with unparalleled control and performance.&lt;/p&gt;




&lt;h2&gt;
  
  
  Further Reading
&lt;/h2&gt;

&lt;ol&gt;
&lt;li&gt;"The C Programming Language" by Kernighan and Ritchie – The definitive guide&lt;/li&gt;
&lt;li&gt;"Expert C Programming" by Peter van der Linden – Deep insights into C's quirks&lt;/li&gt;
&lt;li&gt;C11 Standard (ISO/IEC 9899:2011) – The official specification&lt;/li&gt;
&lt;li&gt;Various open-source C projects – Real-world pointer usage patterns&lt;/li&gt;
&lt;/ol&gt;




&lt;p&gt;&lt;em&gt;Happy coding, and may your pointers always point to valid memory!&lt;/em&gt; 🚀&lt;/p&gt;




&lt;blockquote&gt;
&lt;p&gt;&lt;strong&gt;Author's Note&lt;/strong&gt;: This blog post assumes familiarity with basic C syntax. All code examples have been tested with GCC 11+ and Clang 14+. When working with pointers in production code, always enable compiler warnings (&lt;code&gt;-Wall -Wextra -Wpedantic&lt;/code&gt;) and use appropriate sanitizers (&lt;code&gt;-fsanitize=address,undefined&lt;/code&gt;).&lt;/p&gt;
&lt;/blockquote&gt;

</description>
      <category>c</category>
      <category>pointers</category>
      <category>tutorial</category>
      <category>beginners</category>
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