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    <title>DEV Community: Habibur Rahman Shihab</title>
    <description>The latest articles on DEV Community by Habibur Rahman Shihab (@hrshihab).</description>
    <link>https://dev.to/hrshihab</link>
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      <title>DEV Community: Habibur Rahman Shihab</title>
      <link>https://dev.to/hrshihab</link>
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    <language>en</language>
    <item>
      <title>Is the Era of Clean Code Over?</title>
      <dc:creator>Habibur Rahman Shihab</dc:creator>
      <pubDate>Mon, 13 Apr 2026 08:40:18 +0000</pubDate>
      <link>https://dev.to/hrshihab/is-the-era-of-clean-code-over-462e</link>
      <guid>https://dev.to/hrshihab/is-the-era-of-clean-code-over-462e</guid>
      <description>&lt;p&gt;&lt;strong&gt;The New Transformation of Software Engineering: From High-Level Frameworks to AI-Generated Code&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;One of the biggest myths in software engineering over the past decade was:&lt;br&gt;
&lt;strong&gt;“Code is written for humans to read and machines to execute.”&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;To manage large-scale projects, we followed SOLID principles and relied on frameworks like React or Next.js.&lt;/p&gt;

&lt;p&gt;But in the context of 2026, we are going through a fundamental shift.&lt;br&gt;
The new generation of AI agents no longer feels the need to write code that is easily readable by humans. Instead, they are moving toward an approach that prioritizes performance and scalability above all.&lt;/p&gt;




&lt;h2&gt;
  
  
  💡 AI-Native Architecture
&lt;/h2&gt;

&lt;p&gt;AI is reshaping the long-standing grammar of programming:&lt;/p&gt;

&lt;h3&gt;
  
  
  1. Decline of Framework Dependency
&lt;/h3&gt;

&lt;p&gt;Frameworks such as React, Django, or Spring Boot were originally built to make development easier for humans. However, they introduce additional overhead on browsers or servers.&lt;/p&gt;

&lt;p&gt;Modern AI agents are now bypassing these human-friendly layers and directly generating code in WebAssembly (WASM) or even closer to machine-level instructions.&lt;br&gt;
As a result, software performance can improve by several times. In the future, AI-native applications may not require traditional frameworks at all.&lt;/p&gt;




&lt;h3&gt;
  
  
  2. Folder Structure vs Context Window
&lt;/h3&gt;

&lt;p&gt;Humans cannot hold thousands of lines of code in their minds at once, so we organize code into folders and modules — a concept known as &lt;strong&gt;Separation of Concerns&lt;/strong&gt;.&lt;/p&gt;

&lt;p&gt;But modern AI, with its massive context capacity, can treat an entire project as a single unified entity.&lt;br&gt;
This reduces the importance of traditional folder structures and modular organization.&lt;/p&gt;




&lt;h3&gt;
  
  
  3. Direct UI Generation
&lt;/h3&gt;

&lt;p&gt;The era of pre-designed static interfaces is fading.&lt;br&gt;
AI can now generate user interfaces instantly based on user needs, in real time.&lt;/p&gt;




&lt;h2&gt;
  
  
  Why AI Avoids Human-Readable Code
&lt;/h2&gt;

&lt;p&gt;The primary reason is &lt;strong&gt;speed and efficiency&lt;/strong&gt;.&lt;br&gt;
Structuring code for human readability often introduces abstraction layers that reduce performance.&lt;/p&gt;

&lt;p&gt;When AI works closer to machine-level instructions, it can fully utilize hardware capabilities.&lt;br&gt;
AI has effectively realized that simplifying code for humans slows down its own execution.&lt;/p&gt;




&lt;h2&gt;
  
  
  Our Future Role: System Supervisors
&lt;/h2&gt;

&lt;p&gt;We are rapidly transitioning from traditional programmers to &lt;strong&gt;system supervisors&lt;/strong&gt;.&lt;/p&gt;

&lt;p&gt;Our main responsibility is no longer writing code line by line, but guiding, validating, and orchestrating AI-generated systems.&lt;/p&gt;




&lt;h2&gt;
  
  
  A Critical Question
&lt;/h2&gt;

&lt;p&gt;This transformation raises an important concern:&lt;/p&gt;

&lt;p&gt;If AI produces “black-box” code that humans cannot interpret, how will we handle critical security risks in the future?&lt;br&gt;
Additionally, excessive dependency on specific AI systems could introduce long-term vulnerabilities.&lt;/p&gt;




&lt;h2&gt;
  
  
  What Do You Think?
&lt;/h2&gt;

&lt;p&gt;Will this evolution of clean code and traditional frameworks make our work easier,&lt;br&gt;
or will we gradually lose control over software as humans?&lt;/p&gt;

&lt;p&gt;Share your thoughts in the comments.&lt;/p&gt;




</description>
      <category>javascript</category>
      <category>webdev</category>
      <category>ai</category>
      <category>programming</category>
    </item>
    <item>
      <title>20 Essential Problem-Solving Patterns in C++</title>
      <dc:creator>Habibur Rahman Shihab</dc:creator>
      <pubDate>Fri, 25 Oct 2024 06:02:36 +0000</pubDate>
      <link>https://dev.to/hrshihab/20-essential-problem-solving-patterns-in-c-mfb</link>
      <guid>https://dev.to/hrshihab/20-essential-problem-solving-patterns-in-c-mfb</guid>
      <description>&lt;p&gt;Data Structures and Algorithms (DSA) are crucial for efficient problem-solving. Here are 20 key patterns, with use cases and examples, to help tackle real-world problems. This guide includes concise C++ examples to demonstrate each pattern in action.&lt;/p&gt;




&lt;p&gt;&lt;strong&gt;1. Sliding Window Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Efficiently solve problems involving subarrays in a linear array by sliding a window across the array.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Find the maximum sum subarray of size &lt;code&gt;k&lt;/code&gt;.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Find the maximum sum of any contiguous subarray of size &lt;code&gt;k&lt;/code&gt;.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;maxSumSubarray&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&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;k&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;maxSum&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;windowSum&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;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="n"&gt;windowSum&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;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;maxSum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;windowSum&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="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;&amp;lt;&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;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;windowSum&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;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;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="n"&gt;k&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
        &lt;span class="n"&gt;maxSum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;maxSum&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;windowSum&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;maxSum&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;2. Two Pointer Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Two pointers work towards a solution by converging from different ends of an array.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Find pairs in a sorted array.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Find two numbers that sum up to a target.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;twoSum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&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;target&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;0&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="n"&gt;arr&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="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;left&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&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;int&lt;/span&gt; &lt;span class="n"&gt;sum&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;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;arr&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="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;sum&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;target&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="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="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;sum&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;target&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="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="n"&gt;right&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="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;3. Fast &amp;amp; Slow Pointers Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Move two pointers at different speeds to detect cycles in linked lists or arrays.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Detect a cycle in a linked list.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Find if a linked list has a cycle.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;hasCycle&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;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="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="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="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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;p&gt;&lt;strong&gt;4. Merge Intervals Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Merge overlapping intervals in an array of intervals.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Merge intervals in a list.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Merge overlapping intervals in a list of meeting times.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;mergeIntervals&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;intervals&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;intervals&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&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;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;intervals&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;begin&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;intervals&lt;/span&gt;&lt;span class="p"&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;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;merged&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;merged&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;intervals&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;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="n"&gt;intervals&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;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="n"&gt;merged&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;back&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="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="n"&gt;intervals&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="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;merged&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;back&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="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;merged&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;back&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;intervals&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="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;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;merged&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;intervals&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="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;merged&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;5. Cyclic Sort Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Sort a cyclically rotated array or group of elements.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Sort an array of &lt;code&gt;1&lt;/code&gt; to &lt;code&gt;n&lt;/code&gt; numbers.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Find the missing number in an array of &lt;code&gt;n&lt;/code&gt; numbers.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;missingNumber&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&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="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;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="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="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="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="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;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;&amp;lt;=&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;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;swap&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="n"&gt;arr&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="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;else&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="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;arr&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;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="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="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;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="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="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;p&gt;&lt;strong&gt;6. In-place Reversal of Linked List Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Reverse parts of a linked list in-place.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Reverse a sub-list in a linked list.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Reverse a part of the list between positions &lt;code&gt;m&lt;/code&gt; and &lt;code&gt;n&lt;/code&gt;.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&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;reverseBetween&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;m&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;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;nullptr&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;nullptr&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;=&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;m&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="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;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;m&lt;/span&gt;&lt;span class="o"&gt;--&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;n&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;ListNode&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;connection&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="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="n"&gt;current&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;n&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="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;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="n"&gt;n&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="n"&gt;connection&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;connection&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="k"&gt;else&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;prev&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;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;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;p&gt;&lt;strong&gt;7. Tree BFS Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Traverse a tree level by level using BFS.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Traverse a binary tree.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Perform level-order traversal on a binary tree.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;levelOrder&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="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;result&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="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;queue&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;TreeNode&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="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;push&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;q&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&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;size&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;size&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
        &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;currentLevel&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;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;q&lt;/span&gt;&lt;span class="p"&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="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="n"&gt;currentLevel&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&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;q&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="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;q&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="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;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;currentLevel&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;result&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;8. Tree DFS Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Traverse a tree using Depth First Search.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Explore all nodes in a tree.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Perform pre-order traversal of a binary tree.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;preorder&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;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;result&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;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&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="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;preorder&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;result&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="n"&gt;preorder&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;result&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;preorderTraversal&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="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;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;preorder&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;result&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;result&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;9. Binary Search Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Efficiently search for elements in sorted arrays using binary search.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Search in a sorted array.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Find the index of a target value in a sorted array.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;binarySearch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&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;target&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;0&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="n"&gt;arr&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="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;left&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&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;int&lt;/span&gt; &lt;span class="n"&gt;mid&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="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="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="mi"&gt;2&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="n"&gt;mid&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;target&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;mid&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;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;mid&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;target&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;mid&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;else&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;mid&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="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="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;p&gt;&lt;strong&gt;10. Backtracking Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Explore all potential solutions using recursive backtracking.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Solve constraint satisfaction problems.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Solve the N-Queens problem.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;isSafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;string&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;board&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;row&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;col&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;col&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;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;board&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;row&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;'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="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="n"&gt;row&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="n"&gt;col&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;j&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="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;j&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;board&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="sc"&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="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="n"&gt;row&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="n"&gt;col&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="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;j&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="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;j&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;board&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="sc"&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="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;void&lt;/span&gt; &lt;span class="nf"&gt;solveNQueens&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;col&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;string&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;string&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;solutions&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;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;col&lt;/span&gt; &lt;span class="o"&gt;==&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="n"&gt;solutions&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;board&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="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="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;isSafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;board&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;col&lt;/span&gt;&lt;span class="p"&gt;,&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="n"&gt;board&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;col&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sc"&gt;'Q'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;solveNQueens&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;col&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;board&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;solutions&lt;/span&gt;&lt;span class="p"&gt;,&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;board&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;col&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="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;11. Topological Sort Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Sort nodes in a directed graph using topological ordering.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Resolve task dependency problems.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Find the order in which tasks should be completed given dependencies.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;topologicalSort&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;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;edges&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;sortedOrder&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;vertices&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="n"&gt;sortedOrder&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="n"&gt;unordered_map&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&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="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;inDegree&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;unordered_map&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;graph&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="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;inDegree&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="mi"&gt;0&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="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;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;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="k"&gt;auto&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;edge&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;edges&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;parent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;edge&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;child&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;edge&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;graph&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;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;child&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="n"&gt;inDegree&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;child&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="n"&gt;queue&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;sources&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="k"&gt;auto&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&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;inDegree&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;entry&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;second&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;sources&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="n"&gt;entry&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;first&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;sources&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&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;vertex&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;sources&lt;/span&gt;&lt;span class="p"&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;sources&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="n"&gt;sortedOrder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vertex&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;child&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;vertex&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;inDegree&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;child&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="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;inDegree&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;child&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="n"&gt;sources&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="n"&gt;child&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;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;sortedOrder&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="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;return&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;  &lt;span class="c1"&gt;// cycle detected&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;sortedOrder&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;12. Trie Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Use a trie (prefix tree) to solve problems involving word searches.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Efficiently store and search strings.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Implement a word search using a Trie.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;TrieNode&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
&lt;span class="nl"&gt;public:&lt;/span&gt;
    &lt;span class="n"&gt;TrieNode&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;children&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;26&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;isEndOfWord&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;TrieNode&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="mi"&gt;26&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;children&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;nullptr&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;isEndOfWord&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="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;};&lt;/span&gt;

&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Trie&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
&lt;span class="nl"&gt;private:&lt;/span&gt;
    &lt;span class="n"&gt;TrieNode&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="nl"&gt;public:&lt;/span&gt;
    &lt;span class="n"&gt;Trie&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="k"&gt;new&lt;/span&gt; &lt;span class="n"&gt;TrieNode&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;insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;string&lt;/span&gt; &lt;span class="n"&gt;word&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;TrieNode&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;root&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;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;word&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;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;children&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;'a'&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;children&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;'a'&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="n"&gt;TrieNode&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;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;children&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;'a'&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;isEndOfWord&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="p"&gt;}&lt;/span&gt;

    &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;search&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;string&lt;/span&gt; &lt;span class="n"&gt;word&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;TrieNode&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;root&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;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;word&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;node&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;children&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;'a'&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;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;children&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;'a'&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;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;isEndOfWord&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;p&gt;&lt;strong&gt;13. Greedy Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Make the most optimal choice at each step to ensure the best overall solution.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Solve optimization problems.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Find the minimum number of coins required to make a specific amount.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;minCoins&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;coins&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;amount&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;coins&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;rbegin&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;coins&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;rend&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="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;coin&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;coins&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;amount&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;break&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="n"&gt;amount&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;coin&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;amount&lt;/span&gt; &lt;span class="o"&gt;%=&lt;/span&gt; &lt;span class="n"&gt;coin&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;amount&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;count&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;p&gt;&lt;strong&gt;14. Knapsack (Dynamic Programming) Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Solve problems involving choices using dynamic programming (DP).&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Maximize value within weight constraints.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Solve the 0/1 Knapsack problem.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;knapsack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;weights&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;values&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="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="n"&gt;weights&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;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;dp&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&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;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&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;1&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;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="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="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;w&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;w&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&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;w&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="n"&gt;weights&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;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;w&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;dp&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;w&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&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dp&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="n"&gt;w&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;dp&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="n"&gt;w&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;weights&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="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="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="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;dp&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;w&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;dp&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="n"&gt;w&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;dp&lt;/span&gt;&lt;span class="p"&gt;[&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;capacity&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;15. Subsets Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Solve problems by generating all subsets of a given set.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Solve combination or subset problems.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Generate all subsets of a set of numbers.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;subsets&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;result&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;num&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="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="n"&gt;result&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;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;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;subset&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="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
            &lt;span class="n"&gt;subset&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;num&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;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;subset&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;result&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;16. Bit Manipulation Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Efficiently solve problems involving bitwise operations.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Solve problems using bitwise operators.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Find the single number in an array where every element appears twice except for one.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;singleNumber&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;nums&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="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;num&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="p"&gt;{&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;num&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;result&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;17. Union-Find Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Efficiently solve problems involving connected components or dynamic connectivity.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Solve problems involving finding connected components in graphs.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Find if there is a cycle in an undirected graph.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;UnionFind&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
&lt;span class="nl"&gt;public:&lt;/span&gt;
    &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;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;rank&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="n"&gt;UnionFind&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="o"&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;n&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;rank&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&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="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="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;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="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="nf"&gt;find&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;p&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;p&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;parent&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="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;find&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;p&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;parent&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="p"&gt;}&lt;/span&gt;

    &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;unionSets&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;p&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;q&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;rootP&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;find&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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;rootQ&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;find&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;rootP&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;rootQ&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="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rank&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rootP&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;rank&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rootQ&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;rootQ&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;rootP&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;rank&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rootP&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;rank&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rootQ&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;rootP&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;rootQ&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;parent&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rootQ&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;rootP&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="n"&gt;rank&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rootP&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="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="p"&gt;};&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;p&gt;&lt;strong&gt;18. Monotonic Stack Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Use a stack to maintain a sequence of elements that are either increasing or decreasing to solve certain problems.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Solve problems involving the next greater/smaller element.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Find the next greater element for each element in an array.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;nextGreaterElement&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;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;nums&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="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;stack&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;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;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;nums&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;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;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;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&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;nums&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="n"&gt;top&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;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="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;s&lt;/span&gt;&lt;span class="p"&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;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="n"&gt;s&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="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="n"&gt;push&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="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;result&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;19. Dynamic Programming Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Solve problems by breaking them down into overlapping subproblems and storing the results of subproblems to avoid redundant computations.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Solve problems involving optimal substructure and overlapping subproblems.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Solve the longest increasing subsequence problem.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;longestIncreasingSubsequence&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;nums&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;nums&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&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;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;dp&lt;/span&gt;&lt;span class="p"&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;size&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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;maxLength&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;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="n"&gt;nums&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;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;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="k"&gt;if&lt;/span&gt; &lt;span class="p"&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="o"&gt;&amp;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;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;dp&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;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dp&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;dp&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;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="n"&gt;maxLength&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;maxLength&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dp&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="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;maxLength&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;20. Segment Tree Pattern&lt;/strong&gt;&lt;br&gt;&lt;br&gt;
Efficiently solve range query problems by using a segment tree data structure.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Use Case:&lt;/strong&gt; Solve problems involving range queries and updates on an array.&lt;br&gt;&lt;br&gt;
&lt;strong&gt;Example:&lt;/strong&gt; Range sum query and update on an array.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;SegmentTree&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
&lt;span class="nl"&gt;private:&lt;/span&gt;
    &lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;tree&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="kt"&gt;void&lt;/span&gt; &lt;span class="n"&gt;buildTree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&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;start&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;end&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;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;start&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="n"&gt;tree&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="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;start&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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;mid&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="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="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;2&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="n"&gt;buildTree&lt;/span&gt;&lt;span class="p"&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;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;mid&lt;/span&gt;&lt;span class="p"&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;node&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;buildTree&lt;/span&gt;&lt;span class="p"&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;mid&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;end&lt;/span&gt;&lt;span class="p"&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;node&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;tree&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="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;tree&lt;/span&gt;&lt;span class="p"&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;node&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;tree&lt;/span&gt;&lt;span class="p"&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;node&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;updateTree&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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;end&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;idx&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="kt"&gt;int&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;start&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="n"&gt;tree&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="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="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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;mid&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="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="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;2&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;idx&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;mid&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;updateTree&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;mid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&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;node&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;else&lt;/span&gt; &lt;span class="nf"&gt;updateTree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;mid&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;end&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;idx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&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;node&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;tree&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="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;tree&lt;/span&gt;&lt;span class="p"&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;node&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;tree&lt;/span&gt;&lt;span class="p"&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;node&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;rangeSum&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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;end&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;l&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;r&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;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;start&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;r&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;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;l&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;if&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;gt;=&lt;/span&gt; &lt;span class="n"&gt;l&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;end&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;r&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;tree&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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;mid&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="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="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;2&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;rangeSum&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;mid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;l&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="p"&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;node&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;rangeSum&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;mid&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;end&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;l&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;r&lt;/span&gt;&lt;span class="p"&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;node&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="k"&gt;public&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;
    &lt;span class="n"&gt;SegmentTree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;nums&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;n&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;size&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
        &lt;span class="n"&gt;tree&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;resize&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt; &lt;span class="o"&gt;*&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;buildTree&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;nums&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;n&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="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;update&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;idx&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;updateTree&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;n&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;idx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;val&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="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;sumRange&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;l&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;r&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;rangeSum&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;n&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;l&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;r&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="p"&gt;};&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;These 20 problem-solving patterns are crucial for mastering DSA. Each pattern can be applied to a wide range of real-world problems, providing an efficient path to optimal solutions.&lt;/p&gt;

</description>
      <category>cpp</category>
      <category>programming</category>
      <category>learning</category>
      <category>career</category>
    </item>
    <item>
      <title>Digital Image Processing Notes</title>
      <dc:creator>Habibur Rahman Shihab</dc:creator>
      <pubDate>Mon, 25 Dec 2023 01:28:24 +0000</pubDate>
      <link>https://dev.to/hrshihab/digital-image-processing-notes-851</link>
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</description>
      <category>image</category>
      <category>core</category>
      <category>digitalimageprocessing</category>
      <category>tutorial</category>
    </item>
    <item>
      <title>Computer Network Notes</title>
      <dc:creator>Habibur Rahman Shihab</dc:creator>
      <pubDate>Mon, 25 Dec 2023 01:22:37 +0000</pubDate>
      <link>https://dev.to/hrshihab/computer-network-notes-2ihn</link>
      <guid>https://dev.to/hrshihab/computer-network-notes-2ihn</guid>
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      &lt;div class="c-embed__cover"&gt;
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          Notion – The all-in-one workspace for your notes, tasks, wikis, and databases.
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</description>
      <category>network</category>
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    </item>
    <item>
      <title>Authentication &amp; Authorization</title>
      <dc:creator>Habibur Rahman Shihab</dc:creator>
      <pubDate>Fri, 22 Dec 2023 06:00:15 +0000</pubDate>
      <link>https://dev.to/hrshihab/authentication-authorization-2j3f</link>
      <guid>https://dev.to/hrshihab/authentication-authorization-2j3f</guid>
      <description>&lt;p&gt;Simply meaning of : &lt;br&gt;
Authentication --&amp;gt; &lt;strong&gt;Who are you ?&lt;/strong&gt;&lt;br&gt;
Authorization --&amp;gt; &lt;strong&gt;What you are allowed for ?&lt;/strong&gt;&lt;/p&gt;

</description>
      <category>webdev</category>
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    </item>
    <item>
      <title>Stock Prediction in Neural Network</title>
      <dc:creator>Habibur Rahman Shihab</dc:creator>
      <pubDate>Thu, 21 Dec 2023 12:01:00 +0000</pubDate>
      <link>https://dev.to/hrshihab/stock-prediction-in-neural-network-3b44</link>
      <guid>https://dev.to/hrshihab/stock-prediction-in-neural-network-3b44</guid>
      <description>&lt;p&gt;Stock Prediction  হল একটি স্টকের ভবিষ্যতের দাম অনুমান করার একটি process । এটি  বিভিন্ন কারণ দ্বারা প্রভাবিত হতে পারে , যেমন অর্থনৈতিক অবস্থা এবং বাজারের পরিস্থিতি এবং কোম্পানির আর্থিক তথ্য।&lt;/p&gt;

&lt;p&gt;Stock Prediction এ নিউরাল নেটওয়ার্কগুলির ইনপুট: &lt;br&gt;
স্টকের অতীতের দাম&lt;br&gt;
স্টকের ভলিউম&lt;br&gt;
স্টকের  দামের পরিবর্তনের পরিমাণ &lt;/p&gt;

&lt;p&gt;স্টকের আর্থিক বিবরণ (কোম্পানির আর্থিক অবস্থা)&lt;br&gt;
অর্থনীতির সামগ্রিক অবস্থা &lt;/p&gt;

&lt;p&gt;Stock Prediction এ  নিউরাল নেটওয়ার্কগুলির আউটপুট :&lt;/p&gt;

&lt;p&gt;ভবিষ্যতে স্টকের নির্দিষ্ট  দাম&lt;br&gt;
ভবিষ্যতে স্টকের দামের সম্ভাব্য পরিসর&lt;/p&gt;

&lt;p&gt;Neural networks টাইম সিরিজ ডেটা থেকে জটিল প্যাটার্ন শিখতে পারে, যা স্টকের দামের ভবিষ্যতের prediction দেওয়ার জন্য ব্যবহার করা হয় ।&lt;br&gt;
( টাইম সিরিজ ডেটা  হল এমন ডেটা যা সময়ের সাথে সাথে পরিবর্তিত হয়)&lt;br&gt;
এটি  স্টকের দাম অতীতে কীভাবে পরিবর্তিত হচ্ছিল তা বুঝতে পারে ।ডেটার পরিবর্তনগুলিতে খাপ খাইয়ে নিতে পারে। স্টক মার্কেট একটি  চলমান পরিবেশ, এবং নিউরাল নেটওয়ার্কগুলি এই পরিবর্তনগুলিতে মানিয়ে  নিতে সক্ষম।&lt;/p&gt;

&lt;p&gt;নিউরাল নেটওয়ার্কগুলি Stock Prediction এর  জন্য একটি টুল , তবে  ভবিষ্যতের দামকে নিখুঁতভাবে predict করতে পারে না  ।&lt;/p&gt;

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