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      <title>Debugging Java ClassNotFoundException: A Beginner's Guide to Finding Missing Dependencies</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Sun, 16 Nov 2025 01:42:04 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/debugging-java-classnotfoundexception-a-beginners-guide-to-finding-missing-dependencies-1i9p</link>
      <guid>https://dev.to/itzsrikanth/debugging-java-classnotfoundexception-a-beginners-guide-to-finding-missing-dependencies-1i9p</guid>
      <description>&lt;h2&gt;
  
  
  Introduction
&lt;/h2&gt;

&lt;p&gt;If you've ever encountered a &lt;code&gt;ClassNotFoundException&lt;/code&gt; or &lt;code&gt;NoClassDefFoundError&lt;/code&gt; in Java, you know how frustrating it can be. Your code compiled fine, but at runtime, Java can't find a class it needs. This guide will teach you a systematic approach to debugging these issues, using a real-world Apache Flink example.&lt;/p&gt;

&lt;p&gt;In this tutorial, we'll walk through diagnosing and fixing a missing Hadoop dependency in a Flink application. More importantly, you'll learn a repeatable framework you can apply to any Java dependency issue.&lt;/p&gt;




&lt;h2&gt;
  
  
  Table of Contents
&lt;/h2&gt;

&lt;ul&gt;
&lt;li&gt;The Problem: Understanding the Error&lt;/li&gt;
&lt;li&gt;The Debugging Process&lt;/li&gt;
&lt;li&gt;Common Java Dependency Errors&lt;/li&gt;
&lt;li&gt;Step-by-Step Framework&lt;/li&gt;
&lt;li&gt;Practical Tools and Commands&lt;/li&gt;
&lt;li&gt;Advanced Tips&lt;/li&gt;
&lt;li&gt;Practice Exercise&lt;/li&gt;
&lt;li&gt;Resources&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  The Problem: Understanding the Error
&lt;/h2&gt;

&lt;p&gt;Let's start with the error message we encountered:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Caused by: java.lang.NoClassDefFoundError: org/apache/hadoop/conf/Configurable
    at java.base/java.lang.ClassLoader.defineClass1(Native Method)
    at java.base/java.lang.ClassLoader.defineClass(ClassLoader.java:1017)
    ...
Caused by: java.lang.ClassNotFoundException: org.apache.hadoop.conf.Configurable
    at java.base/jdk.internal.loader.BuiltinClassLoader.loadClass(BuiltinClassLoader.java:581)
    at java.base/java.lang.ClassLoader.loadClass(ClassLoader.java:522)
    ...
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;At first glance, this looks intimidating. But let's break it down systematically.&lt;/p&gt;




&lt;h2&gt;
  
  
  The Debugging Process
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Step 1: Read the Stack Trace Bottom-Up
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Key Principle:&lt;/strong&gt; Always start with the deepest "Caused by" clause. This is your root cause.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Main Exception: ProgramInvocationException
    ↓
Caused by: TableException
    ↓
Caused by: ServiceConfigurationError
    ↓
Caused by: NoClassDefFoundError         ← Near root cause
    ↓
Caused by: ClassNotFoundException       ← ROOT CAUSE! Start here!
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;In our case, the root cause is:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight java"&gt;&lt;code&gt;&lt;span class="nl"&gt;ClassNotFoundException:&lt;/span&gt; &lt;span class="n"&gt;org&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;apache&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;hadoop&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;conf&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;Configurable&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;What this tells us:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Java can't find the class &lt;code&gt;Configurable&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;It's in package &lt;code&gt;org.apache.hadoop.conf&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;This is a Hadoop class&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Step 2: Identify the Library
&lt;/h3&gt;

&lt;p&gt;From the fully qualified class name, you can identify which library it belongs to:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;org.apache.hadoop.conf.Configurable
└──────┬─────┘ └──┬──┘ └────┬────┘
   Vendor    Module  Class
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;Common package patterns:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;org.apache.flink.*         → Apache Flink
org.apache.hadoop.*        → Apache Hadoop  
org.apache.kafka.*         → Apache Kafka
com.fasterxml.jackson.*    → Jackson JSON library
org.springframework.*      → Spring Framework
com.google.gson.*          → Google Gson
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Step 3: Understand the Context
&lt;/h3&gt;

&lt;p&gt;Look at where the error occurred in your stack trace:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight java"&gt;&lt;code&gt;&lt;span class="n"&gt;at&lt;/span&gt; &lt;span class="n"&gt;com&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;example&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;MyTableFactory&lt;/span&gt;&lt;span class="o"&gt;.&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;init&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;(&lt;/span&gt;&lt;span class="nc"&gt;MyTableFactory&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;java&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&lt;span class="mi"&gt;127&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This tells us:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;The &lt;code&gt;MyTableFactory&lt;/code&gt; class is being initialized&lt;/li&gt;
&lt;li&gt;It requires Hadoop classes to work&lt;/li&gt;
&lt;li&gt;The Hadoop library is missing from the classpath&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Step 4: Search for the JAR
&lt;/h3&gt;

&lt;p&gt;Now we need to find where the missing class should be. Let's search systematically:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Search in your application directory&lt;/span&gt;
find &lt;span class="nb"&gt;.&lt;/span&gt; &lt;span class="nt"&gt;-name&lt;/span&gt; &lt;span class="s2"&gt;"*.jar"&lt;/span&gt; &lt;span class="nt"&gt;-exec&lt;/span&gt; &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="nt"&gt;-l&lt;/span&gt; &lt;span class="s2"&gt;"org/apache/hadoop"&lt;/span&gt; &lt;span class="o"&gt;{}&lt;/span&gt; &lt;span class="se"&gt;\;&lt;/span&gt;

&lt;span class="c"&gt;# For Apache Flink specifically, check both lib and opt directories&lt;/span&gt;
&lt;span class="nb"&gt;ls &lt;/span&gt;build/flink/lib/ | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="nt"&gt;-i&lt;/span&gt; hadoop
&lt;span class="nb"&gt;ls &lt;/span&gt;build/flink/opt/ | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="nt"&gt;-i&lt;/span&gt; hadoop
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;Why check both &lt;code&gt;lib/&lt;/code&gt; and &lt;code&gt;opt/&lt;/code&gt;?&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;lib/&lt;/code&gt; → JARs loaded automatically by the framework&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;opt/&lt;/code&gt; → Optional JARs that must be explicitly enabled&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;In our case, we found:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="nv"&gt;$ &lt;/span&gt;&lt;span class="nb"&gt;ls &lt;/span&gt;build/flink/opt/ | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="nt"&gt;-i&lt;/span&gt; hadoop

flink-s3-fs-hadoop-1.16.1.jar       ← Contains Hadoop classes!
flink-azure-fs-hadoop-1.16.1.jar
flink-gs-fs-hadoop-1.16.1.jar
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Step 5: Verify the JAR Contains the Missing Class
&lt;/h3&gt;

&lt;p&gt;Before proceeding, let's confirm this JAR actually contains the class we need:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Method 1: Using unzip&lt;/span&gt;
unzip &lt;span class="nt"&gt;-l&lt;/span&gt; flink-s3-fs-hadoop-1.16.1.jar | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="s2"&gt;"org/apache/hadoop/conf/Configurable"&lt;/span&gt;

&lt;span class="c"&gt;# Method 2: Using jar command  &lt;/span&gt;
jar &lt;span class="nt"&gt;-tf&lt;/span&gt; flink-s3-fs-hadoop-1.16.1.jar | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="s2"&gt;"Configurable"&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;Output:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;717  2025-09-27 03:45   org/apache/hadoop/conf/Configurable.class  ✓ Found it!
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Step 6: Fix the Issue
&lt;/h3&gt;

&lt;p&gt;Now that we've identified the problem and the solution, we can fix it:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Copy the JAR from opt/ to lib/ so it's loaded automatically&lt;/span&gt;
&lt;span class="nb"&gt;cp &lt;/span&gt;build/flink/opt/flink-s3-fs-hadoop-1.16.1.jar build/flink/lib/
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;Alternative solutions depending on your setup:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Add the JAR to your application's classpath&lt;/li&gt;
&lt;li&gt;Include it as a runtime dependency in Maven/Gradle&lt;/li&gt;
&lt;li&gt;Set the &lt;code&gt;CLASSPATH&lt;/code&gt; environment variable&lt;/li&gt;
&lt;li&gt;Use the &lt;code&gt;-cp&lt;/code&gt; flag when running Java&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  Common Java Dependency Errors
&lt;/h2&gt;

&lt;p&gt;Understanding these common errors will help you debug faster:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Error&lt;/th&gt;
&lt;th&gt;Meaning&lt;/th&gt;
&lt;th&gt;Common Causes&lt;/th&gt;
&lt;th&gt;Solution&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;ClassNotFoundException&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Java can't find the &lt;code&gt;.class&lt;/code&gt; file at runtime&lt;/td&gt;
&lt;td&gt;Missing JAR in classpath&lt;/td&gt;
&lt;td&gt;Add the JAR containing the class&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;NoClassDefFoundError&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Class was available at compile time but missing at runtime&lt;/td&gt;
&lt;td&gt;Missing dependency JAR, or initialization failure&lt;/td&gt;
&lt;td&gt;Check runtime classpath; verify static initializers&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;NoSuchMethodError&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Method exists but with different signature&lt;/td&gt;
&lt;td&gt;Version conflict between JARs&lt;/td&gt;
&lt;td&gt;Check for duplicate dependencies with different versions&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;LinkageError&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Class loaded by incompatible classloaders&lt;/td&gt;
&lt;td&gt;Duplicate JARs in classpath&lt;/td&gt;
&lt;td&gt;Remove duplicate JARs; use dependency management&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;&lt;code&gt;IncompatibleClassChangeError&lt;/code&gt;&lt;/td&gt;
&lt;td&gt;Class structure changed between compile and runtime&lt;/td&gt;
&lt;td&gt;Mismatched library versions&lt;/td&gt;
&lt;td&gt;Ensure compile and runtime versions match&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h2&gt;
  
  
  Step-by-Step Framework
&lt;/h2&gt;

&lt;p&gt;Here's a repeatable process for debugging any &lt;code&gt;ClassNotFoundException&lt;/code&gt;:&lt;/p&gt;

&lt;h3&gt;
  
  
  1. &lt;strong&gt;Identify the Missing Class&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;ClassNotFoundException: com.example.MyClass
                        └──────┬──────┘
                           Package name
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Extract:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Package:&lt;/strong&gt; &lt;code&gt;com.example&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Class:&lt;/strong&gt; &lt;code&gt;MyClass&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Likely library:&lt;/strong&gt; Based on package naming convention&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  2. &lt;strong&gt;Search Your Dependencies&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;For Maven projects:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# View all dependencies&lt;/span&gt;
mvn dependency:tree

&lt;span class="c"&gt;# Search for specific dependency&lt;/span&gt;
mvn dependency:tree | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="nt"&gt;-i&lt;/span&gt; &lt;span class="s2"&gt;"hadoop"&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;For Gradle projects:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# View all dependencies&lt;/span&gt;
./gradlew dependencies

&lt;span class="c"&gt;# View specific configuration&lt;/span&gt;
./gradlew dependencies &lt;span class="nt"&gt;--configuration&lt;/span&gt; runtimeClasspath
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  3. &lt;strong&gt;Check JAR Contents&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Quick check if a JAR contains a class:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Using jar command (shows all files)&lt;/span&gt;
jar &lt;span class="nt"&gt;-tf&lt;/span&gt; myapp.jar | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="s2"&gt;"MyClass"&lt;/span&gt;

&lt;span class="c"&gt;# Using unzip (more detailed)&lt;/span&gt;
unzip &lt;span class="nt"&gt;-l&lt;/span&gt; myapp.jar | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="s2"&gt;"com/example/MyClass"&lt;/span&gt;

&lt;span class="c"&gt;# Using zipgrep (searches file contents)&lt;/span&gt;
zipgrep &lt;span class="s2"&gt;"MyClass"&lt;/span&gt; myapp.jar
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  4. &lt;strong&gt;Verify Runtime Classpath&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Add temporary debugging code:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight java"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nn"&gt;java.net.URL&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nn"&gt;java.net.URLClassLoader&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;

&lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;ClasspathDebugger&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;public&lt;/span&gt; &lt;span class="kd"&gt;static&lt;/span&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;String&lt;/span&gt;&lt;span class="o"&gt;[]&lt;/span&gt; &lt;span class="n"&gt;args&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="nc"&gt;ClassLoader&lt;/span&gt; &lt;span class="n"&gt;cl&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;ClassLoader&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;getSystemClassLoader&lt;/span&gt;&lt;span class="o"&gt;();&lt;/span&gt;
        &lt;span class="no"&gt;URL&lt;/span&gt;&lt;span class="o"&gt;[]&lt;/span&gt; &lt;span class="n"&gt;urls&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;((&lt;/span&gt;&lt;span class="nc"&gt;URLClassLoader&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt;&lt;span class="n"&gt;cl&lt;/span&gt;&lt;span class="o"&gt;).&lt;/span&gt;&lt;span class="na"&gt;getURLs&lt;/span&gt;&lt;span class="o"&gt;();&lt;/span&gt;

        &lt;span class="nc"&gt;System&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;out&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;println&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Current Classpath:"&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;for&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="no"&gt;URL&lt;/span&gt; &lt;span class="nl"&gt;url:&lt;/span&gt; &lt;span class="n"&gt;urls&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="nc"&gt;System&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;out&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;println&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"  "&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;url&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;getFile&lt;/span&gt;&lt;span class="o"&gt;());&lt;/span&gt;
        &lt;span class="o"&gt;}&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;Or use JVM flags:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Shows all classes being loaded and their source&lt;/span&gt;
java &lt;span class="nt"&gt;-verbose&lt;/span&gt;:class &lt;span class="nt"&gt;-jar&lt;/span&gt; myapp.jar

&lt;span class="c"&gt;# Shows classpath being used&lt;/span&gt;
java &lt;span class="nt"&gt;-XX&lt;/span&gt;:+TraceClassPaths &lt;span class="nt"&gt;-jar&lt;/span&gt; myapp.jar
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  5. &lt;strong&gt;Compare Compile vs Runtime Dependencies&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;This is a common source of issues:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight gradle"&gt;&lt;code&gt;&lt;span class="k"&gt;dependencies&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
    &lt;span class="c1"&gt;// Compile-time only (not included in runtime)&lt;/span&gt;
    &lt;span class="n"&gt;compileOnly&lt;/span&gt; &lt;span class="s1"&gt;'org.apache.hadoop:hadoop-common:3.3.0'&lt;/span&gt;

    &lt;span class="c1"&gt;// Runtime dependency (included when running)&lt;/span&gt;
    &lt;span class="n"&gt;runtimeOnly&lt;/span&gt; &lt;span class="s1"&gt;'org.apache.hadoop:hadoop-common:3.3.0'&lt;/span&gt;

    &lt;span class="c1"&gt;// Both compile and runtime (recommended)&lt;/span&gt;
    &lt;span class="n"&gt;implementation&lt;/span&gt; &lt;span class="s1"&gt;'org.apache.hadoop:hadoop-common:3.3.0'&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Practical Tools and Commands
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Tool 1: Finding Classes in JARs
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Script to search all JARs for a class:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;#!/bin/bash&lt;/span&gt;
&lt;span class="c"&gt;# find-class.sh - Search for a class in all JARs&lt;/span&gt;

&lt;span class="nv"&gt;CLASS_NAME&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="nv"&gt;$1&lt;/span&gt;
&lt;span class="nv"&gt;SEARCH_DIR&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="k"&gt;${&lt;/span&gt;&lt;span class="nv"&gt;2&lt;/span&gt;&lt;span class="k"&gt;:-&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;}&lt;/span&gt;

&lt;span class="nb"&gt;echo&lt;/span&gt; &lt;span class="s2"&gt;"Searching for &lt;/span&gt;&lt;span class="nv"&gt;$CLASS_NAME&lt;/span&gt;&lt;span class="s2"&gt; in &lt;/span&gt;&lt;span class="nv"&gt;$SEARCH_DIR&lt;/span&gt;&lt;span class="s2"&gt;..."&lt;/span&gt;

find &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$SEARCH_DIR&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt; &lt;span class="nt"&gt;-name&lt;/span&gt; &lt;span class="s2"&gt;"*.jar"&lt;/span&gt; | &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="nb"&gt;read &lt;/span&gt;jar&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="k"&gt;do
    if &lt;/span&gt;jar &lt;span class="nt"&gt;-tf&lt;/span&gt; &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$jar&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt; | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="nt"&gt;-q&lt;/span&gt; &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$CLASS_NAME&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="k"&gt;then
        &lt;/span&gt;&lt;span class="nb"&gt;echo&lt;/span&gt; &lt;span class="s2"&gt;"Found in: &lt;/span&gt;&lt;span class="nv"&gt;$jar&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;
    &lt;span class="k"&gt;fi
done&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;Usage:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="nb"&gt;chmod&lt;/span&gt; +x find-class.sh
./find-class.sh &lt;span class="s2"&gt;"org/apache/hadoop/conf/Configurable"&lt;/span&gt; ./lib
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Tool 2: Analyze JAR Dependencies
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Using &lt;code&gt;jdeps&lt;/code&gt; (Java Dependency Analysis Tool):&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Analyze what a JAR depends on&lt;/span&gt;
jdeps myapp.jar

&lt;span class="c"&gt;# Show missing dependencies&lt;/span&gt;
jdeps &lt;span class="nt"&gt;-s&lt;/span&gt; myapp.jar

&lt;span class="c"&gt;# Generate dot file for visualization&lt;/span&gt;
jdeps &lt;span class="nt"&gt;-dotoutput&lt;/span&gt; &lt;span class="nb"&gt;.&lt;/span&gt; myapp.jar
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Tool 3: Maven Helper Commands
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Show dependency tree with conflicts&lt;/span&gt;
mvn dependency:tree &lt;span class="nt"&gt;-Dverbose&lt;/span&gt;

&lt;span class="c"&gt;# Show effective POM (resolved dependencies)&lt;/span&gt;
mvn &lt;span class="nb"&gt;help&lt;/span&gt;:effective-pom

&lt;span class="c"&gt;# Analyze dependencies&lt;/span&gt;
mvn dependency:analyze

&lt;span class="c"&gt;# Copy all dependencies to a directory&lt;/span&gt;
mvn dependency:copy-dependencies &lt;span class="nt"&gt;-DoutputDirectory&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;./lib
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Tool 4: Gradle Helper Commands
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Show all dependencies&lt;/span&gt;
./gradlew dependencies

&lt;span class="c"&gt;# Show dependency insight (why a dependency is included)&lt;/span&gt;
./gradlew dependencyInsight &lt;span class="nt"&gt;--dependency&lt;/span&gt; hadoop-common

&lt;span class="c"&gt;# Show build scan for web-based analysis&lt;/span&gt;
./gradlew build &lt;span class="nt"&gt;--scan&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Advanced Tips
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Tip 1: Use Smart Search Queries
&lt;/h3&gt;

&lt;p&gt;When Googling errors, be specific:&lt;/p&gt;

&lt;p&gt;❌ &lt;strong&gt;Bad:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

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

&lt;/div&gt;



&lt;p&gt;✅ &lt;strong&gt;Good:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;"NoClassDefFoundError org.apache.hadoop.conf.Configurable"
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;✅ &lt;strong&gt;Better:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;"NoClassDefFoundError hadoop Configurable flink"
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;✅ &lt;strong&gt;Best:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;"apache flink hadoop-common missing dependency"
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Tip 2: Check for Version Conflicts
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Scenario:&lt;/strong&gt; You have two versions of the same library:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;lib/
  ├── hadoop-common-2.7.3.jar
  └── hadoop-common-3.3.0.jar
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;How to detect:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Maven&lt;/span&gt;
mvn dependency:tree | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="nt"&gt;-A&lt;/span&gt; 5 &lt;span class="s2"&gt;"conflicts"&lt;/span&gt;

&lt;span class="c"&gt;# Gradle&lt;/span&gt;
./gradlew dependencies | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="s2"&gt;"(*)"&lt;/span&gt;  &lt;span class="c"&gt;# (*) indicates version conflict&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;How to fix in Gradle:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight gradle"&gt;&lt;code&gt;&lt;span class="n"&gt;configurations&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;all&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;resolutionStrategy&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="c1"&gt;// Force a specific version&lt;/span&gt;
        &lt;span class="n"&gt;force&lt;/span&gt; &lt;span class="s1"&gt;'org.apache.hadoop:hadoop-common:3.3.0'&lt;/span&gt;

        &lt;span class="c1"&gt;// Or fail on version conflict&lt;/span&gt;
        &lt;span class="n"&gt;failOnVersionConflict&lt;/span&gt;&lt;span class="o"&gt;()&lt;/span&gt;
    &lt;span class="o"&gt;}&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Tip 3: Understand Dependency Scopes
&lt;/h3&gt;

&lt;p&gt;Different scopes affect when dependencies are available:&lt;/p&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Scope&lt;/th&gt;
&lt;th&gt;Compile Time&lt;/th&gt;
&lt;th&gt;Runtime&lt;/th&gt;
&lt;th&gt;Example Use Case&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;code&gt;compile&lt;/code&gt; (Maven) / &lt;code&gt;implementation&lt;/code&gt; (Gradle)&lt;/td&gt;
&lt;td&gt;✓&lt;/td&gt;
&lt;td&gt;✓&lt;/td&gt;
&lt;td&gt;Your main dependencies&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;code&gt;provided&lt;/code&gt; (Maven) / &lt;code&gt;compileOnly&lt;/code&gt; (Gradle)&lt;/td&gt;
&lt;td&gt;✓&lt;/td&gt;
&lt;td&gt;✗&lt;/td&gt;
&lt;td&gt;APIs provided by container&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;code&gt;runtime&lt;/code&gt; (Maven) / &lt;code&gt;runtimeOnly&lt;/code&gt; (Gradle)&lt;/td&gt;
&lt;td&gt;✗&lt;/td&gt;
&lt;td&gt;✓&lt;/td&gt;
&lt;td&gt;Database drivers&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;
&lt;code&gt;test&lt;/code&gt; (Maven) / &lt;code&gt;testImplementation&lt;/code&gt; (Gradle)&lt;/td&gt;
&lt;td&gt;✓ (tests)&lt;/td&gt;
&lt;td&gt;✓ (tests)&lt;/td&gt;
&lt;td&gt;Testing libraries&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;

&lt;h3&gt;
  
  
  Tip 4: Create a Dependency Report
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Generate a comprehensive report:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Maven&lt;/span&gt;
mvn project-info-reports:dependencies
&lt;span class="c"&gt;# Opens in: target/site/dependencies.html&lt;/span&gt;

&lt;span class="c"&gt;# Gradle&lt;/span&gt;
./gradlew htmlDependencyReport
&lt;span class="c"&gt;# Opens in: build/reports/project/dependencies/index.html&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Tip 5: Use IDE Features
&lt;/h3&gt;

&lt;p&gt;Modern IDEs can help significantly:&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;IntelliJ IDEA:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Right-click on a class → "Go To" → "Declaration" (shows which JAR it's from)&lt;/li&gt;
&lt;li&gt;View → Tool Windows → "Maven/Gradle" (visual dependency tree)&lt;/li&gt;
&lt;li&gt;Ctrl+Shift+Alt+U on a class (shows full dependency diagram)&lt;/li&gt;
&lt;/ul&gt;

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

&lt;ul&gt;
&lt;li&gt;Ctrl+Shift+T (Open Type) shows JAR location&lt;/li&gt;
&lt;li&gt;Project → Properties → Java Build Path (view all JARs)&lt;/li&gt;
&lt;li&gt;Dependency Hierarchy plugin&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;VS Code:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Java Dependency Viewer extension&lt;/li&gt;
&lt;li&gt;Maven for Java extension&lt;/li&gt;
&lt;li&gt;Gradle for Java extension&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  Practice Exercise
&lt;/h2&gt;

&lt;p&gt;Here's an exercise to test your understanding. Given this error:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Exception in thread "main" java.lang.NoClassDefFoundError: com/fasterxml/jackson/databind/ObjectMapper
    at com.example.MyApp.main(MyApp.java:15)
Caused by: java.lang.ClassNotFoundException: com.fasterxml.jackson.databind.ObjectMapper
    at java.base/java.lang.ClassLoader.loadClass(ClassLoader.java:522)
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;Your task:&lt;/strong&gt;&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;What library is missing?&lt;/li&gt;
&lt;li&gt;What Maven/Gradle dependency would you add?&lt;/li&gt;
&lt;li&gt;How would you verify which version to use?&lt;/li&gt;
&lt;li&gt;What commands would you run to debug this?&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;Click to see solution&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;1. Identify the library:&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Package: &lt;code&gt;com.fasterxml.jackson.databind&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;Library: Jackson Databind (JSON processing library)&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;2. Add dependency:&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Maven:&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight xml"&gt;&lt;code&gt;
    com.fasterxml.jackson.core
    jackson-databind
    2.15.2

&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;
&lt;p&gt;Gradle:&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight gradle"&gt;&lt;code&gt;&lt;span class="n"&gt;implementation&lt;/span&gt; &lt;span class="s1"&gt;'com.fasterxml.jackson.core:jackson-databind:2.15.2'&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;
&lt;p&gt;&lt;strong&gt;3. Verify version:&lt;/strong&gt;&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Check what other libraries use&lt;/span&gt;
mvn dependency:tree | &lt;span class="nb"&gt;grep &lt;/span&gt;jackson

&lt;span class="c"&gt;# Check Maven Central for latest&lt;/span&gt;
&lt;span class="c"&gt;# Visit: https://mvnrepository.com/artifact/com.fasterxml.jackson.core/jackson-databind&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;
&lt;p&gt;&lt;strong&gt;4. Debug commands:&lt;/strong&gt;&lt;/p&gt;
&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Search for existing Jackson JARs&lt;/span&gt;
find &lt;span class="nb"&gt;.&lt;/span&gt; &lt;span class="nt"&gt;-name&lt;/span&gt; &lt;span class="s2"&gt;"*jackson*.jar"&lt;/span&gt;

&lt;span class="c"&gt;# Check if class exists in a specific JAR&lt;/span&gt;
jar &lt;span class="nt"&gt;-tf&lt;/span&gt; jackson-databind-2.15.2.jar | &lt;span class="nb"&gt;grep &lt;/span&gt;ObjectMapper

&lt;span class="c"&gt;# View current dependencies&lt;/span&gt;
mvn dependency:tree
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  Common Pitfalls and Solutions
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Pitfall 1: "It Works on My Machine"
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Problem:&lt;/strong&gt; Application works locally but fails in production.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Cause:&lt;/strong&gt; Different classpaths or dependency versions.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Solution:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Package dependencies with your application&lt;/span&gt;
mvn package &lt;span class="nt"&gt;-DincludeDependencies&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="nb"&gt;true&lt;/span&gt;

&lt;span class="c"&gt;# Or create a fat JAR&lt;/span&gt;
mvn clean package assembly:single
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Pitfall 2: Transitive Dependency Conflicts
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Problem:&lt;/strong&gt; Library A needs version 1.0, Library B needs version 2.0 of the same dependency.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Solution:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight gradle"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Gradle - Exclude transitive dependency&lt;/span&gt;
&lt;span class="n"&gt;implementation&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="s1"&gt;'com.example:library-a:1.0'&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;exclude&lt;/span&gt; &lt;span class="nl"&gt;group:&lt;/span&gt; &lt;span class="s1"&gt;'com.conflicting'&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="nl"&gt;module:&lt;/span&gt; &lt;span class="s1"&gt;'dependency'&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Then explicitly add the version you need&lt;/span&gt;
&lt;span class="n"&gt;implementation&lt;/span&gt; &lt;span class="s1"&gt;'com.conflicting:dependency:2.0'&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Pitfall 3: Shaded JARs
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;Problem:&lt;/strong&gt; Can't find a class even though the JAR is present.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Cause:&lt;/strong&gt; Some libraries "shade" (rename) their dependencies to avoid conflicts.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Solution:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Check for shaded classes&lt;/span&gt;
jar &lt;span class="nt"&gt;-tf&lt;/span&gt; myapp.jar | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="s2"&gt;"shaded"&lt;/span&gt;

&lt;span class="c"&gt;# Look for relocated packages&lt;/span&gt;
jar &lt;span class="nt"&gt;-tf&lt;/span&gt; myapp.jar | &lt;span class="nb"&gt;grep&lt;/span&gt; &lt;span class="nt"&gt;-E&lt;/span&gt; &lt;span class="s2"&gt;"shadow|shaded|relocated"&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Checklist for Debugging ClassNotFoundException
&lt;/h2&gt;

&lt;p&gt;Use this checklist whenever you encounter a &lt;code&gt;ClassNotFoundException&lt;/code&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;[ ] Identify the fully qualified class name from the error&lt;/li&gt;
&lt;li&gt;[ ] Determine which library the class belongs to (from package name)&lt;/li&gt;
&lt;li&gt;[ ] Check if the JAR is in your dependencies (&lt;code&gt;mvn dependency:tree&lt;/code&gt; or &lt;code&gt;./gradlew dependencies&lt;/code&gt;)&lt;/li&gt;
&lt;li&gt;[ ] Verify the JAR is in the runtime classpath (not just compile-time)&lt;/li&gt;
&lt;li&gt;[ ] Check for version conflicts (&lt;code&gt;grep "(*)"&lt;/code&gt; in Gradle output)&lt;/li&gt;
&lt;li&gt;[ ] Ensure the class exists in the JAR version you have (&lt;code&gt;jar -tf&lt;/code&gt;)&lt;/li&gt;
&lt;li&gt;[ ] Look for shaded or relocated classes&lt;/li&gt;
&lt;li&gt;[ ] Check if it's a provided/compileOnly dependency that needs to be changed&lt;/li&gt;
&lt;li&gt;[ ] Verify no exclusions are removing the dependency&lt;/li&gt;
&lt;li&gt;[ ] Test with a clean build (&lt;code&gt;mvn clean install&lt;/code&gt; or &lt;code&gt;./gradlew clean build&lt;/code&gt;)&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  Resources
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Official Documentation
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;&lt;a href="https://docs.oracle.com/javase/8/docs/technotes/tools/windows/classpath.html" rel="noopener noreferrer"&gt;Java Classpath Documentation&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://maven.apache.org/guides/introduction/introduction-to-dependency-mechanism.html" rel="noopener noreferrer"&gt;Maven Dependency Mechanism&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://docs.gradle.org/current/userguide/dependency_management.html" rel="noopener noreferrer"&gt;Gradle Dependency Management&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Tools
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;a href="https://mvnrepository.com/" rel="noopener noreferrer"&gt;Maven Repository&lt;/a&gt; - Find dependencies and versions&lt;/li&gt;
&lt;li&gt;
&lt;a href="https://jitpack.io/" rel="noopener noreferrer"&gt;JitPack&lt;/a&gt; - Build GitHub projects as Maven artifacts&lt;/li&gt;
&lt;li&gt;
&lt;a href="https://docs.oracle.com/javase/8/docs/technotes/tools/unix/jdeps.html" rel="noopener noreferrer"&gt;jdeps&lt;/a&gt; - Java dependency analysis tool&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Learning Resources
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;&lt;a href="https://www.baeldung.com/java-classnotfoundexception-and-noclassdeffounderror" rel="noopener noreferrer"&gt;Baeldung - Java ClassNotFoundException vs NoClassDefFoundError&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://maven.apache.org/guides/getting-started/maven-in-five-minutes.html" rel="noopener noreferrer"&gt;Maven in 5 Minutes&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://docs.gradle.org/current/userguide/getting_started.html" rel="noopener noreferrer"&gt;Gradle Tutorial&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;




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

&lt;p&gt;Debugging &lt;code&gt;ClassNotFoundException&lt;/code&gt; errors doesn't have to be mysterious. By following a systematic approach:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Read&lt;/strong&gt; the stack trace bottom-up to find the root cause&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Identify&lt;/strong&gt; which library the missing class belongs to&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Search&lt;/strong&gt; for the JAR in your dependencies and filesystem&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Verify&lt;/strong&gt; the JAR contains the class you need&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Fix&lt;/strong&gt; by adding it to the correct classpath location&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;With practice, you'll be able to diagnose and fix these issues in minutes rather than hours. Remember: every dependency error is a puzzle with a logical solution. Keep calm, follow the process, and you'll find the answer.&lt;/p&gt;

&lt;p&gt;Happy debugging! 🐛🔍&lt;/p&gt;




&lt;h2&gt;
  
  
  About This Guide
&lt;/h2&gt;

&lt;p&gt;This guide was created to help Java beginners develop systematic debugging skills. If you found it helpful, please share it with others who might benefit. Feel free to adapt and expand upon these techniques in your own projects.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Questions or feedback?&lt;/strong&gt; The best way to learn is through practice. Try the exercise above, and experiment with the tools and commands in your own projects.&lt;/p&gt;

</description>
      <category>beginners</category>
      <category>java</category>
      <category>tutorial</category>
    </item>
    <item>
      <title>CheatSheet: Python for DSA</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Sat, 08 Nov 2025 10:36:35 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/cheatsheet-python-for-dsa-2g3f</link>
      <guid>https://dev.to/itzsrikanth/cheatsheet-python-for-dsa-2g3f</guid>
      <description>&lt;h1&gt;
  
  
  Python DSA Cheatsheet - Complete Reference
&lt;/h1&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;em&gt;Note: I took help of LLMs to arrange the structure and come up with few of the examples in the list below&lt;/em&gt;&lt;/p&gt;
&lt;/blockquote&gt;

&lt;h2&gt;
  
  
  Table of Contents
&lt;/h2&gt;

&lt;ol&gt;
&lt;li&gt;Numeric Operations&lt;/li&gt;
&lt;li&gt;List / Array Operations&lt;/li&gt;
&lt;li&gt;String Operations&lt;/li&gt;
&lt;li&gt;Dictionary / HashMap Operations&lt;/li&gt;
&lt;li&gt;Set Operations&lt;/li&gt;
&lt;li&gt;Heap / Priority Queue&lt;/li&gt;
&lt;li&gt;Deque Operations&lt;/li&gt;
&lt;li&gt;Collections Module&lt;/li&gt;
&lt;li&gt;Itertools&lt;/li&gt;
&lt;li&gt;Matrix Operations&lt;/li&gt;
&lt;li&gt;Bit Manipulation&lt;/li&gt;
&lt;li&gt;Binary Search&lt;/li&gt;
&lt;li&gt;Common Patterns&lt;/li&gt;
&lt;li&gt;Input/Output Tricks&lt;/li&gt;
&lt;/ol&gt;




&lt;h2&gt;
  
  
  Numeric Operations
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Setting min / max
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;math&lt;/span&gt;

&lt;span class="n"&gt;cost&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;float&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;inf&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Infinity
&lt;/span&gt;&lt;span class="n"&gt;cost&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="nf"&gt;float&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;inf&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c1"&gt;# Negative infinity
&lt;/span&gt;&lt;span class="n"&gt;cost&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;inf&lt;/span&gt;      &lt;span class="c1"&gt;# Alternative
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Division Types
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Floor division
&lt;/span&gt;&lt;span class="mi"&gt;7&lt;/span&gt; &lt;span class="o"&gt;//&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;  &lt;span class="c1"&gt;# Output: 3
&lt;/span&gt;
&lt;span class="c1"&gt;# Regular division (returns float)
&lt;/span&gt;&lt;span class="mi"&gt;7&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;   &lt;span class="c1"&gt;# Output: 3.5
&lt;/span&gt;
&lt;span class="c1"&gt;# Ceiling division
&lt;/span&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;math&lt;/span&gt;
&lt;span class="n"&gt;math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;ceil&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;7&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="c1"&gt;# Output: 4
&lt;/span&gt;
&lt;span class="c1"&gt;# Python's floor division with negative numbers
&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;7&lt;/span&gt; &lt;span class="o"&gt;//&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;   &lt;span class="c1"&gt;# Output: -4 (rounds down/toward negative infinity)
&lt;/span&gt;&lt;span class="nf"&gt;int&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;7&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="c1"&gt;# Output: -3 (truncates toward zero)
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Modulo Operations
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Positive modulo
&lt;/span&gt;&lt;span class="mi"&gt;7&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;   &lt;span class="c1"&gt;# Output: 1
&lt;/span&gt;
&lt;span class="c1"&gt;# Negative modulo (Python always returns positive result)
&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;7&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;  &lt;span class="c1"&gt;# Output: 2
&lt;/span&gt;
&lt;span class="c1"&gt;# To get true modulo
&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Power and Root
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Power
&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;  &lt;span class="c1"&gt;# Output: 1024
&lt;/span&gt;&lt;span class="nf"&gt;pow&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Output: 1024
&lt;/span&gt;
&lt;span class="c1"&gt;# Modular exponentiation (for large numbers)
&lt;/span&gt;&lt;span class="nf"&gt;pow&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1000&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Output: 24 (2^10 mod 1000)
&lt;/span&gt;
&lt;span class="c1"&gt;# Square root
&lt;/span&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;math&lt;/span&gt;
&lt;span class="n"&gt;math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;sqrt&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;16&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Output: 4.0
&lt;/span&gt;&lt;span class="mi"&gt;16&lt;/span&gt; &lt;span class="o"&gt;**&lt;/span&gt; &lt;span class="mf"&gt;0.5&lt;/span&gt;      &lt;span class="c1"&gt;# Output: 4.0
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  GCD and LCM
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;math&lt;/span&gt;

&lt;span class="c1"&gt;# GCD
&lt;/span&gt;&lt;span class="n"&gt;math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;gcd&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;12&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;18&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Output: 6
&lt;/span&gt;
&lt;span class="c1"&gt;# Multiple GCD
&lt;/span&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;functools&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nb"&gt;reduce&lt;/span&gt;
&lt;span class="nf"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;gcd&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;12&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;18&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;24&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;  &lt;span class="c1"&gt;# Output: 6
&lt;/span&gt;
&lt;span class="c1"&gt;# LCM
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;lcm&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;//&lt;/span&gt; &lt;span class="n"&gt;math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;gcd&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# Multiple LCM
&lt;/span&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;functools&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nb"&gt;reduce&lt;/span&gt;
&lt;span class="nf"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;lcm&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;12&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;18&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;24&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  List / Array Operations
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Initialization
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# 1D array with zeros
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="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="mi"&gt;5&lt;/span&gt;  &lt;span class="c1"&gt;# Output: [0, 0, 0, 0, 0]
&lt;/span&gt;
&lt;span class="c1"&gt;# 2D array with zeros (CORRECT way)
&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;_&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;

&lt;span class="c1"&gt;# WRONG way (all rows reference same list!)
# matrix = [[0] * cols] * rows  # DON'T USE THIS
&lt;/span&gt;
&lt;span class="c1"&gt;# Initialize with specific value
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nf"&gt;float&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;inf&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;

&lt;span class="c1"&gt;# List comprehension
&lt;/span&gt;&lt;span class="n"&gt;squares&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;  &lt;span class="c1"&gt;# Output: [0, 1, 4, 9, 16]
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Insertion
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="c1"&gt;# At the end - O(1)
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# [1, 2, 3, 4]
&lt;/span&gt;
&lt;span class="c1"&gt;# At specific index - O(n)
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# [1, 5, 2, 3, 4]
&lt;/span&gt;
&lt;span class="c1"&gt;# Extend with another list
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;extend&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;7&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;  &lt;span class="c1"&gt;# [1, 5, 2, 3, 4, 6, 7]
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;9&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;       &lt;span class="c1"&gt;# Alternative
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Removal
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="c1"&gt;# Pop at the end - O(1)
&lt;/span&gt;&lt;span class="n"&gt;last&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="nf"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;  &lt;span class="c1"&gt;# Returns 5, arr = [1, 2, 3, 4]
&lt;/span&gt;
&lt;span class="c1"&gt;# Pop at specific index - O(n)
&lt;/span&gt;&lt;span class="n"&gt;first&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="nf"&gt;pop&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="c1"&gt;# Returns 1, arr = [2, 3, 4]
&lt;/span&gt;
&lt;span class="c1"&gt;# Remove by value (first occurrence) - O(n)
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;remove&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# arr = [2, 4]
&lt;/span&gt;
&lt;span class="c1"&gt;# Clear all
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;clear&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;  &lt;span class="c1"&gt;# arr = []
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Slicing (IMPORTANT!)
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="c1"&gt;# Basic slicing [start:end:step]
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;      &lt;span class="c1"&gt;# [1, 2, 3] (end is exclusive)
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[:&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;       &lt;span class="c1"&gt;# [0, 1, 2] (from start)
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;:]&lt;/span&gt;       &lt;span class="c1"&gt;# [3, 4, 5] (to end)
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[:]&lt;/span&gt;        &lt;span class="c1"&gt;# [0, 1, 2, 3, 4, 5] (copy entire list)
&lt;/span&gt;
&lt;span class="c1"&gt;# Step
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[::&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;      &lt;span class="c1"&gt;# [0, 2, 4] (every 2nd element)
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;::&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;     &lt;span class="c1"&gt;# [1, 3, 5] (every 2nd starting from index 1)
&lt;/span&gt;
&lt;span class="c1"&gt;# Reverse
&lt;/span&gt;&lt;span class="n"&gt;arr&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="c1"&gt;# [5, 4, 3, 2, 1, 0]
&lt;/span&gt;&lt;span class="n"&gt;arr&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="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;   &lt;span class="c1"&gt;# Same as above
&lt;/span&gt;
&lt;span class="c1"&gt;# Negative indices
&lt;/span&gt;&lt;span class="n"&gt;arr&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="c1"&gt;# 5 (last element)
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;:]&lt;/span&gt;      &lt;span class="c1"&gt;# [3, 4, 5] (last 3 elements)
&lt;/span&gt;&lt;span class="n"&gt;arr&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="c1"&gt;# [0, 1, 2, 3] (all except last 2)
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Sorting
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;9&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="c1"&gt;# In-place sort - O(n log n)
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;  &lt;span class="c1"&gt;# arr is modified
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;reverse&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Descending order
&lt;/span&gt;
&lt;span class="c1"&gt;# Return new sorted list
&lt;/span&gt;&lt;span class="n"&gt;sorted_arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;sorted&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="c1"&gt;# arr is unchanged
&lt;/span&gt;
&lt;span class="c1"&gt;# Custom sorting with key
&lt;/span&gt;&lt;span class="n"&gt;students&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Alice&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;20&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Bob&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;18&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Charlie&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;22&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;
&lt;span class="n"&gt;sorted_students&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;sorted&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;students&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="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="c1"&gt;# Sort by age
&lt;/span&gt;
&lt;span class="c1"&gt;# Multi-level sorting
&lt;/span&gt;&lt;span class="n"&gt;envelopes&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;7&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;]]&lt;/span&gt;
&lt;span class="c1"&gt;# Sort by x[0] ASC, then x[1] DESC
&lt;/span&gt;&lt;span class="n"&gt;envelopes&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;x&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="c1"&gt;# Sort with custom comparator (use functools.cmp_to_key)
&lt;/span&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;functools&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;cmp_to_key&lt;/span&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;  &lt;span class="c1"&gt;# Ascending
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="nf"&gt;cmp_to_key&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Binary Search (bisect module)
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;bisect&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;bisect_left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bisect_right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;insort&lt;/span&gt;

&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;7&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="c1"&gt;# bisect_left: leftmost insertion point
&lt;/span&gt;&lt;span class="nf"&gt;bisect_left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;   &lt;span class="c1"&gt;# Output: 2 (index of first 4)
&lt;/span&gt;&lt;span class="nf"&gt;bisect_left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;   &lt;span class="c1"&gt;# Output: 2 (would insert before 4)
&lt;/span&gt;
&lt;span class="c1"&gt;# bisect_right (or bisect): rightmost insertion point
&lt;/span&gt;&lt;span class="nf"&gt;bisect_right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Output: 4 (after last 4)
&lt;/span&gt;
&lt;span class="c1"&gt;# Insert and maintain sorted order
&lt;/span&gt;&lt;span class="nf"&gt;insort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# arr = [1, 2, 3, 4, 4, 5, 7]
&lt;/span&gt;
&lt;span class="c1"&gt;# Check if element exists
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;exists&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;x&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="nf"&gt;bisect_left&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;x&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nf"&gt;len&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="ow"&gt;and&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;x&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  List Comprehension and Filtering
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Basic list comprehension
&lt;/span&gt;&lt;span class="n"&gt;squares&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;

&lt;span class="c1"&gt;# With condition
&lt;/span&gt;&lt;span class="n"&gt;evens&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="mi"&gt;2&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="c1"&gt;# Nested comprehension (flatten)
&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;]]&lt;/span&gt;
&lt;span class="n"&gt;flat&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;row&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;matrix&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;row&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;  &lt;span class="c1"&gt;# [1, 2, 3, 4, 5, 6]
&lt;/span&gt;
&lt;span class="c1"&gt;# Extract specific column from 2D list
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;c&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;]]&lt;/span&gt;
&lt;span class="n"&gt;second_col&lt;/span&gt; &lt;span class="o"&gt;=&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="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="n"&gt;row&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;  &lt;span class="c1"&gt;# [1, 2, 3]
&lt;/span&gt;
&lt;span class="c1"&gt;# Enumerate with comprehension
&lt;/span&gt;&lt;span class="n"&gt;indexed&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="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="k"&gt;for&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;val&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;enumerate&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Other Useful Operations
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;9&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="c1"&gt;# Min/Max
&lt;/span&gt;&lt;span class="nf"&gt;min&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="c1"&gt;# 1
&lt;/span&gt;&lt;span class="nf"&gt;max&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="c1"&gt;# 9
&lt;/span&gt;&lt;span class="nf"&gt;min&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;default&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="c1"&gt;# Returns 0 if arr is empty
&lt;/span&gt;
&lt;span class="c1"&gt;# Sum
&lt;/span&gt;&lt;span class="nf"&gt;sum&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="c1"&gt;# 31
&lt;/span&gt;
&lt;span class="c1"&gt;# Count occurrences
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;count&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="c1"&gt;# 2
&lt;/span&gt;
&lt;span class="c1"&gt;# Find index of element
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;index&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# 2 (first occurrence)
&lt;/span&gt;
&lt;span class="c1"&gt;# Check existence
&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;  &lt;span class="c1"&gt;# True
&lt;/span&gt;
&lt;span class="c1"&gt;# Reverse in-place
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;reverse&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

&lt;span class="c1"&gt;# Length
&lt;/span&gt;&lt;span class="nf"&gt;len&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="c1"&gt;# 8
&lt;/span&gt;
&lt;span class="c1"&gt;# All/Any
&lt;/span&gt;&lt;span class="nf"&gt;all&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="bp"&gt;False&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;  &lt;span class="c1"&gt;# False
&lt;/span&gt;&lt;span class="nf"&gt;any&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="bp"&gt;False&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="bp"&gt;False&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;  &lt;span class="c1"&gt;# True
&lt;/span&gt;
&lt;span class="c1"&gt;# Zip (combine multiple lists)
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;zip&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;c&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt;  &lt;span class="c1"&gt;# [(1, 'a'), (2, 'b'), (3, 'c')]
&lt;/span&gt;
&lt;span class="c1"&gt;# Unzip
&lt;/span&gt;&lt;span class="n"&gt;pairs&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;c&lt;/span&gt;&lt;span class="sh"&gt;'&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;chars&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;zip&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;pairs&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# nums = (1, 2, 3), chars = ('a', 'b', 'c')
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  String Operations
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Basic Operations
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;s&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;hello world&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;

&lt;span class="c1"&gt;# Length
&lt;/span&gt;&lt;span class="nf"&gt;len&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="c1"&gt;# 11
&lt;/span&gt;
&lt;span class="c1"&gt;# Access by index
&lt;/span&gt;&lt;span class="n"&gt;s&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="c1"&gt;# 'h'
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;   &lt;span class="c1"&gt;# 'd'
&lt;/span&gt;
&lt;span class="c1"&gt;# Slicing (same as list)
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;  &lt;span class="c1"&gt;# "hello"
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;[::&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="c1"&gt;# "dlrow olleh" (reverse)
&lt;/span&gt;
&lt;span class="c1"&gt;# Concatenation
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt; &lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;s2&lt;/span&gt;
&lt;span class="sh"&gt;""&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;join&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;s2&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;  &lt;span class="c1"&gt;# More efficient for multiple strings
&lt;/span&gt;
&lt;span class="c1"&gt;# Repeat
&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;abc&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;  &lt;span class="c1"&gt;# "abcabcabc"
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  String Methods
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;s&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Hello World&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;

&lt;span class="c1"&gt;# Case conversion
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;lower&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;      &lt;span class="c1"&gt;# "hello world"
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;upper&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;      &lt;span class="c1"&gt;# "HELLO WORLD"
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;title&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;      &lt;span class="c1"&gt;# "Hello World"
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;capitalize&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="c1"&gt;# "Hello world"
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;swapcase&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;   &lt;span class="c1"&gt;# "hELLO wORLD"
&lt;/span&gt;
&lt;span class="c1"&gt;# Check properties
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isalpha&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;    &lt;span class="c1"&gt;# False (has space)
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isdigit&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;    &lt;span class="c1"&gt;# False
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isalnum&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;    &lt;span class="c1"&gt;# False
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isspace&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;    &lt;span class="c1"&gt;# False
&lt;/span&gt;
&lt;span class="c1"&gt;# Strip whitespace
&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;  hello  &lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;strip&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;   &lt;span class="c1"&gt;# "hello"
&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;  hello  &lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;lstrip&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;  &lt;span class="c1"&gt;# "hello  "
&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;  hello  &lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;rstrip&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;  &lt;span class="c1"&gt;# "  hello"
&lt;/span&gt;
&lt;span class="c1"&gt;# Split and Join
&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;a,b,c&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;split&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;,&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;    &lt;span class="c1"&gt;# ['a', 'b', 'c']
&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;a b c&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;split&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;       &lt;span class="c1"&gt;# ['a', 'b', 'c'] (splits on any whitespace)
&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;,&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;join&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;  &lt;span class="c1"&gt;# "a,b"
&lt;/span&gt;
&lt;span class="c1"&gt;# Replace
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;replace&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;World&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Python&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# "Hello Python"
&lt;/span&gt;
&lt;span class="c1"&gt;# Find and Index
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;find&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;o&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;     &lt;span class="c1"&gt;# 4 (first occurrence, returns -1 if not found)
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;index&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;o&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;    &lt;span class="c1"&gt;# 4 (raises exception if not found)
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;rfind&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;o&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;    &lt;span class="c1"&gt;# 7 (last occurrence)
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;count&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;l&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;    &lt;span class="c1"&gt;# 3
&lt;/span&gt;
&lt;span class="c1"&gt;# Check prefix/suffix
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;startswith&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;Hello&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# True
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;endswith&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;World&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;    &lt;span class="c1"&gt;# True
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  String Building (Performance)
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# SLOW - string concatenation in loop
&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sh"&gt;""&lt;/span&gt;
&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;chars&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;c&lt;/span&gt;  &lt;span class="c1"&gt;# Creates new string each time
&lt;/span&gt;
&lt;span class="c1"&gt;# FAST - use list and join
&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sh"&gt;''&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;join&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;chars&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# For complex building
&lt;/span&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;io&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;StringIO&lt;/span&gt;
&lt;span class="n"&gt;builder&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;StringIO&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;write&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;hello&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;write&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt; world&lt;/span&gt;&lt;span class="sh"&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;builder&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getvalue&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;  &lt;span class="c1"&gt;# "hello world"
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Character Operations
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# ASCII conversion
&lt;/span&gt;&lt;span class="nf"&gt;ord&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;A&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;    &lt;span class="c1"&gt;# 65
&lt;/span&gt;&lt;span class="nf"&gt;chr&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;65&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;     &lt;span class="c1"&gt;# 'A'
&lt;/span&gt;
&lt;span class="c1"&gt;# Check if character
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;
&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isalpha&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;   &lt;span class="c1"&gt;# True
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isdigit&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;   &lt;span class="c1"&gt;# False
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;islower&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;   &lt;span class="c1"&gt;# True
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isupper&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;   &lt;span class="c1"&gt;# False
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Dictionary / HashMap Operations
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Initialization
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Empty dict
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{}&lt;/span&gt;
&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;dict&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

&lt;span class="c1"&gt;# With initial values
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;dict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&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;b&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;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;dict&lt;/span&gt;&lt;span class="p"&gt;([(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)])&lt;/span&gt;

&lt;span class="c1"&gt;# From keys with default value
&lt;/span&gt;&lt;span class="n"&gt;keys&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;c&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;dict&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;fromkeys&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;keys&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="c1"&gt;# {'a': 0, 'b': 0, 'c': 0}
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Access and Modification
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;# Access
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;           &lt;span class="c1"&gt;# 1 (raises KeyError if not exists)
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;       &lt;span class="c1"&gt;# 1 (returns None if not exists)
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;get&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;c&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;    &lt;span class="c1"&gt;# 0 (custom default)
&lt;/span&gt;
&lt;span class="c1"&gt;# Set
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;c&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;       &lt;span class="c1"&gt;# Add or update
&lt;/span&gt;
&lt;span class="c1"&gt;# Delete
&lt;/span&gt;&lt;span class="k"&gt;del&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;         &lt;span class="c1"&gt;# Remove and return value
&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;x&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="bp"&gt;None&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;   &lt;span class="c1"&gt;# Safe pop with default
&lt;/span&gt;
&lt;span class="c1"&gt;# Check existence
&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;         &lt;span class="c1"&gt;# True
&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt; &lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;     &lt;span class="c1"&gt;# False
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Iteration
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;c&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;# Keys
&lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;           &lt;span class="c1"&gt;# Iterate over keys
&lt;/span&gt;    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;keys&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;    &lt;span class="c1"&gt;# Explicit
&lt;/span&gt;    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# Values
&lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;values&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
    &lt;span class="nf"&gt;print&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="c1"&gt;# Key-value pairs
&lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;items&lt;/span&gt;&lt;span class="p"&gt;():&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Useful Operations
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Get all keys/values as list
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;keys&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;    &lt;span class="c1"&gt;# ['a', 'b', 'c']
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;values&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;  &lt;span class="c1"&gt;# [1, 2, 3]
&lt;/span&gt;
&lt;span class="c1"&gt;# Update dictionary
&lt;/span&gt;&lt;span class="n"&gt;d1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;d2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;c&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;d1&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;update&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;     &lt;span class="c1"&gt;# d1 = {'a': 1, 'b': 3, 'c': 4}
&lt;/span&gt;
&lt;span class="c1"&gt;# Merge dictionaries (Python 3.9+)
&lt;/span&gt;&lt;span class="n"&gt;d3&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;d1&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="n"&gt;d2&lt;/span&gt;

&lt;span class="c1"&gt;# Copy
&lt;/span&gt;&lt;span class="n"&gt;d_copy&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;copy&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;  &lt;span class="c1"&gt;# Shallow copy
&lt;/span&gt;
&lt;span class="c1"&gt;# Clear
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;clear&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

&lt;span class="c1"&gt;# Length
&lt;/span&gt;&lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# setdefault (get or set if not exists)
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;setdefault&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;d&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Returns 0 and sets d['d'] = 0 if not exists
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Sorting Dictionary
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;c&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;# Sort by key
&lt;/span&gt;&lt;span class="n"&gt;sorted_d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;dict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;sorted&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;items&lt;/span&gt;&lt;span class="p"&gt;()))&lt;/span&gt;

&lt;span class="c1"&gt;# Sort by value
&lt;/span&gt;&lt;span class="n"&gt;sorted_d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;dict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;sorted&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;items&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="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="c1"&gt;# Sort by value (descending)
&lt;/span&gt;&lt;span class="n"&gt;sorted_d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;dict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;sorted&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;items&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="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;reverse&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Set Operations
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Initialization
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Empty set (NOT {})
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;set&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

&lt;span class="c1"&gt;# With values
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;s&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;set&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Basic Operations
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;s&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;# Add
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;        &lt;span class="c1"&gt;# {1, 2, 3, 4}
&lt;/span&gt;
&lt;span class="c1"&gt;# Remove
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;remove&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;     &lt;span class="c1"&gt;# Raises KeyError if not exists
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;discard&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;    &lt;span class="c1"&gt;# No error if not exists
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;         &lt;span class="c1"&gt;# Remove and return arbitrary element
&lt;/span&gt;
&lt;span class="c1"&gt;# Check membership
&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;          &lt;span class="c1"&gt;# True
&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt; &lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;s&lt;/span&gt;      &lt;span class="c1"&gt;# True
&lt;/span&gt;
&lt;span class="c1"&gt;# Length
&lt;/span&gt;&lt;span class="nf"&gt;len&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="c1"&gt;# 3
&lt;/span&gt;
&lt;span class="c1"&gt;# Clear
&lt;/span&gt;&lt;span class="n"&gt;s&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;clear&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Set Operations
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="n"&gt;s1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="n"&gt;s2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;# Union
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="n"&gt;s2&lt;/span&gt;                &lt;span class="c1"&gt;# {1, 2, 3, 4, 5, 6}
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;union&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;           &lt;span class="c1"&gt;# Same
&lt;/span&gt;
&lt;span class="c1"&gt;# Intersection
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;s2&lt;/span&gt;                &lt;span class="c1"&gt;# {3, 4}
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;intersection&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;    &lt;span class="c1"&gt;# Same
&lt;/span&gt;
&lt;span class="c1"&gt;# Difference
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;s2&lt;/span&gt;                &lt;span class="c1"&gt;# {1, 2} (in s1 but not s2)
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;difference&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;      &lt;span class="c1"&gt;# Same
&lt;/span&gt;
&lt;span class="c1"&gt;# Symmetric difference (XOR)
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt; &lt;span class="o"&gt;^&lt;/span&gt; &lt;span class="n"&gt;s2&lt;/span&gt;                &lt;span class="c1"&gt;# {1, 2, 5, 6}
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;symmetric_difference&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Same
&lt;/span&gt;
&lt;span class="c1"&gt;# Subset/Superset
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;issubset&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;        &lt;span class="c1"&gt;# False
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;issuperset&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;      &lt;span class="c1"&gt;# False
&lt;/span&gt;&lt;span class="n"&gt;s1&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isdisjoint&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;s2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;      &lt;span class="c1"&gt;# False
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Heap / Priority Queue
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;heapq&lt;/span&gt;

&lt;span class="c1"&gt;# Min heap by default
&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;

&lt;span class="c1"&gt;# Push - O(log n)
&lt;/span&gt;&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heappush&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heappush&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heappush&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# Pop min - O(log n)
&lt;/span&gt;&lt;span class="n"&gt;min_val&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heappop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# 1
&lt;/span&gt;
&lt;span class="c1"&gt;# Peek min - O(1)
&lt;/span&gt;&lt;span class="n"&gt;min_val&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;  &lt;span class="c1"&gt;# Don't pop
&lt;/span&gt;
&lt;span class="c1"&gt;# Heapify existing list - O(n)
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;9&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heapify&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="c1"&gt;# arr is now a heap
&lt;/span&gt;
&lt;span class="c1"&gt;# Push and pop in one operation
&lt;/span&gt;&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heappushpop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Push 5, then pop min
&lt;/span&gt;&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heapreplace&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Pop min, then push 5
&lt;/span&gt;
&lt;span class="c1"&gt;# N largest/smallest elements
&lt;/span&gt;&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;nlargest&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;   &lt;span class="c1"&gt;# [9, 5, 4]
&lt;/span&gt;&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;nsmallest&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# [1, 1, 2]
&lt;/span&gt;
&lt;span class="c1"&gt;# Max heap trick (negate values)
&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;
&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heappush&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heappush&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&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;max_val&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heappop&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_heap&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# 3
&lt;/span&gt;
&lt;span class="c1"&gt;# Heap with custom objects
&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;
&lt;span class="n"&gt;heapq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;heappush&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;heap&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;priority&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;item&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;  &lt;span class="c1"&gt;# Use tuple
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Deque Operations
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;collections&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;deque&lt;/span&gt;

&lt;span class="c1"&gt;# Initialize
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;deque&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;span class="n"&gt;dq&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;deque&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;span class="n"&gt;dq&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;deque&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;maxlen&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Fixed size
&lt;/span&gt;
&lt;span class="c1"&gt;# Append - O(1)
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;        &lt;span class="c1"&gt;# Add to right: [1, 2, 3, 4]
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;appendleft&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="c1"&gt;# Add to left: [0, 1, 2, 3, 4]
&lt;/span&gt;
&lt;span class="c1"&gt;# Pop - O(1)
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;            &lt;span class="c1"&gt;# Remove from right, returns 4
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;popleft&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;        &lt;span class="c1"&gt;# Remove from left, returns 0
&lt;/span&gt;
&lt;span class="c1"&gt;# Extend - O(k)
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;extend&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;6&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;        &lt;span class="c1"&gt;# [1, 2, 3, 5, 6]
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;extendleft&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;   &lt;span class="c1"&gt;# [-1, 0, 1, 2, 3, 5, 6]
&lt;/span&gt;
&lt;span class="c1"&gt;# Access
&lt;/span&gt;&lt;span class="n"&gt;dq&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="c1"&gt;# First element
&lt;/span&gt;&lt;span class="n"&gt;dq&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="c1"&gt;# Last element
&lt;/span&gt;
&lt;span class="c1"&gt;# Rotate
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;rotate&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="c1"&gt;# Rotate right: [6, 1, 2, 3, 5]
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;rotate&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="c1"&gt;# Rotate left: [1, 2, 3, 5, 6]
&lt;/span&gt;
&lt;span class="c1"&gt;# Other operations
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;count&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;        &lt;span class="c1"&gt;# Count occurrences
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;remove&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;       &lt;span class="c1"&gt;# Remove first occurrence
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;reverse&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;       &lt;span class="c1"&gt;# Reverse in-place
&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;clear&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;         &lt;span class="c1"&gt;# Clear all
&lt;/span&gt;&lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;dq&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;            &lt;span class="c1"&gt;# Length
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Collections Module
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Counter
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;collections&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;Counter&lt;/span&gt;

&lt;span class="c1"&gt;# Initialize
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;Counter&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;  &lt;span class="c1"&gt;# Counter({3: 3, 2: 2, 1: 1})
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;Counter&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;hello&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;              &lt;span class="c1"&gt;# Counter({'l': 2, 'h': 1, 'e': 1, 'o': 1})
&lt;/span&gt;
&lt;span class="c1"&gt;# Most common
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;most_common&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;   &lt;span class="c1"&gt;# [(3, 3), (2, 2)]
&lt;/span&gt;
&lt;span class="c1"&gt;# Access counts
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;               &lt;span class="c1"&gt;# 2
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;               &lt;span class="c1"&gt;# 0 (no KeyError)
&lt;/span&gt;
&lt;span class="c1"&gt;# Update
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;update&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;

&lt;span class="c1"&gt;# Subtract
&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;subtract&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;

&lt;span class="c1"&gt;# Arithmetic operations
&lt;/span&gt;&lt;span class="n"&gt;c1&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;Counter&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt;
&lt;span class="n"&gt;c2&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;Counter&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt;
&lt;span class="n"&gt;c1&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;c2&lt;/span&gt;            &lt;span class="c1"&gt;# Counter({'a': 4, 'b': 3})
&lt;/span&gt;&lt;span class="n"&gt;c1&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;c2&lt;/span&gt;            &lt;span class="c1"&gt;# Counter({'a': 2}) (keeps only positive)
&lt;/span&gt;
&lt;span class="c1"&gt;# Convert to dict
&lt;/span&gt;&lt;span class="nf"&gt;dict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;c&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  defaultdict
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;collections&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;defaultdict&lt;/span&gt;

&lt;span class="c1"&gt;# With int (default 0)
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;defaultdict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;        &lt;span class="c1"&gt;# No KeyError, starts at 0
&lt;/span&gt;
&lt;span class="c1"&gt;# With list (default [])
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;defaultdict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;list&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nf"&gt;append&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="c1"&gt;# No KeyError, starts with []
&lt;/span&gt;
&lt;span class="c1"&gt;# With set
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;defaultdict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;set&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nf"&gt;add&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="c1"&gt;# With lambda
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;defaultdict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;lambda&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nf"&gt;float&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;inf&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;

&lt;span class="c1"&gt;# Convert to normal dict
&lt;/span&gt;&lt;span class="nf"&gt;dict&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  OrderedDict (less needed in Python 3.7+)
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;collections&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;OrderedDict&lt;/span&gt;

&lt;span class="c1"&gt;# Maintains insertion order (dicts do this by default now)
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nc"&gt;OrderedDict&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;

&lt;span class="c1"&gt;# Move to end
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;move_to_end&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Move 'a' to end
&lt;/span&gt;
&lt;span class="c1"&gt;# Pop last
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;popitem&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;last&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;   &lt;span class="c1"&gt;# Pop from end
&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;popitem&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;last&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;False&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Pop from beginning
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Itertools
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;itertools&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt;

&lt;span class="c1"&gt;# Combinations
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;combinations&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;  &lt;span class="c1"&gt;# [(1, 2), (1, 3), (2, 3)]
&lt;/span&gt;
&lt;span class="c1"&gt;# Permutations
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;permutations&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;  &lt;span class="c1"&gt;# [(1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2)]
&lt;/span&gt;
&lt;span class="c1"&gt;# Product (Cartesian product)
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;product&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt;  &lt;span class="c1"&gt;# [(1, 'a'), (1, 'b'), (2, 'a'), (2, 'b')]
&lt;/span&gt;
&lt;span class="c1"&gt;# Combinations with replacement
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;combinations_with_replacement&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;  &lt;span class="c1"&gt;# [(1, 1), (1, 2), (2, 2)]
&lt;/span&gt;
&lt;span class="c1"&gt;# Chain (flatten)
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;chain&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt;  &lt;span class="c1"&gt;# [1, 2, 3, 4]
&lt;/span&gt;
&lt;span class="c1"&gt;# Accumulate (cumulative sum by default)
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;accumulate&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt;  &lt;span class="c1"&gt;# [1, 3, 6, 10]
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;accumulate&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="nb"&gt;max&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;  &lt;span class="c1"&gt;# [1, 2, 3, 4] (running max)
&lt;/span&gt;
&lt;span class="c1"&gt;# Groupby
&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;a&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;b&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;
&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;group&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;groupby&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;data&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="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="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;span class="c1"&gt;# Output: a [('a', 1), ('a', 2)]
#         b [('b', 3), ('b', 4)]
&lt;/span&gt;
&lt;span class="c1"&gt;# Cycle (infinite)
&lt;/span&gt;&lt;span class="n"&gt;counter&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;
&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;item&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;cycle&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;]):&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;item&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;counter&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;counter&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;break&lt;/span&gt;

&lt;span class="c1"&gt;# Repeat
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;repeat&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;  &lt;span class="c1"&gt;# [10, 10, 10]
&lt;/span&gt;
&lt;span class="c1"&gt;# Islice (slice iterator)
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;islice&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;8&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;  &lt;span class="c1"&gt;# [2, 4, 6]
&lt;/span&gt;
&lt;span class="c1"&gt;# Pairwise (Python 3.10+)
&lt;/span&gt;&lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;pairwise&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt;  &lt;span class="c1"&gt;# [(1, 2), (2, 3), (3, 4)]
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Matrix Operations
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Initialize matrix
&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;
&lt;span class="n"&gt;matrix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;_&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;

&lt;span class="c1"&gt;# Fill with specific value
&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;_&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;

&lt;span class="c1"&gt;# Traverse
&lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
        &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;

&lt;span class="c1"&gt;# Get dimensions
&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="n"&gt;cols&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="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="n"&gt;matrix&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;

&lt;span class="c1"&gt;# Transpose
&lt;/span&gt;&lt;span class="n"&gt;transposed&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;
&lt;span class="c1"&gt;# Or using zip
&lt;/span&gt;&lt;span class="n"&gt;transposed&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;map&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;list&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nf"&gt;zip&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;)))&lt;/span&gt;

&lt;span class="c1"&gt;# Rotate 90 degrees clockwise
&lt;/span&gt;&lt;span class="n"&gt;rotated&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;j&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;

&lt;span class="c1"&gt;# Flatten
&lt;/span&gt;&lt;span class="n"&gt;flat&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;row&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;matrix&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;val&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;row&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="c1"&gt;# Diagonal traversal
&lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;  &lt;span class="c1"&gt;# Main diagonal
&lt;/span&gt;
&lt;span class="c1"&gt;# 4-directional movement
&lt;/span&gt;&lt;span class="n"&gt;directions&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="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="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="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="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="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="c1"&gt;# right, down, left, up
&lt;/span&gt;&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;dx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;dy&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="n"&gt;directions&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="n"&gt;new_x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;new_y&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;dx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;dy&lt;/span&gt;

&lt;span class="c1"&gt;# 8-directional movement
&lt;/span&gt;&lt;span class="n"&gt;directions&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[(&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="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="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="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;1&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="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="mi"&gt;0&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="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)]&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Bit Manipulation
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Basic operations
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;  &lt;span class="c1"&gt;# 101 in binary
&lt;/span&gt;
&lt;span class="c1"&gt;# AND
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;     &lt;span class="c1"&gt;# Check if odd: 1 (True)
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c1"&gt;# Remove rightmost set bit: 4 (100)
&lt;/span&gt;
&lt;span class="c1"&gt;# OR
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;     &lt;span class="c1"&gt;# Set rightmost bit: 5
&lt;/span&gt;
&lt;span class="c1"&gt;# XOR
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;^&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;     &lt;span class="c1"&gt;# Flip rightmost bit: 4
&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;^&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt;     &lt;span class="c1"&gt;# Always 0
&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;^&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;     &lt;span class="c1"&gt;# Always a
&lt;/span&gt;
&lt;span class="c1"&gt;# NOT
&lt;/span&gt;&lt;span class="o"&gt;~&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;        &lt;span class="c1"&gt;# Flip all bits: -6
&lt;/span&gt;
&lt;span class="c1"&gt;# Left shift (multiply by 2)
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;    &lt;span class="c1"&gt;# 10 (1010)
&lt;/span&gt;
&lt;span class="c1"&gt;# Right shift (divide by 2)
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;    &lt;span class="c1"&gt;# 2 (10)
&lt;/span&gt;
&lt;span class="c1"&gt;# Check if power of 2
&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="ow"&gt;and&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;

&lt;span class="c1"&gt;# Count set bits
&lt;/span&gt;&lt;span class="nf"&gt;bin&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;count&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="s"&gt;1&lt;/span&gt;&lt;span class="sh"&gt;'&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# 2
&lt;/span&gt;
&lt;span class="c1"&gt;# Get bit at position i
&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;

&lt;span class="c1"&gt;# Set bit at position i
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&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="c1"&gt;# Clear bit at position i
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="o"&gt;~&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&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="c1"&gt;# Toggle bit at position i
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;^&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&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="c1"&gt;# Get rightmost set bit
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;

&lt;span class="c1"&gt;# Common tricks
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;           &lt;span class="c1"&gt;# Check if odd
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;       &lt;span class="c1"&gt;# Remove rightmost 1
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;       &lt;span class="c1"&gt;# Set rightmost 0
&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;          &lt;span class="c1"&gt;# Get rightmost 1
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Binary Search
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Template 1: Find exact value
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;binary_search&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;target&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="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="nf"&gt;len&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="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="k"&gt;while&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="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="k"&gt;if&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="k"&gt;elif&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="k"&gt;else&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;mid&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&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="c1"&gt;# Template 2: Find leftmost position
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;binary_search_left&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;target&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="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="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="k"&gt;while&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="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="k"&gt;if&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="k"&gt;else&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;mid&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt;

&lt;span class="c1"&gt;# Template 3: Find rightmost position
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;binary_search_right&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;target&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="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="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="k"&gt;while&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="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="k"&gt;if&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="k"&gt;else&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;mid&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;

&lt;span class="c1"&gt;# Using bisect module
&lt;/span&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;bisect&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;bisect_left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;bisect_right&lt;/span&gt;

&lt;span class="c1"&gt;# Find leftmost &amp;gt;= target
&lt;/span&gt;&lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;bisect_left&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;target&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# Find rightmost &amp;lt;= target
&lt;/span&gt;&lt;span class="n"&gt;idx&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;bisect_right&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;target&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Common Patterns
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Sliding Window
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Fixed size window
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;max_sum_subarray&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;k&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;window_sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;sum&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;k&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
    &lt;span class="n"&gt;max_sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;window_sum&lt;/span&gt;

    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;k&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nf"&gt;len&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;window_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;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;max_sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_sum&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;window_sum&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;max_sum&lt;/span&gt;

&lt;span class="c1"&gt;# Variable size window
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;longest_substring_k_distinct&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;k&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="mi"&gt;0&lt;/span&gt;
    &lt;span class="n"&gt;max_len&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;
    &lt;span class="n"&gt;char_count&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="n"&gt;right&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;len&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;char_count&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;right&lt;/span&gt;&lt;span class="p"&gt;]]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;char_count&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;get&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;right&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;

        &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;char_count&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;k&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="n"&gt;char_count&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;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;1&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;char_count&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;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;0&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
                &lt;span class="k"&gt;del&lt;/span&gt; &lt;span class="n"&gt;char_count&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;left&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="mi"&gt;1&lt;/span&gt;

        &lt;span class="n"&gt;max_len&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;max_len&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="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;max_len&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Two Pointers
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Opposite direction
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;two_sum_sorted&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;target&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="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="nf"&gt;len&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="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="k"&gt;while&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="n"&gt;curr_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="n"&gt;curr_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;elif&lt;/span&gt; &lt;span class="n"&gt;curr_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="mi"&gt;1&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;right&lt;/span&gt; &lt;span class="o"&gt;-=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
    &lt;span class="k"&gt;return&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="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

&lt;span class="c1"&gt;# Same direction
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;remove_duplicates&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="ow"&gt;not&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;

    &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&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="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;)):&lt;/span&gt;
        &lt;span class="k"&gt;if&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;fast&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;slow&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="mi"&gt;1&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;slow&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;fast&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Prefix Sum
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# 1D prefix sum
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;prefix_sum&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;prefix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;num&lt;/span&gt; &lt;span class="ow"&gt;in&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;prefix&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;prefix&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="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="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;prefix&lt;/span&gt;

&lt;span class="c1"&gt;# Range sum query
&lt;/span&gt;&lt;span class="n"&gt;prefix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;prefix_sum&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;range_sum&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="mi"&gt;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;prefix&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="c1"&gt;# 2D prefix sum
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;build_prefix_2d&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;cols&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="nf"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
    &lt;span class="n"&gt;prefix&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cols&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;_&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="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="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&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;rows&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="n"&gt;j&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&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;cols&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;prefix&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="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;matrix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="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;j&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; 
                           &lt;span class="n"&gt;prefix&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;j&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; 
                           &lt;span class="n"&gt;prefix&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="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;prefix&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;j&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;prefix&lt;/span&gt;

&lt;span class="c1"&gt;# Range sum 2D
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;range_sum_2d&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;r1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;c1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;r2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;c2&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="nf"&gt;return &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;r2&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;c2&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;prefix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;r1&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;c2&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;prefix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;r2&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;c1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; 
            &lt;span class="n"&gt;prefix&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;r1&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="n"&gt;c1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Fast/Slow Pointers (Cycle Detection)
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Floyd's cycle detection
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;has_cycle&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;head&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="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="ow"&gt;and&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;next&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;next&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="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;next&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;next&lt;/span&gt;
        &lt;span class="k"&gt;if&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="bp"&gt;True&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="bp"&gt;False&lt;/span&gt;

&lt;span class="c1"&gt;# Find cycle start
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;detect_cycle&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;head&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="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="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;head&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt; &lt;span class="ow"&gt;and&lt;/span&gt; &lt;span class="n"&gt;fast&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;next&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;slow&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;next&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="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;next&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;next&lt;/span&gt;
        &lt;span class="k"&gt;if&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="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="k"&gt;while&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="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="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;next&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="p"&gt;.&lt;/span&gt;&lt;span class="nb"&gt;next&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;slow&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="bp"&gt;None&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Monotonic Stack
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Next greater element
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;next_greater_elements&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;n&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;len&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;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;
    &lt;span class="n"&gt;stack&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[]&lt;/span&gt;  &lt;span class="c1"&gt;# Store indices
&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&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="k"&gt;while&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt; &lt;span class="ow"&gt;and&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;stack&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="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;i&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;stack&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;pop&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="p"&gt;]&lt;/span&gt;
        &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;

&lt;span class="c1"&gt;# Previous smaller element
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;previous_smaller_elements&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;n&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;len&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;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;
    &lt;span class="n"&gt;stack&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="n"&gt;i&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&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="k"&gt;while&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt; &lt;span class="ow"&gt;and&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;stack&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="o"&gt;&amp;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;stack&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;stack&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="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="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;append&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Input/Output Tricks
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Fast input (for competitive programming)
&lt;/span&gt;&lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="n"&gt;sys&lt;/span&gt;
&lt;span class="nb"&gt;input&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;sys&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;stdin&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;readline&lt;/span&gt;

&lt;span class="c1"&gt;# Read single integer
&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;int&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;input&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;

&lt;span class="c1"&gt;# Read multiple integers from one line
&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&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="nf"&gt;map&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nf"&gt;input&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="nf"&gt;split&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;

&lt;span class="c1"&gt;# Read list of integers
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;map&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nf"&gt;input&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="nf"&gt;split&lt;/span&gt;&lt;span class="p"&gt;()))&lt;/span&gt;

&lt;span class="c1"&gt;# Read multiple lines
&lt;/span&gt;&lt;span class="n"&gt;lines&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;sys&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;stdin&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;readlines&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;

&lt;span class="c1"&gt;# Fast output
&lt;/span&gt;&lt;span class="nf"&gt;print&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="c1"&gt;# Prints list elements separated by space
&lt;/span&gt;
&lt;span class="c1"&gt;# Format output
&lt;/span&gt;&lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="si"&gt;:&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="n"&gt;f&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# 2 decimal places
&lt;/span&gt;&lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sa"&gt;f&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="si"&gt;{&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="si"&gt;:&lt;/span&gt;&lt;span class="mi"&gt;05&lt;/span&gt;&lt;span class="n"&gt;d&lt;/span&gt;&lt;span class="si"&gt;}&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;  &lt;span class="c1"&gt;# Pad with zeros to width 5
&lt;/span&gt;
&lt;span class="c1"&gt;# Multiple test cases
&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;int&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;input&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;
&lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;_&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;t&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="c1"&gt;# Solve each test case
&lt;/span&gt;    &lt;span class="k"&gt;pass&lt;/span&gt;

&lt;span class="c1"&gt;# EOF handling
&lt;/span&gt;&lt;span class="k"&gt;try&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="bp"&gt;True&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="n"&gt;line&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;input&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
        &lt;span class="c1"&gt;# Process line
&lt;/span&gt;&lt;span class="k"&gt;except&lt;/span&gt; &lt;span class="nb"&gt;EOFError&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="k"&gt;pass&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  Miscellaneous
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Lambda Functions
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Basic lambda
&lt;/span&gt;&lt;span class="n"&gt;square&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;**&lt;/span&gt;&lt;span class="mi"&gt;2&lt;/span&gt;

&lt;span class="c1"&gt;# Multiple arguments
&lt;/span&gt;&lt;span class="n"&gt;add&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;

&lt;span class="c1"&gt;# With conditional
&lt;/span&gt;&lt;span class="n"&gt;max_fn&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;

&lt;span class="c1"&gt;# In sorting
&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;x&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="c1"&gt;# In filter
&lt;/span&gt;&lt;span class="n"&gt;evens&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;filter&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;

&lt;span class="c1"&gt;# In map
&lt;/span&gt;&lt;span class="n"&gt;squares&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;list&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;map&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="o"&gt;**&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;arr&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Functools
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="kn"&gt;from&lt;/span&gt; &lt;span class="n"&gt;functools&lt;/span&gt; &lt;span class="kn"&gt;import&lt;/span&gt; &lt;span class="nb"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;lru_cache&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;cmp_to_key&lt;/span&gt;

&lt;span class="c1"&gt;# Reduce
&lt;/span&gt;&lt;span class="n"&gt;product&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;reduce&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;lambda&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;x&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;y&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;  &lt;span class="c1"&gt;# 24
&lt;/span&gt;
&lt;span class="c1"&gt;# LRU Cache (memoization)
&lt;/span&gt;&lt;span class="nd"&gt;@lru_cache&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;maxsize&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="bp"&gt;None&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;fib&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="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&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;n&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;fib&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="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;fib&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;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# Custom comparator
&lt;/span&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;
&lt;span class="n"&gt;arr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="nf"&gt;cmp_to_key&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;compare&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Try-Except
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="c1"&gt;# Basic
&lt;/span&gt;&lt;span class="k"&gt;try&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="mi"&gt;10&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;
&lt;span class="k"&gt;except&lt;/span&gt; &lt;span class="nb"&gt;ZeroDivisionError&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="s"&gt;Cannot divide by zero&lt;/span&gt;&lt;span class="sh"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# Multiple exceptions
&lt;/span&gt;&lt;span class="k"&gt;try&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="c1"&gt;# code
&lt;/span&gt;&lt;span class="nf"&gt;except &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;ValueError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nb"&gt;TypeError&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# Catch all
&lt;/span&gt;&lt;span class="k"&gt;try&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="c1"&gt;# code
&lt;/span&gt;&lt;span class="k"&gt;except&lt;/span&gt; &lt;span class="nb"&gt;Exception&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="nf"&gt;print&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;e&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c1"&gt;# Finally
&lt;/span&gt;&lt;span class="k"&gt;try&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="c1"&gt;# code
&lt;/span&gt;&lt;span class="k"&gt;finally&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="c1"&gt;# Always executes
&lt;/span&gt;    &lt;span class="k"&gt;pass&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



</description>
      <category>algorithms</category>
      <category>tutorial</category>
      <category>computerscience</category>
      <category>python</category>
    </item>
    <item>
      <title>Quick Select Algorithm</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Wed, 01 Oct 2025 17:53:29 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/quick-select-algorithm-2kd3</link>
      <guid>https://dev.to/itzsrikanth/quick-select-algorithm-2kd3</guid>
      <description>&lt;p&gt;I would not take full credits for this writing this code by hand, some of it goes to the Leetcode discussion section and "Claude Sonnet 4 Thinking" model. Purpose of this series is to document for my learning and if it proves to be useful for others.&lt;/p&gt;

&lt;p&gt;There are two popular parition schemes to find the pivot:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;hoare&lt;/li&gt;
&lt;li&gt;lomuto&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Lomute partition scheme
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;partition&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&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="nb"&gt;int&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="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;

        &lt;span class="c1"&gt;# choose rightmost element (not the index) as the pivot
&lt;/span&gt;        &lt;span class="n"&gt;pivot&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;self&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;right&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

        &lt;span class="c1"&gt;# boundary pointer - tracks the end of the "≤ pivot" region
&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;left&lt;/span&gt;

        &lt;span class="c1"&gt;# scanner pointer - explores the array from left to right
&lt;/span&gt;        &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;j&lt;/span&gt; &lt;span class="ow"&gt;in&lt;/span&gt; &lt;span class="nf"&gt;range&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;if&lt;/span&gt; &lt;span class="n"&gt;self&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;j&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;pivot&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
                &lt;span class="n"&gt;self&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;self&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;j&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;self&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;j&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;self&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;i&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;
        &lt;span class="n"&gt;self&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;self&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;right&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;self&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;right&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="n"&gt;self&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="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;The idea behind &lt;code&gt;i&lt;/code&gt; and &lt;code&gt;j&lt;/code&gt; pointer is that the former needs to hold the place for numbers smaller than pivot point to be place. It is moved ahead only when we are going to attempt a swap. The latter would scan the elements looking for a lower value to swap.&lt;/p&gt;

&lt;p&gt;Taking the example from &lt;code&gt;geeksforgeeks&lt;/code&gt;:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Array: [10, 4, 5, 8, 6, 11, 26]  pivot = 26
       left=0, right=6

Initial: [10, 4, 5, 8, 6, 11, 26]  i=0
         ^i                    ^pivot

j=0: arr[0]=10 ≤ 26? Yes → swap(i=0,j=0), i=1
     [10, 4, 5, 8, 6, 11, 26]  i=1
         ^i

j=1: arr[1]=4 ≤ 26? Yes → swap(i=1,j=1), i=2
     [10, 4, 5, 8, 6, 11, 26]  i=2
            ^i

j=2: arr[2]=5 ≤ 26? Yes → swap(i=2,j=2), i=3
     [10, 4, 5, 8, 6, 11, 26]  i=3
               ^i

...continuing this pattern...

Final: [10, 4, 5, 8, 6, 11, 26]  i=6
                           ^i

Place pivot: swap(i=6, right=6) → no change
Return i=6
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;The goal is to rearrange array so that:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;all elements ≤ pivot are on the left, and&lt;/li&gt;
&lt;li&gt;all elements &amp;gt; pivot are on the right, with pivot in its correct 
final position.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;[ ≤ pivot | &amp;gt; pivot | unprocessed | pivot]
left  i-1   i    j-1  j    right-1  right
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  __main__
&lt;/h2&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight python"&gt;&lt;code&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Solution&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;__init__&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&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;List&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]):&lt;/span&gt;
        &lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;arr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;arr&lt;/span&gt;

    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;partition&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&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="nb"&gt;int&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="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt;
        &lt;span class="c1"&gt;# ...
&lt;/span&gt;
    &lt;span class="k"&gt;def&lt;/span&gt; &lt;span class="nf"&gt;quickselect&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;self&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="nb"&gt;int&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="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="nb"&gt;int&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;self&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;left&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;

        &lt;span class="n"&gt;pivot_index&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;partition&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;if&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;pivot_index&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="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;self&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;pivot_index&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="k"&gt;elif&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;pivot_index&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="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;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;quickselect&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;pivot_index&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;k&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="k"&gt;else&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;self&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;quickselect&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pivot_index&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;k&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;pivot_index&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="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h2&gt;
  
  
  References
&lt;/h2&gt;

&lt;ul&gt;
&lt;li&gt;&lt;a href="https://www.geeksforgeeks.org/dsa/quickselect-algorithm/" rel="noopener noreferrer"&gt;https://www.geeksforgeeks.org/dsa/quickselect-algorithm/&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

</description>
      <category>dsa</category>
      <category>competativeprogramming</category>
      <category>leetcode</category>
    </item>
    <item>
      <title>Comment system: API Gateway &amp; DynamoDB Integration in Pulumi</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Wed, 24 Jul 2024 05:26:22 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/comment-system-api-gateway-dynamodb-integration-in-pulumi-46l4</link>
      <guid>https://dev.to/itzsrikanth/comment-system-api-gateway-dynamodb-integration-in-pulumi-46l4</guid>
      <description>&lt;p&gt;Inspired by Alex DeBrie's &lt;a href="https://x.com/alexbdebrie/status/1097537089434988550" rel="noopener noreferrer"&gt;tweet&lt;/a&gt; to use API Gateway with DynamoDB proxy integration, I built a Comment system in Pulumi.&lt;/p&gt;

&lt;h2&gt;
  
  
  Background
&lt;/h2&gt;

&lt;p&gt;The idea is to create a comment system in AWS by skipping the Lambda function and using API Gateway and DynamoDB integration. This is possible by using the &lt;code&gt;AWS_PROXY&lt;/code&gt; integration type in API Gateway. This integration type allows you to pass the request directly to the backend service without any transformation.&lt;/p&gt;

&lt;p&gt;We assume to have a site with 100 pages and each page has 10 recent comments. So, we would create a DynamoDB table which has &lt;code&gt;slug&lt;/code&gt; as Hash key and &lt;code&gt;createdAt&lt;/code&gt; as Range key. The &lt;code&gt;slug&lt;/code&gt; would be the page URL and &lt;code&gt;createdAt&lt;/code&gt; would be the timestamp when the comment was created. This way, we can query the table to get the 10 most recent comments for a given page. &lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;For simplicity, we are going to skip the user table etc.**&lt;/p&gt;
&lt;/blockquote&gt;

&lt;h2&gt;
  
  
  Pulumi Code
&lt;/h2&gt;

&lt;h3&gt;
  
  
  Create a DynamoDB table to store comments:
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Create a DynamoDB table to store comments&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;commentsTable&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nx"&gt;aws&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;dynamodb&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nc"&gt;Table&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;CommentsTable&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;attributes&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="na"&gt;name&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;slug&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;type&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;S&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;createdAt&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;type&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;N&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="na"&gt;hashKey&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;slug&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;rangeKey&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;createdAt&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;billingMode&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;PROVISIONED&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;readCapacity&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;writeCapacity&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;We need to define attributes for the fields on which we would query the table. In this case, we are querying based on &lt;code&gt;slug&lt;/code&gt; and &lt;code&gt;createdAt&lt;/code&gt;.&lt;/p&gt;

&lt;h4&gt;
  
  
  DB Provisioning and cost calculation:
&lt;/h4&gt;

&lt;p&gt;Next, the &lt;code&gt;billingMode&lt;/code&gt; is set to &lt;code&gt;PROVISIONED&lt;/code&gt;. We can arrive at the &lt;code&gt;readCapacity&lt;/code&gt; and &lt;code&gt;writeCapacity&lt;/code&gt; based on the expected traffic. For that we need have some rough assumptions. In this case, &lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;we are assuming a site deployed with ISR (Incremental Static Regeneration) and the pages are cached in CDN (Cloudfront) for a day. So, the traffic would be 10 pages x 1 read query per page. &lt;/li&gt;
&lt;li&gt;for simplicity, the queries will not be parallel. We can distribute the reads over 60 seconds.&lt;/li&gt;
&lt;li&gt;no additional writes are happening during the build process.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;100 reads / 60 seconds ≈ 1.67 reads/second&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;Once we have our stack running, these values can be adjusted based on the actual traffic.&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;So the cost will be:&lt;/p&gt;

&lt;p&gt;2 RCUs * $0.00013 per RCU-hour = $0.00026 per hour&lt;br&gt;
and,&lt;br&gt;
Monthly cost = $0.00026 * 24 * 30 = $0.1872&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;The cost is based on the us-east-1 region. The cost may vary based on the region.&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;Similar calculation would go in for &lt;code&gt;writeCapacity&lt;/code&gt;. For now, we will take it as 1 WCU.&lt;/p&gt;
&lt;h3&gt;
  
  
  Create a Rest API Gateway:
&lt;/h3&gt;

&lt;p&gt;&lt;code&gt;RestApi&lt;/code&gt; Resource is the top-level container for your API. It defines the basic information about your API, such as its name and description.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Create an API Gateway Rest API&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;api&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nx"&gt;aws&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;apigateway&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nc"&gt;RestApi&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Backend&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;name&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Backend&lt;/span&gt;&lt;span class="dl"&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="na"&gt;dependsOn&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;commentsTable&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;Once we have the API Gateway, we need to create a resource and method to handle the POST request. The &lt;code&gt;Resource&lt;/code&gt; resource is a logical container for the resources that make up your API. In terms of URL path, it corresponds to a collection of API resources. Multiple resources can be created to represent different parts of your API's URL structure. For our case, we would create a resource for &lt;code&gt;comments&lt;/code&gt; under the &lt;code&gt;Backend&lt;/code&gt; API Gateway.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Create a resource for comments&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;commentsResource&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nx"&gt;aws&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;apigateway&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nc"&gt;Resource&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;CommentsResource&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;parentId&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;api&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;rootResourceId&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;pathPart&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;comments&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;restApi&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;api&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;    &lt;span class="c1"&gt;// &amp;lt;--- Reference to the Rest API&lt;/span&gt;
&lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;dependsOn&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;api&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;     &lt;span class="c1"&gt;// &amp;lt;--- Make sure the API is created first&lt;/span&gt;
&lt;span class="p"&gt;});&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Similarly, we need to create a method to handle the POST request. The &lt;code&gt;Method&lt;/code&gt; resource defines the HTTP method that clients can use to interact with your API. For our case, we would create a POST method under the &lt;code&gt;comments&lt;/code&gt; resource.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Create a method for POST requests to /comments&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;commentsMethod&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nx"&gt;aws&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;apigateway&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nc"&gt;Method&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;CommentsMethod&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;restApi&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;api&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;resourceId&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;commentsResource&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;    &lt;span class="c1"&gt;// &amp;lt;--- Reference to the comments resource&lt;/span&gt;
    &lt;span class="na"&gt;httpMethod&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;POST&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;authorization&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;NONE&lt;/span&gt;&lt;span class="dl"&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="na"&gt;dependsOn&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;commentsResource&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
&lt;span class="p"&gt;});&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Integration with DynamoDB:
&lt;/h3&gt;

&lt;p&gt;Specifying a role is crucial for security and access control while integrating API Gateway with AWS services using the AWS_PROXY integration type. The role specified in the integration is assumed by API Gateway, not the AWS service being called. This role includes permissions that API Gateway needs to invoke actions on the integrated AWS service.with other AWS services.&lt;/p&gt;

&lt;p&gt;This approach follows the principle of least privilege, where the role grants only the necessary permissions for API Gateway to perform specific actions. This minimizes the risk of unauthorized access or actions within your AWS environment.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;apigatewayRole&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nx"&gt;aws&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;iam&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nc"&gt;Role&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;ApigatewayRole&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;assumeRolePolicy&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="na"&gt;Version&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;2012-10-17&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="na"&gt;Statement&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[{&lt;/span&gt;
            &lt;span class="na"&gt;Action&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;sts:AssumeRole&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
            &lt;span class="na"&gt;Effect&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Allow&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
            &lt;span class="na"&gt;Principal&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="na"&gt;Service&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;apigateway.amazonaws.com&lt;/span&gt;&lt;span class="dl"&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;span class="p"&gt;});&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;





&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Create an integration with DynamoDB&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;commentsIntegration&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nx"&gt;aws&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;apigateway&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nc"&gt;Integration&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;DynamodbIntegration&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;restApi&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;api&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;resourceId&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;commentsResource&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;httpMethod&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;commentsMethod&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;httpMethod&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;type&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;AWS&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;integrationHttpMethod&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;POST&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;credentials&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;apigatewayRole&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;arn&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;uri&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="s2"&gt;`arn:aws:apigateway:&lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;currentRegion&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;:dynamodb:action/PutItem`&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;requestTemplates&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;application/json&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pulumi&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;interpolate&lt;/span&gt;&lt;span class="s2"&gt;`{
            "TableName": "&lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;commentsTable&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;name&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;",
            "Item": {
                "commentId": {
                    "S": "$context.requestId"
                },
                "comment": {
                    "S": "$input.body"
                }
            }
        }`&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="na"&gt;passthroughBehavior&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;WHEN_NO_MATCH&lt;/span&gt;&lt;span class="dl"&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="na"&gt;dependsOn&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;commentsMethod&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;apigatewayRole&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;The &lt;code&gt;Integration&lt;/code&gt; resource defines how API Gateway integrates with other AWS services. In this case, we are integrating with DynamoDB. The &lt;code&gt;uri&lt;/code&gt; property specifies the ARN of the service action to be called. The &lt;code&gt;requestTemplates&lt;/code&gt; property specifies the mapping templates to transform the request body into the format expected by the backend service.&lt;/p&gt;

&lt;h3&gt;
  
  
  Deploy the stack:
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// Deploy the API&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;deployment&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nx"&gt;aws&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;apigateway&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nc"&gt;Deployment&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;ApiDeployment&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;restApi&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;api&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
    &lt;span class="na"&gt;stageName&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;v1&lt;/span&gt;&lt;span class="dl"&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="na"&gt;dependsOn&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;commentsIntegration&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;Since we would require the recent comments, we need to use &lt;code&gt;ScanIndexForward: false&lt;/code&gt; in the query along with &lt;code&gt;Limit: 10&lt;/code&gt;.&lt;/p&gt;

&lt;p&gt;Checkout &lt;a href="https://github.com/itzsrikanth/pulumi-serverless" rel="noopener noreferrer"&gt;the repo&lt;/a&gt; for full code.&lt;/p&gt;

</description>
      <category>serverless</category>
      <category>aws</category>
      <category>webdev</category>
      <category>node</category>
    </item>
    <item>
      <title>My Next.Js configuration</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Sat, 13 Jul 2024 05:59:25 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/my-nextjs-configuration-5fbh</link>
      <guid>https://dev.to/itzsrikanth/my-nextjs-configuration-5fbh</guid>
      <description>&lt;p&gt;Generally while creating a content-heavy Next.Js project, I prefer to have it initialized with a few params like below:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;npx create-next-app &lt;span class="nt"&gt;--ts&lt;/span&gt; &lt;span class="se"&gt;\&lt;/span&gt;
&lt;span class="nt"&gt;--tailwind&lt;/span&gt; &lt;span class="se"&gt;\&lt;/span&gt;
&lt;span class="nt"&gt;--eslint&lt;/span&gt; &lt;span class="se"&gt;\&lt;/span&gt;
&lt;span class="nt"&gt;--app&lt;/span&gt; &lt;span class="nt"&gt;--src-dir&lt;/span&gt; &lt;span class="se"&gt;\&lt;/span&gt;
&lt;span class="nt"&gt;--import-alias&lt;/span&gt; &lt;span class="se"&gt;\&lt;/span&gt;
&lt;span class="nt"&gt;--use-yarn&lt;/span&gt; &lt;span class="se"&gt;\&lt;/span&gt;
&lt;span class="nt"&gt;-e&lt;/span&gt; app-dir-mdx &amp;lt;app_name&amp;gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



</description>
    </item>
    <item>
      <title>PostCSS: Processor and Plugin module</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Mon, 10 Jan 2022 01:44:21 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/postcss-processor-and-plugin-module-56hk</link>
      <guid>https://dev.to/itzsrikanth/postcss-processor-and-plugin-module-56hk</guid>
      <description>&lt;h1&gt;
  
  
  Table of contents
&lt;/h1&gt;

&lt;ul&gt;
&lt;li&gt;Processor&lt;/li&gt;
&lt;li&gt;LazyResult&lt;/li&gt;
&lt;li&gt;Result&lt;/li&gt;
&lt;li&gt;Plugins&lt;/li&gt;
&lt;li&gt;Warning&lt;/li&gt;
&lt;li&gt;Other Entities&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  Processor &lt;a&gt;&lt;/a&gt;
&lt;/h2&gt;

&lt;p&gt;Creates a &lt;code&gt;Processor&lt;/code&gt; instance. This instance can be used on multiple Stylesheets. &lt;code&gt;postcss&lt;/code&gt; default export function returns a &lt;code&gt;Processor&lt;/code&gt; instance. The main purpose of this module is to process the plugins, which is called &lt;code&gt;Normalization&lt;/code&gt; here, add to the &lt;code&gt;plugins&lt;/code&gt; data member for storage and return a &lt;code&gt;LazyResult&lt;/code&gt; promise.&lt;/p&gt;

&lt;h3&gt;
  
  
  Data members
&lt;/h3&gt;

&lt;h4&gt;
  
  
  plugins - &lt;code&gt;Array&amp;lt;Plugin|Transformer|TransformCallback&amp;gt;&lt;/code&gt;
&lt;/h4&gt;

&lt;p&gt;stores a list of plugins added to this &lt;code&gt;Processor&lt;/code&gt; instance.&lt;/p&gt;

&lt;h3&gt;
  
  
  Methods
&lt;/h3&gt;

&lt;h4&gt;
  
  
  use
&lt;/h4&gt;

&lt;p&gt;takes in a plugin to append to the list of plugins and returns instance of &lt;code&gt;Processor&lt;/code&gt;.&lt;/p&gt;

&lt;h4&gt;
  
  
  process
&lt;/h4&gt;

&lt;p&gt;Parses CSS (can be passed in as various types) to return &lt;code&gt;LazyResult&lt;/code&gt; promise.&lt;/p&gt;

&lt;h4&gt;
  
  
  normalize
&lt;/h4&gt;

&lt;p&gt;Takes in &lt;code&gt;Array&amp;lt; plugin &amp;gt;&lt;/code&gt; are argument. For each of the plugin, the following steps are done:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Normalization involves a preprocessing step where

&lt;ul&gt;
&lt;li&gt;if &lt;code&gt;postcss === true&lt;/code&gt;, it is executed immediately as function without argument.&lt;/li&gt;
&lt;li&gt;if &lt;code&gt;postcss&lt;/code&gt; contains any other truthy value, then the object is destructured to set &lt;code&gt;postcss&lt;/code&gt; as top level value.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;Next step involves added the plugins to normalized list. 

&lt;ul&gt;
&lt;li&gt;if &lt;code&gt;plugin&lt;/code&gt; is &lt;code&gt;object&lt;/code&gt;

&lt;ul&gt;
&lt;li&gt;and &lt;code&gt;plugin.plugins&lt;/code&gt; is &lt;code&gt;Array&lt;/code&gt;, the plugins are merged to the normalized plugin list.&lt;/li&gt;
&lt;li&gt;and &lt;code&gt;plugin.postcssPlugin&lt;/code&gt; is truthy, it is appended to normalized plugin list.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;
&lt;code&gt;type&lt;/code&gt; &lt;code&gt;'function'&lt;/code&gt; directs becomes eligible to be added in normalized list.&lt;/li&gt;

&lt;/ul&gt;

&lt;/li&gt;

&lt;li&gt;Other types are naturally eligible to enter the error conditions.&lt;/li&gt;

&lt;/ul&gt;

&lt;h2&gt;
  
  
  LazyResult &lt;a&gt;&lt;/a&gt;
&lt;/h2&gt;

&lt;h4&gt;
  
  
  constructor
&lt;/h4&gt;

&lt;p&gt;Takes in CSS either as &lt;code&gt;string&lt;/code&gt; or already parsed &lt;code&gt;Node&lt;/code&gt;|&lt;code&gt;Root&lt;/code&gt;, to pass &lt;code&gt;Root&lt;/code&gt; to new instance of &lt;code&gt;Result&lt;/code&gt;. Along with &lt;code&gt;Result&lt;/code&gt;, &lt;code&gt;helpers&lt;/code&gt; and &lt;code&gt;plugins&lt;/code&gt; are also added as data members to this.&lt;/p&gt;

&lt;h2&gt;
  
  
  Result &lt;a&gt;&lt;/a&gt;
&lt;/h2&gt;

&lt;p&gt;This is a very simple data structure to store fields (like a POJO):&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;&lt;code&gt;processor&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;Array&amp;lt;Warning&amp;gt;&lt;/code&gt; as &lt;code&gt;messages&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;&lt;code&gt;root&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;&lt;code&gt;css&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;&lt;code&gt;map&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;opts&lt;/code&gt;
Main processing logic is present in other modules. Here, both &lt;code&gt;content&lt;/code&gt; and &lt;code&gt;toString&lt;/code&gt; returns the same &lt;code&gt;Result.css&lt;/code&gt;.&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  Plugins &lt;a&gt;&lt;/a&gt;
&lt;/h2&gt;

&lt;p&gt;Extends from &lt;code&gt;Processors&lt;/code&gt;. If they are &lt;code&gt;async&lt;/code&gt;, then &lt;code&gt;Promise&lt;/code&gt; must be returned.&lt;/p&gt;

&lt;h4&gt;
  
  
  prepare
&lt;/h4&gt;

&lt;p&gt;takes in &lt;code&gt;Result&lt;/code&gt; and returns &lt;code&gt;Processors&lt;/code&gt;&lt;/p&gt;

&lt;h2&gt;
  
  
  Warning &lt;a&gt;&lt;/a&gt;
&lt;/h2&gt;

&lt;p&gt;A simple structure that is used to get debug info i.e. source and location of the error and the plugin that is causing this. It has got a self-explanatory &lt;code&gt;toString&lt;/code&gt; method.&lt;/p&gt;

&lt;h2&gt;
  
  
  Other Entities &lt;a&gt;&lt;/a&gt;
&lt;/h2&gt;

&lt;h3&gt;
  
  
  AcceptedPlugin
&lt;/h3&gt;

&lt;p&gt;&lt;code&gt;Processor&lt;/code&gt; takes an Array of &lt;code&gt;AcceptedPlugin&lt;/code&gt; which can be of type:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;&lt;code&gt;Plugin&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;&lt;code&gt;PluginCreator&amp;lt;any&amp;gt;&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;&lt;code&gt;OldPlugin&amp;lt;any&amp;gt;&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;&lt;code&gt;TransformCallback&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;&lt;code&gt;{postcss: TransformCallback|Processor}&lt;/code&gt;&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;Processor&lt;/code&gt; - The current &lt;code&gt;Processor&lt;/code&gt; instance will copy this &lt;code&gt;Processor&lt;/code&gt;'s plugins&lt;/li&gt;
&lt;/ul&gt;

</description>
      <category>postcss</category>
      <category>underthehood</category>
      <category>sourcecode</category>
    </item>
    <item>
      <title>PostCSS: Input and other modules source code walk-through</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Sun, 09 Jan 2022 02:40:59 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/postcss-input-and-other-modules-source-code-walk-through-56g1</link>
      <guid>https://dev.to/itzsrikanth/postcss-input-and-other-modules-source-code-walk-through-56g1</guid>
      <description>&lt;h2&gt;
  
  
  Terminal Highlight
&lt;/h2&gt;

&lt;p&gt;Purpose of this module is to enable syntax highlight while printing the stringified CSS (after transformation) to the terminal. &lt;code&gt;picocolors&lt;/code&gt; is used for this (similar to &lt;code&gt;chalk&lt;/code&gt; npm package). For each token, a specific color is defined as a map.&lt;/p&gt;

&lt;h4&gt;
  
  
  getTokenType
&lt;/h4&gt;

&lt;p&gt;When the type is &lt;code&gt;word&lt;/code&gt;, it is very generic and we need to classify them as &lt;code&gt;hash&lt;/code&gt; or &lt;code&gt;class&lt;/code&gt;. Using &lt;code&gt;Tokenizer&lt;/code&gt;, forward lookup is done to detect &lt;code&gt;bracket&lt;/code&gt; or &lt;code&gt;parentheses&lt;/code&gt;.&lt;/p&gt;

&lt;h4&gt;
  
  
  terminalHighlight
&lt;/h4&gt;

&lt;p&gt;Get &lt;code&gt;Processor&lt;/code&gt; instance from &lt;code&gt;Tokenizer&lt;/code&gt; initialization and until &lt;code&gt;EOF&lt;/code&gt; is reached, wrap all the tokens using &lt;code&gt;picocolors&lt;/code&gt; by splitting them by newline character.&lt;/p&gt;

&lt;h2&gt;
  
  
  Input
&lt;/h2&gt;

&lt;p&gt;This takes in CSS as &lt;code&gt;String&lt;/code&gt; type as first argument. The main purpose of this entity is to store CSS, origin, sourcemap and to provide associated functionalities listed below. The steps to initialize are:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Error handling&lt;/li&gt;
&lt;li&gt;
&lt;a href="https://www.w3.org/International/questions/qa-byte-order-mark" rel="noopener noreferrer"&gt;BOM&lt;/a&gt; check and handling&lt;/li&gt;
&lt;li&gt;When &lt;code&gt;from&lt;/code&gt; is specified, it is check if value is a network path or absolute path. Else it is resolved using &lt;code&gt;path&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;When &lt;code&gt;from&lt;/code&gt; is not specified, &lt;code&gt;id&lt;/code&gt; is generated using &lt;code&gt;nanoid&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;Source map added if available, generated from compilation step before PostCSS kicks in.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  fromOffset
&lt;/h4&gt;

&lt;p&gt;Purpose of this method is to return line and column number when offset is provided.&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;CSS string is split by &lt;code&gt;\n&lt;/code&gt; and stored as &lt;code&gt;Array&amp;lt;string&amp;gt;&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;The no of characters in each line is counted incrementally (including the newline), say, if there are 10 lines with each line having 20 characters. The corresponding array created is:
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="nx"&gt;lineToIndex&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;20&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;40&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;60&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;...&lt;/span&gt; &lt;span class="mi"&gt;200&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;This is stored as cache with &lt;code&gt;Symbol('fromOffsetCache')&lt;/code&gt;. Using this the line number and column number is determined in &lt;code&gt;O(log n)&lt;/code&gt; complexity similar to searching sorted Array.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  error
&lt;/h4&gt;

&lt;p&gt;Returns &lt;code&gt;CssSyntaxError&lt;/code&gt;&lt;br&gt;
Parameters are:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;error message (&lt;code&gt;string&lt;/code&gt;)&lt;/li&gt;
&lt;li&gt;any one of:

&lt;ul&gt;
&lt;li&gt;both line and column as &lt;code&gt;{offset?:number; line:number; col:number}&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;line (&lt;code&gt;number&lt;/code&gt;) and column (&lt;code&gt;null&lt;/code&gt;)&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;opts (&lt;code&gt;{plugins: any}&lt;/code&gt;)&lt;/li&gt;

&lt;li&gt;If &lt;code&gt;offset&lt;/code&gt; is present, &lt;code&gt;FilePosition&lt;/code&gt; is determined using &lt;code&gt;fromOffset()&lt;/code&gt;.&lt;/li&gt;

&lt;/ul&gt;

&lt;p&gt;Steps:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;generate the start and end line-column numbers from parameters (which is &lt;code&gt;FilePosition&lt;/code&gt;) and pass to &lt;code&gt;CssSyntaxError&lt;/code&gt; to get &lt;code&gt;result&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;Add &lt;code&gt;{...FilePosition, source, url}&lt;/code&gt; to &lt;code&gt;result&lt;/code&gt;
&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  origin
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;return &lt;code&gt;false&lt;/code&gt; if

&lt;ul&gt;
&lt;li&gt;not having map, or &lt;/li&gt;
&lt;li&gt;map not having source&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;get sourcemap consumer to get the original &lt;code&gt;FilePosition&lt;/code&gt; data before previous stage compilation&lt;/li&gt;

&lt;li&gt;Add &lt;code&gt;url&lt;/code&gt;, &lt;code&gt;source&lt;/code&gt; (&lt;code&gt;sourceContent&lt;/code&gt;) from consumer to &lt;code&gt;FilePosition&lt;/code&gt;
&lt;/li&gt;

&lt;/ul&gt;

&lt;h4&gt;
  
  
  mapResolve
&lt;/h4&gt;

&lt;p&gt;Takes in file path and checks if it has protocol like &lt;code&gt;file://&lt;/code&gt; or &lt;code&gt;http://&lt;/code&gt;. Else, it resolves path from map source.&lt;/p&gt;

&lt;h4&gt;
  
  
  from (getter)
&lt;/h4&gt;

&lt;p&gt;Returns &lt;code&gt;file&lt;/code&gt; or &lt;code&gt;nanoid&lt;/code&gt; generated &lt;code&gt;id&lt;/code&gt; &lt;/p&gt;

&lt;h4&gt;
  
  
  toJSON
&lt;/h4&gt;

&lt;p&gt;Adds the following keys:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;hasBOM&lt;/li&gt;
&lt;li&gt;css&lt;/li&gt;
&lt;li&gt;file&lt;/li&gt;
&lt;li&gt;id&lt;/li&gt;
&lt;li&gt;map
and remove the map.consumerCache&lt;/li&gt;
&lt;/ul&gt;

</description>
      <category>postcss</category>
      <category>underthehood</category>
      <category>sourcecode</category>
    </item>
    <item>
      <title>PostCSS: Architecture overview</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Sun, 09 Jan 2022 02:40:32 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/postcss-architecture-overview-4lem</link>
      <guid>https://dev.to/itzsrikanth/postcss-architecture-overview-4lem</guid>
      <description>&lt;p&gt;I am a big fan of &lt;code&gt;PostCSS&lt;/code&gt; and this is my attempt to understand this package to become an active contributor. I am planning to write a series involving architecture, code walk-through for this amazing package and its top plugins. &lt;/p&gt;

&lt;p&gt;Before diving into very low level details, reading this &lt;a href="https://github.com/postcss/postcss/blob/main/docs/architecture.md" rel="noopener noreferrer"&gt;architecture&lt;/a&gt; is a must. Almost all of the low level detailed info are available in &lt;a href="https://postcss.org/api/" rel="noopener noreferrer"&gt;API page&lt;/a&gt; with multiple theoretical example, generated from static typing &lt;code&gt;jsDoc&lt;/code&gt;. The intention of this series is to provide them in digestible and pragmatic way.  For that many references from &lt;code&gt;PostCSS&lt;/code&gt; plugins will be drawn. This will get extended by diving deep into the codebase as well. As mentioned in the arch doc, the AST conversion is split into. two parts: tokenization and parsing for performance reasons. Lets get started with the basics:&lt;/p&gt;

&lt;p&gt;Everything is a &lt;code&gt;Node&lt;/code&gt; here. The statement is too generic but what it means is the CSS is converted into a tree structure. Which means that many tokens in stylesheet are converted into &lt;code&gt;Node&lt;/code&gt; to form the hierarchical structure. To illustrate this, lets take an example:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight css"&gt;&lt;code&gt;&lt;span class="nc"&gt;.active&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="nl"&gt;transform&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;scale&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="m"&gt;1.1&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;Here, this stylesheet is stored as a series of characters. They are read character by character and converted into tokens. The tokens are then parsed by the parser and converted into the AST structure, which sets the stage for all the plugins to work their magic. So, this is a 2-stage process.&lt;/p&gt;

&lt;p&gt;Lets understand the above code structure after tokenization:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;.active
{
transform
:
scale(1.1)
;
}
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;It is converted into 7 tokens. These tokens are consumed by &lt;code&gt;Parser&lt;/code&gt; using &lt;code&gt;nextToken()&lt;/code&gt; in &lt;code&gt;Tokenizer&lt;/code&gt;.&lt;/p&gt;

</description>
      <category>postcss</category>
      <category>underthehood</category>
      <category>architecture</category>
    </item>
    <item>
      <title>Web Accessibility learned, the hard way...</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Tue, 04 Jan 2022 08:17:55 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/web-accessibility-learned-the-hard-way-2pad</link>
      <guid>https://dev.to/itzsrikanth/web-accessibility-learned-the-hard-way-2pad</guid>
      <description>&lt;p&gt;This post is going to be my ever updating journal to record many learnings which I learned by implementation, from peers, some hints from blogs, sites etc. Main intent is to record everything that is not available in stackoverflow and links for everything available in stackoverflow for reference on &lt;code&gt;a11y&lt;/code&gt;.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Screen readers used&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Voiceover (iOSv15)&lt;/li&gt;
&lt;li&gt;Android Talkback&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  Cookbook recipes
&lt;/h2&gt;

&lt;h4&gt;
  
  
  List item element receiving focus, announcing "bullet"
&lt;/h4&gt;

&lt;p&gt;CSS can help fix this issue by saying &lt;code&gt;list-style-type: none&lt;/code&gt;&lt;/p&gt;

&lt;h4&gt;
  
  
  Link vs Button on pages
&lt;/h4&gt;

&lt;p&gt;When we have a user action causing redirection/navigation to another URL, the &lt;code&gt;role&lt;/code&gt; should be &lt;code&gt;link&lt;/code&gt;. But in cases where the user actions is causing pop-ups etc, it should be &lt;code&gt;button&lt;/code&gt;.&lt;/p&gt;

&lt;h4&gt;
  
  
  Using flexbox to prevent screen-reader focus
&lt;/h4&gt;

&lt;p&gt;I have not come across any articles explaining this, but when we have the children as &lt;code&gt;flexbox&lt;/code&gt;, the screen-reader just focuses on parent container. If you have &lt;code&gt;aria-label&lt;/code&gt; on the parent to &lt;code&gt;flexbox&lt;/code&gt;, it reads it. Else falls back to reading the contents combined.&lt;br&gt;
&lt;iframe height="600" src="https://codepen.io/snow650/embed/qBPKbQK?height=600&amp;amp;default-tab=result&amp;amp;embed-version=2"&gt;
&lt;/iframe&gt;
&lt;/p&gt;

&lt;h4&gt;
  
  
  Removing &lt;code&gt;tabindex&lt;/code&gt; for talkback to prevent focus
&lt;/h4&gt;

&lt;p&gt;In Android, when we have &lt;code&gt;tabindex&lt;/code&gt; set, it becomes eligible for receiving focus, irrespective of its value. So, its text contents are read. Removal of that attribute prevents the focus.&lt;/p&gt;

&lt;h4&gt;
  
  
  Announcing status or toast updates
&lt;/h4&gt;

&lt;h5&gt;
  
  
  using HTML attributes
&lt;/h5&gt;

&lt;p&gt;This method involves creating a &lt;code&gt;live-region&lt;/code&gt; and setting politeness for announcing the alerts.&lt;/p&gt;

&lt;h5&gt;
  
  
  using JS
&lt;/h5&gt;

&lt;p&gt;This itself involves having multiple approaches. One of them is to create a singleton placeholder and push content inside this region. The attributes like &lt;code&gt;aria-hidden&lt;/code&gt;, &lt;code&gt;aria-live&lt;/code&gt; etc needs to be set and this can be unset after some fixed/dynamic timeout duration.&lt;/p&gt;

&lt;h4&gt;
  
  
  Focus elements on page load in voiceover in Javascript
&lt;/h4&gt;

&lt;p&gt;&lt;a href="https://linkedlist.ch/setting_voiceover_focus_with_javascript_17/" rel="noopener noreferrer"&gt;This is the best&lt;/a&gt; I have come across to achieve this. Tried using various &lt;code&gt;focusInterval&lt;/code&gt; with &lt;code&gt;setTimeout&lt;/code&gt; instead of &lt;code&gt;setInterval&lt;/code&gt; but faced certain drawbacks each time.&lt;br&gt;
When &lt;code&gt;30ms&lt;/code&gt; is used with &lt;code&gt;setTimeout&lt;/code&gt;, focus was missing for some cases. With &lt;code&gt;50ms&lt;/code&gt;, the default focus announces an element followed by shift in focus to read the current one.&lt;/p&gt;

&lt;h2&gt;
  
  
  Understanding screen reader behaviours
&lt;/h2&gt;

&lt;h4&gt;
  
  
  &lt;code&gt;tabindex&lt;/code&gt; interpretation
&lt;/h4&gt;

&lt;p&gt;&lt;iframe height="600" src="https://codepen.io/snow650/embed/MWERYbJ?height=600&amp;amp;default-tab=result&amp;amp;embed-version=2"&gt;
&lt;/iframe&gt;
&lt;br&gt;
In the codepen above, various scenarios of &lt;code&gt;tabindex&lt;/code&gt; are added on both parent and child. In &lt;code&gt;voiceover&lt;/code&gt; the &lt;code&gt;tabindex&lt;/code&gt; attributes are not considered much and screen-reader focuses mainly on presence of text/content rather than the attribute. Whereas for &lt;code&gt;talkback&lt;/code&gt;, based on how we specify the &lt;code&gt;tabindex&lt;/code&gt; the behaviour changes drastically. Example:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;When we have &lt;code&gt;tabindex&lt;/code&gt; only on parent&lt;/strong&gt;: the focus does not come to the child element since the parent already has the attribute.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;When both parent and child has the attribute&lt;/strong&gt;: the focus comes to both of them and inner content read repetition happens.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;When there in attribute only on child&lt;/strong&gt;: it is equivalent of no attribute because the child being a text node, it will naturally receive the focus.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;No attribute anywhere&lt;/strong&gt;: same as case 3&lt;/li&gt;
&lt;/ul&gt;

</description>
      <category>a11y</category>
    </item>
    <item>
      <title>Generic list of dev features required to bootstrap a great frontend project</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Sun, 02 Jan 2022 07:04:14 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/generic-list-of-dev-features-required-to-bootstrap-a-great-frontend-project-12op</link>
      <guid>https://dev.to/itzsrikanth/generic-list-of-dev-features-required-to-bootstrap-a-great-frontend-project-12op</guid>
      <description>&lt;p&gt;Bootstrapping a new project from scratch or creating a generic boilerplate code is not an easy task when seen from a long time duration standpoint. The perspective and requirements might change rapidly if not analyzed minutely. I am listing here few of the implementations that I have included in many of my official and pet-projects:&lt;/p&gt;

&lt;h3&gt;
  
  
  CSS implementations
&lt;/h3&gt;

&lt;p&gt;There are a variety of solutions available for adding stylings to your project including the new way of CSS-in-JS. But each has their own pros and cons. They must chosen based on the type of project. I will include more elaboration on my next post but in short, as an example, the requirements of a website is very different from that of a WebApp or a hybrid mobile application.&lt;/p&gt;

&lt;p&gt;In websites, the metrics like TTFB, FCP, CLS etc plays a vital role (&lt;a href="https://web.dev/metrics/" rel="noopener noreferrer"&gt;source&lt;/a&gt;) in not only in enhancing the user experience but also is a big contributor towards the terms like SEO, marketing expenditure, churn rate and ultimately in overall revenue. So, JS executions might take a lot of time to reflect the styles when compared to CSS counterparts. We might not benefit from CSS-in-JS solutions here unless it is extracted as separate stylesheet using some plugins like &lt;a href="https://webpack.js.org/plugins/mini-css-extract-plugin/" rel="noopener noreferrer"&gt;MiniCssExtractPlugin&lt;/a&gt;.&lt;/p&gt;

&lt;p&gt;The same metrics are important for WebApp as well but no web-crawler is going to penalize your SEO value or others. But once your app warms up, you need to have reactive performance and a great frame rate, silky smooth navigations etc similar to a native app.&lt;/p&gt;

&lt;h5&gt;
  
  
  CSS Modules
&lt;/h5&gt;

&lt;p&gt;This brings in best of both worlds and could be very subjective. But I am happy that I do not have to spend effort in thinking of a long class name based on BEM, SMACSS etc.&lt;/p&gt;

&lt;h3&gt;
  
  
  JS implementations
&lt;/h3&gt;

&lt;h5&gt;
  
  
  A global loader for all API/Ajax calls
&lt;/h5&gt;

&lt;p&gt;It should be initialized as a singleton and a counter should be provisioned in such a way that when no of pending calls is zero, it is hidden. In other cases it should be visible&lt;/p&gt;

&lt;h5&gt;
  
  
  Common Modals / Drawer widgets
&lt;/h5&gt;

&lt;h3&gt;
  
  
  Project configuration
&lt;/h3&gt;

&lt;h5&gt;
  
  
  Linters
&lt;/h5&gt;

&lt;ul&gt;
&lt;li&gt;Code linting&lt;/li&gt;
&lt;li&gt;Commit message linting like &lt;a href="https://www.npmjs.com/package/commitizen" rel="noopener noreferrer"&gt;commitizen&lt;/a&gt;
&lt;/li&gt;
&lt;/ul&gt;

&lt;h5&gt;
  
  
  In case of multi-package project usage of tools
&lt;/h5&gt;

&lt;p&gt;like:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;&lt;a href="https://npmjs.com/package/lerna" rel="noopener noreferrer"&gt;lerna&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://rushjs.io/" rel="noopener noreferrer"&gt;rush&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;h5&gt;
  
  
  Managing environment configs using
&lt;/h5&gt;

&lt;ul&gt;
&lt;li&gt;&lt;a href="https://www.npmjs.com/package/dotenv" rel="noopener noreferrer"&gt;dotenv&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;h5&gt;
  
  
  &lt;a href="https://www.npmjs.com/package/@vercel/ncc" rel="noopener noreferrer"&gt;Compiling a Node.js module into a single file&lt;/a&gt;
&lt;/h5&gt;

&lt;p&gt;This is not a mandatory process, but for some cases this can help avoid the &lt;code&gt;npm&lt;/code&gt; modules installation step by converting all the &lt;code&gt;node_modules&lt;/code&gt; dependencies into a single JS file.&lt;/p&gt;

&lt;h5&gt;
  
  
  Project automation packages
&lt;/h5&gt;

&lt;ul&gt;
&lt;li&gt;&lt;a href="https://www.npmjs.com/package/scripty" rel="noopener noreferrer"&gt;Scripty&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://www.npmjs.com/package/husky" rel="noopener noreferrer"&gt;Husky&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

</description>
      <category>tutorial</category>
      <category>webdev</category>
      <category>programming</category>
      <category>javascript</category>
    </item>
    <item>
      <title>New to Java, my journey so far...</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Sun, 21 Nov 2021 16:06:13 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/new-to-java-my-journey-so-far-3fne</link>
      <guid>https://dev.to/itzsrikanth/new-to-java-my-journey-so-far-3fne</guid>
      <description>&lt;h1&gt;
  
  
  Introduction
&lt;/h1&gt;

&lt;p&gt;Talked to few senior backend engineers before my dive into Java. One valuable suggestion was to learn &lt;code&gt;Class&lt;/code&gt;, &lt;code&gt;Abstract class&lt;/code&gt; and &lt;code&gt;Interface&lt;/code&gt;. Some of good articles are:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;&lt;a href="https://www.infoworld.com/article/2076841/designing-with-interfaces.html" rel="noopener noreferrer"&gt;Designing with interfaces&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://phrase.com/blog/posts/guide-to-the-icu-message-format/" rel="noopener noreferrer"&gt;ICU Internationalization (i18n)&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

</description>
      <category>java</category>
      <category>programming</category>
      <category>webdev</category>
    </item>
    <item>
      <title>Dev blog posts that helped me in frontend journey</title>
      <dc:creator>itzsrikanth</dc:creator>
      <pubDate>Sun, 17 Oct 2021 10:29:57 +0000</pubDate>
      <link>https://dev.to/itzsrikanth/dev-blog-posts-that-helped-me-in-frontend-journey-87</link>
      <guid>https://dev.to/itzsrikanth/dev-blog-posts-that-helped-me-in-frontend-journey-87</guid>
      <description>&lt;p&gt;There any many useful resources and some awesome guides like &lt;a href="https://roadmap.sh/" rel="noopener noreferrer"&gt;roadmap.sh&lt;/a&gt; which gives good perspective of where we stand. Apart from those there are few other blogs that I would like to highlight, like:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;a href="https://blog.theodo.com/2021/04/library-tree-shaking/" rel="noopener noreferrer"&gt;Theodo blog&lt;/a&gt; about JS library tree shaking and related module concept.&lt;/li&gt;
&lt;li&gt;
&lt;a href="https://www.joshwcomeau.com/css/stacking-contexts/" rel="noopener noreferrer"&gt;Josh Comeau's blog&lt;/a&gt; on &lt;code&gt;z-index&lt;/code&gt; stacking introduced me to his CSS courses.&lt;/li&gt;
&lt;li&gt;&lt;a href="https://www.michaelmang.dev/blog/" rel="noopener noreferrer"&gt;michaelmang&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://kruschecompany.com/ember-jQuery-angular-react-vue-what-to-choose/" rel="noopener noreferrer"&gt;Guide to help choose frameworks | kruschecompany.com&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://usehooks.com/" rel="noopener noreferrer"&gt;usehooks.com&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="http://dmitrysoshnikov.com/ecmascript/javascript-the-core/" rel="noopener noreferrer"&gt;Understanding the core JavaScript | dmitrysoshnikov.com&lt;/a&gt;&lt;/li&gt;
&lt;li&gt;&lt;a href="https://www.patterns.dev/" rel="noopener noreferrer"&gt;https://www.patterns.dev/&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  React Native
&lt;/h2&gt;

&lt;ul&gt;
&lt;li&gt;&lt;a href="https://kadikraman.github.io/react-native-beyond-basics/docs/welcome/" rel="noopener noreferrer"&gt;React Native - Beyond Basics | kadikraman.github.io&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  Webpack
&lt;/h2&gt;

&lt;ul&gt;
&lt;li&gt;&lt;a href="https://engineering.tines.com/blog/understanding-why-our-build-got-15x-slower-with-webpack" rel="noopener noreferrer"&gt;Node v8 deep-dive webpack 5 fix | engineering.tines.com&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  Mobile browsers
&lt;/h2&gt;

&lt;ul&gt;
&lt;li&gt;&lt;a href="https://developer.mozilla.org/en-US/docs/Web/API/Intersection_Observer_API/Timing_element_visibility" rel="noopener noreferrer"&gt;MDN | Detect tab switches and browser app sleep/awake cycle&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  Build tools
&lt;/h2&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;a href="//solitr.com/blog/2014/02/broccoli-first-release/"&gt;Broccoli blog&lt;/a&gt; gives overall architecture and comparison with &lt;code&gt;gulp&lt;/code&gt; and &lt;code&gt;grunt&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;
&lt;a href="https://hacks.mozilla.org/2013/05/compiling-to-javascript-and-debugging-with-source-maps/" rel="noopener noreferrer"&gt;Compiling to JavaScript, and Debugging with Source Maps&lt;/a&gt;, along with &lt;a href="https://docs.google.com/document/d/1U1RGAehQwRypUTovF1KRlpiOFze0b-_2gc6fAH0KY0k/edit" rel="noopener noreferrer"&gt;Source Map Revision 3 Proposal&lt;/a&gt;
&lt;/li&gt;
&lt;li&gt;&lt;a href="https://tomdale.net/2017/04/making-the-jump/" rel="noopener noreferrer"&gt;New insights on modern frameworks, 2017&lt;/a&gt;&lt;/li&gt;
&lt;/ul&gt;

</description>
      <category>webdev</category>
      <category>frontend</category>
    </item>
  </channel>
</rss>
