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    <title>DEV Community: Piyush Chauhan</title>
    <description>The latest articles on DEV Community by Piyush Chauhan (@frorning).</description>
    <link>https://dev.to/frorning</link>
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      <title>DEV Community: Piyush Chauhan</title>
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      <title>Backtracking Unveiled: Mastering Depth-First Search and Pruning Techniques</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Sat, 22 Feb 2025 09:04:27 +0000</pubDate>
      <link>https://dev.to/frorning/backtracking-unveiled-mastering-depth-first-search-and-pruning-techniques-251c</link>
      <guid>https://dev.to/frorning/backtracking-unveiled-mastering-depth-first-search-and-pruning-techniques-251c</guid>
      <description>&lt;p&gt;Backtracking is a systematic way to iterate through all possible configurations of a problem. It is often used to solve problems where a sequence of decisions must be made, and each decision leads to a new set of possibilities. Backtracking uses &lt;strong&gt;depth-first search (DFS)&lt;/strong&gt; to explore the state space, and it employs &lt;strong&gt;pruning functions&lt;/strong&gt; to eliminate invalid or suboptimal paths early in the search process.&lt;/p&gt;




&lt;h3&gt;
  
  
  Components of Backtracking Problems
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Initial State&lt;/strong&gt;: The starting point of the problem.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Target/Goal State&lt;/strong&gt;: The desired solution.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Intermediate States&lt;/strong&gt;: States generated while moving from the initial state to the target state.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Path&lt;/strong&gt;: The sequence of states from the initial state to the target state.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Operators&lt;/strong&gt;: Rules or actions that transform one state into another.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pruning Function&lt;/strong&gt;: A heuristic to eliminate invalid or suboptimal states early.&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  Backtracking Algorithm
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;Start with the initial state.&lt;/li&gt;
&lt;li&gt;Use DFS to explore all possible states.&lt;/li&gt;
&lt;li&gt;If a state is invalid (based on the pruning function), backtrack and try another path.&lt;/li&gt;
&lt;li&gt;If a state is the goal state, return the solution.&lt;/li&gt;
&lt;li&gt;Repeat until all possible states are explored or a solution is found.&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  Example Problems Solved Using Backtracking
&lt;/h3&gt;

&lt;h4&gt;
  
  
  1. &lt;strong&gt;3-Digit Lock Problem&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Initial State&lt;/strong&gt;: "111"&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Target State&lt;/strong&gt;: The correct combination (e.g., "352")&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Operators&lt;/strong&gt;: Increment each digit by 1 (from 1 to 9).&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pruning Function&lt;/strong&gt;: If a digit is correct (e.g., produces a "click"), fix it and move to the next digit.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Implementation:
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;findLockCombination&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;combination&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;combination&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Found combination:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;combination&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;index&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&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="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="mi"&gt;9&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;newCombination&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;combination&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;slice&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="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;combination&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;slice&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;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="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newCombination&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;index&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Click at position&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;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="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;with digit&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
                &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newCombination&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;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="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;111&lt;/span&gt;&lt;span class="dl"&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="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;targetCombination&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;352&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="nf"&gt;findLockCombination&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;targetCombination&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h4&gt;
  
  
  2. &lt;strong&gt;Monks and Demons Problem&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Initial State&lt;/strong&gt;: 3 monks, 3 demons, and the boat on the left shore.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Target State&lt;/strong&gt;: All monks and demons on the right shore.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Operators&lt;/strong&gt;: Move 1 or 2 people in the boat.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pruning Function&lt;/strong&gt;: Ensure that monks are never outnumbered by demons on either shore.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Implementation:
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;solveMonksAndDemons&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;initialState&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;left&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;monks&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="na"&gt;demons&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="na"&gt;right&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;monks&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="na"&gt;demons&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="na"&gt;boat&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Set&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;

    &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;isSafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;return &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
            &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
            &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&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="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;JSON&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;stringify&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;has&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="nx"&gt;visited&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="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Solution found:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;

        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;moves&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;monks&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="na"&gt;demons&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="na"&gt;monks&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;demons&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="na"&gt;monks&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="na"&gt;demons&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="na"&gt;monks&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="na"&gt;demons&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="na"&gt;monks&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="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="p"&gt;];&lt;/span&gt;

        &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt; &lt;span class="k"&gt;of&lt;/span&gt; &lt;span class="nx"&gt;moves&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
                &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&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="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;right&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&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="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                    &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
                    &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
                &lt;span class="p"&gt;};&lt;/span&gt;
                &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                    &lt;span class="na"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;right&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;monks&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
                    &lt;span class="na"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;right&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;demons&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
                &lt;span class="p"&gt;};&lt;/span&gt;
                &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;newState&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                    &lt;span class="na"&gt;left&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                    &lt;span class="na"&gt;right&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
                    &lt;span class="na"&gt;boat&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&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;right&lt;/span&gt;&lt;span class="dl"&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;left&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="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;isSafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
                &lt;span class="p"&gt;}&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;initialState&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="nf"&gt;solveMonksAndDemons&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h4&gt;
  
  
  3. &lt;strong&gt;Farmer, Goat, Cabbage, and Wolf Problem&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Initial State&lt;/strong&gt;: Farmer, goat, cabbage, and wolf on the left shore.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Target State&lt;/strong&gt;: All on the right shore.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Operators&lt;/strong&gt;: Farmer can take one item (goat, cabbage, or wolf) in the boat.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pruning Function&lt;/strong&gt;: Ensure the goat is not left alone with the cabbage, and the wolf is not left alone with the goat.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Implementation:
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;solveFarmerProblem&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;initialState&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;left&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;farmer&lt;/span&gt;&lt;span class="dl"&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;goat&lt;/span&gt;&lt;span class="dl"&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;cabbage&lt;/span&gt;&lt;span class="dl"&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;wolf&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
    &lt;span class="na"&gt;right&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[],&lt;/span&gt;
    &lt;span class="na"&gt;boat&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&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="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Set&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;

  &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;isSafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;unsafe&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;
      &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;goat&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
        &lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;cabbage&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
        &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt;
      &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;wolf&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
        &lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;goat&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
        &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;side&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;includes&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;unsafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="nf"&gt;unsafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;stateKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;JSON&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;stringify&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Solution found:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;stateKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;has&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="nx"&gt;visited&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="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;fromShore&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="c1"&gt;// Possible moves: Farmer alone or Farmer + one item&lt;/span&gt;
    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;item&lt;/span&gt; &lt;span class="k"&gt;of&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;fromShore&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kc"&gt;null&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="kc"&gt;null&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="nx"&gt;item&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&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="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
        &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&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="nx"&gt;newLeft&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;newLeft&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="nx"&gt;x&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
          &lt;span class="nx"&gt;newRight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;newRight&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
          &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
          &lt;span class="nx"&gt;newRight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;newRight&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="nx"&gt;x&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;!==&lt;/span&gt; &lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
          &lt;span class="nx"&gt;newLeft&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;newLeft&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;farmer&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
          &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;

        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;newState&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
          &lt;span class="na"&gt;left&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;newLeft&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
          &lt;span class="na"&gt;right&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;newRight&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
          &lt;span class="na"&gt;boat&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;boat&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;left&lt;/span&gt;&lt;span class="dl"&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;right&lt;/span&gt;&lt;span class="dl"&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;left&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="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;isSafe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;newState&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
          &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
      &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;initialState&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="nf"&gt;solveFarmerProblem&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h4&gt;
  
  
  4. &lt;strong&gt;Water Jug Problem&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Initial State&lt;/strong&gt;: Both jugs are empty.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Target State&lt;/strong&gt;: 2 gallons in the 4-gallon jug.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Operators&lt;/strong&gt;: Fill, empty, or pour water between jugs.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pruning Function&lt;/strong&gt;: Avoid revisiting states.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  Implementation:
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;solveWaterJug&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;initialState&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;jug4&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="na"&gt;jug3&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="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;target&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="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Set&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;

    &lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;,&lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;has&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="nx"&gt;visited&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="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;jug4&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="nx"&gt;target&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Solution found:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;

        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;jug3&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;state&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;moves&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;jug4&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="nx"&gt;jug3&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="c1"&gt;// Fill jug4&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;jug3&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;// Fill jug3&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;jug4&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="nx"&gt;jug3&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="c1"&gt;// Empty jug4&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;jug3&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;// Empty jug3&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;max&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="nx"&gt;jug4&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="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;)),&lt;/span&gt; &lt;span class="na"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;min&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="nx"&gt;jug3&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="c1"&gt;// Pour jug4 to jug3&lt;/span&gt;
            &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;min&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="nx"&gt;jug4&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="na"&gt;jug3&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;max&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="nx"&gt;jug3&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;jug4&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="c1"&gt;// Pour jug3 to jug4&lt;/span&gt;
        &lt;span class="p"&gt;];&lt;/span&gt;

        &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt; &lt;span class="k"&gt;of&lt;/span&gt; &lt;span class="nx"&gt;moves&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;[...&lt;/span&gt;&lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;move&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
                &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
            &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="nf"&gt;backtrack&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;initialState&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="nf"&gt;solveWaterJug&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  Key Points:
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;Backtracking is a &lt;strong&gt;systematic way&lt;/strong&gt; to explore all possible solutions.&lt;/li&gt;
&lt;li&gt;It uses &lt;strong&gt;depth-first search&lt;/strong&gt; and &lt;strong&gt;pruning functions&lt;/strong&gt; to eliminate invalid paths.&lt;/li&gt;
&lt;li&gt;It is useful for solving &lt;strong&gt;NP-hard problems&lt;/strong&gt; like puzzles, constraint satisfaction problems, and combinatorial optimization.&lt;/li&gt;
&lt;/ol&gt;

</description>
      <category>javascript</category>
      <category>algorithms</category>
      <category>programming</category>
      <category>beginners</category>
    </item>
    <item>
      <title>A* Search Algorithm and Iterative Deepening A* in JavaScript</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Sat, 08 Feb 2025 05:44:55 +0000</pubDate>
      <link>https://dev.to/frorning/a-search-algorithm-and-iterative-deepening-a-in-javascript-4c0o</link>
      <guid>https://dev.to/frorning/a-search-algorithm-and-iterative-deepening-a-in-javascript-4c0o</guid>
      <description>&lt;h3&gt;
  
  
  &lt;strong&gt;1. Introduction&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Search algorithms play a crucial role in solving problems across computer science, robotics, game development, and beyond. Among them, heuristic-based search algorithms stand out for their ability to efficiently find solutions by leveraging additional knowledge about the problem domain. This article delves into two such algorithms: the widely used A* search algorithm and its memory-efficient counterpart, Iterative Deepening A* (IDA*).&lt;/p&gt;

&lt;p&gt;By the end of this article, you will:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Understand the core principles of A* and IDA*.&lt;/li&gt;
&lt;li&gt;Learn how these algorithms work through code implementations in JavaScript.&lt;/li&gt;
&lt;li&gt;Explore their mathematical underpinnings and use cases.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;2. Understanding A* Search Algorithm&lt;/strong&gt;
&lt;/h3&gt;

&lt;h4&gt;
  
  
  What is A*?
&lt;/h4&gt;

&lt;p&gt;A* is a best-first search algorithm that aims to find the shortest path from a start node to a goal node. It uses an evaluation function:&lt;/p&gt;

&lt;p&gt;

&lt;/p&gt;
&lt;div class="katex-element"&gt;
  &lt;span class="katex-display"&gt;&lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;f(n)=g(n)+h(n)
f(n) = g(n) + h(n)
&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;=&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;+&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/div&gt;


&lt;p&gt;Where:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;g(n)g(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
: The cost of the path from the start node to the current node 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;nn &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
.&lt;/li&gt;
&lt;li&gt;
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(n)h(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
: A heuristic estimate of the cost to reach the goal node from 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;nn &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The algorithm prioritizes nodes with the smallest 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;f(n)f(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 value, making it both optimal and complete, provided the heuristic 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(n)h(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 is admissible (never overestimates the true cost).&lt;/p&gt;
&lt;h4&gt;
  
  
  Properties of A*
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Completeness&lt;/strong&gt;: Guaranteed to find a solution if one exists.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Optimality&lt;/strong&gt;: Finds the shortest path with an admissible heuristic.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Admissibility and Consistency&lt;/strong&gt;: Ensures the heuristic is reliable for optimal solutions.&lt;/li&gt;
&lt;/ul&gt;
&lt;h4&gt;
  
  
  &lt;a href="https://en.wikipedia.org/wiki/A*_search_algorithm#Pseudocode" rel="noopener noreferrer"&gt;Wikipedia Pseudocode for A*&lt;/a&gt;
&lt;/h4&gt;


&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;function reconstruct_path(cameFrom, current)
    total_path := {current}
    while current in cameFrom.Keys:
        current := cameFrom[current]
        total_path.prepend(current)
    return total_path

// A* finds a path from start to goal.
// h is the heuristic function. h(n) estimates the cost to reach goal from node n.
function A_Star(start, goal, h)
    // The set of discovered nodes that may need to be (re-)expanded.
    // Initially, only the start node is known.
    // This is usually implemented as a min-heap or priority queue rather than a hash-set.
    openSet := {start}

    // For node n, cameFrom[n] is the node immediately preceding it on the cheapest path from the start
    // to n currently known.
    cameFrom := an empty map

    // For node n, gScore[n] is the currently known cost of the cheapest path from start to n.
    gScore := map with default value of Infinity
    gScore[start] := 0

    // For node n, fScore[n] := gScore[n] + h(n). fScore[n] represents our current best guess as to
    // how cheap a path could be from start to finish if it goes through n.
    fScore := map with default value of Infinity
    fScore[start] := h(start)

    while openSet is not empty
        // This operation can occur in O(Log(N)) time if openSet is a min-heap or a priority queue
        current := the node in openSet having the lowest fScore[] value
        if current = goal
            return reconstruct_path(cameFrom, current)

        openSet.Remove(current)
        for each neighbor of current
            // d(current,neighbor) is the weight of the edge from current to neighbor
            // tentative_gScore is the distance from start to the neighbor through current
            tentative_gScore := gScore[current] + d(current, neighbor)
            if tentative_gScore &amp;lt; gScore[neighbor]
                // This path to neighbor is better than any previous one. Record it!
                cameFrom[neighbor] := current
                gScore[neighbor] := tentative_gScore
                fScore[neighbor] := tentative_gScore + h(neighbor)
                if neighbor not in openSet
                    openSet.add(neighbor)

    // Open set is empty but goal was never reached
    return failure
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;3. Implementing A* in JavaScript&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Below is a JavaScript implementation of A* for a grid-based shortest path problem:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;assert&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;require&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;assert&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="kd"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;PriorityQueue&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="nf"&gt;constructor&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;elements&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[];&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="nf"&gt;enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;priority&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;elements&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;push&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;priority&lt;/span&gt; &lt;span class="p"&gt;});&lt;/span&gt;
    &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;elements&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="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;priority&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;priority&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="nf"&gt;dequeue&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;elements&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;shift&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="nx"&gt;item&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="nf"&gt;isEmpty&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;elements&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;aStar&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;rows&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;cols&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;grid&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="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;openSet&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;PriorityQueue&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
  &lt;span class="nx"&gt;openSet&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&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="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;cameFrom&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;gScore&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;from&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;length&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;rows&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nc"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;fill&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kc"&gt;Infinity&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
  &lt;span class="nx"&gt;gScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;start&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="nx"&gt;start&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;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;fScore&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;from&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;length&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;rows&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt; &lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nc"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cols&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;fill&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kc"&gt;Infinity&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;
  &lt;span class="nx"&gt;fScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;start&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="nx"&gt;start&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="nf"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

  &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;openSet&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isEmpty&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;openSet&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;dequeue&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;x&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;y&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;current&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="nx"&gt;goal&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;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;current&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="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;reconstructPath&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;

    &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;dx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="k"&gt;of&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="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="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;neighbor&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;x&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;dx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;y&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nx"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
      &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

      &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;nx&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;rows&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;ny&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;ny&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;cols&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;tentative_gScore&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;gScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;x&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;y&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

        &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;tentative_gScore&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;gScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
          &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
          &lt;span class="nx"&gt;gScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;tentative_gScore&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
          &lt;span class="nx"&gt;fScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;tentative_gScore&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

          &lt;span class="nx"&gt;openSet&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;enqueue&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;fScore&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&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;span class="k"&gt;return&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&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="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;([&lt;/span&gt;&lt;span class="nx"&gt;x1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;y1&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;x2&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;y2&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;x1&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;x2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nb"&gt;Math&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;abs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;y1&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="nx"&gt;y2&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;reconstructPath&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
  &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;unshift&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;current&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c1"&gt;// Test A* Algorithm&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&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;0&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;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="mi"&gt;0&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;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="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;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;0&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;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
&lt;span class="p"&gt;];&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;start&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;0&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt; &lt;span class="o"&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="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;aStar&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Found Path:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;notStrictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;strictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isArray&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;path&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// Test for no path&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;blockedGrid&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;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;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;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="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="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;noPathResult&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;aStar&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;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;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="nx"&gt;blockedGrid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;strictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;noPathResult&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  &lt;strong&gt;4. Mathematical Proofs and Analysis&lt;/strong&gt;
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Proof of Optimality
&lt;/h4&gt;

&lt;p&gt;A* guarantees the shortest path if the heuristic 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(n)h(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 is admissible and consistent.&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Admissibility&lt;/strong&gt;: 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(n)h(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 never overestimates the true cost to the goal. This ensures that A* will not bypass the optimal path.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Consistency&lt;/strong&gt;: For every pair of nodes 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;nn &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 and 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;n′n' &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, the heuristic satisfies:

&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(n)≤c(n,n′)+h(n′)h(n) \leq c(n, n') + h(n') &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;≤&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;c&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;+&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;

where 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;c(n,n′)c(n, n') &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;c&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 is the cost of transitioning from 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;nn &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 to 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;n′n' &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
. This property ensures that the 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;f(n)f(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 values along a path are non-decreasing.&lt;/li&gt;
&lt;/ol&gt;

&lt;h4&gt;
  
  
  Time and Space Complexity
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Time Complexity&lt;/strong&gt;: In the worst case, A* explores all nodes with 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;f(n)f(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 less than the cost of the optimal solution. This can grow exponentially with the branching factor 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;bb &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;b&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 and the depth 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;dd &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;d&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 of the solution: 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;O(bd)O(b^d) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;b&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mathnormal mtight"&gt;d&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Space Complexity&lt;/strong&gt;: A* stores all explored nodes in memory, leading to 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;O(bd)O(b^d) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;b&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mathnormal mtight"&gt;d&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 space usage.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;5. Limitations of A&lt;/strong&gt;*
&lt;/h3&gt;

&lt;p&gt;While A* is highly efficient for many problems, it has significant limitations:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Memory Requirements&lt;/strong&gt;: Storing all explored nodes can become infeasible for large graphs.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Performance&lt;/strong&gt;: On graphs with high branching factors or inaccurate heuristics, A* may perform poorly.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;6. Iterative Deepening A* (IDA*)&lt;/strong&gt;
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Why IDA*?
&lt;/h4&gt;

&lt;p&gt;IDA* addresses A*'s memory limitations by combining the benefits of A*'s heuristic-guided search with the memory efficiency of depth-first search. Instead of maintaining a priority queue, IDA* performs iterative depth-first searches with increasing 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;ff &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
-cost thresholds.&lt;/p&gt;

&lt;h4&gt;
  
  
  How It Works
&lt;/h4&gt;

&lt;ol&gt;
&lt;li&gt;Initialize the threshold to 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(start)h(start) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;s&lt;/span&gt;&lt;span class="mord mathnormal"&gt;t&lt;/span&gt;&lt;span class="mord mathnormal"&gt;a&lt;/span&gt;&lt;span class="mord mathnormal"&gt;r&lt;/span&gt;&lt;span class="mord mathnormal"&gt;t&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
.&lt;/li&gt;
&lt;li&gt;Perform a depth-first search, pruning paths with 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;f(n)&amp;gt;f(n) &amp;gt; &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;&amp;gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 threshold.&lt;/li&gt;
&lt;li&gt;If no solution is found, increase the threshold to the smallest 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;f(n)f(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 value that exceeded the current threshold.&lt;/li&gt;
&lt;li&gt;Repeat until the goal is reached.&lt;/li&gt;
&lt;/ol&gt;

&lt;h4&gt;
  
  
  &lt;a href="https://en.wikipedia.org/wiki/Iterative_deepening_A*#Pseudocode" rel="noopener noreferrer"&gt;Wikipedia Pseudocode for IDA*&lt;/a&gt;
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;path              current search path (acts like a stack)
node              current node (last node in current path)
g                 the cost to reach current node
f                 estimated cost of the cheapest path (root..node..goal)
h(node)           estimated cost of the cheapest path (node..goal)
cost(node, succ)  step cost function
is_goal(node)     goal test
successors(node)  node expanding function, expand nodes ordered by g + h(node)
ida_star(root)    return either NOT_FOUND or a pair with the best path and its cost

procedure ida_star(root)
    bound := h(root)
    path := [root]
    loop
        t := search(path, 0, bound)
        if t = FOUND then return (path, bound)
        if t = ∞ then return NOT_FOUND
        bound := t
    end loop
end procedure

function search(path, g, bound)
    node := path.last
    f := g + h(node)
    if f &amp;gt; bound then return f
    if is_goal(node) then return FOUND
    min := ∞
    for succ in successors(node) do
        if succ not in path then
            path.push(succ)
            t := search(path, g + cost(node, succ), bound)
            if t = FOUND then return FOUND
            if t &amp;lt; min then min := t
            path.pop()
        end if
    end for
    return min
end function
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  &lt;strong&gt;7. Implementing IDA* in JavaScript&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;idaStar&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;threshold&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

  &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;cameFrom&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;dfs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
      &lt;span class="nx"&gt;start&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="nx"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Set&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;
    &lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;found&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;reconstructPath&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;threshold&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="kc"&gt;Infinity&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&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="nx"&gt;threshold&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;threshold&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="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;dfs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;g&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;f&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;g&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;f&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;threshold&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="na"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;f&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;found&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
  &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;node&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="nx"&gt;goal&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;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nx"&gt;node&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="nx"&gt;goal&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;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;found&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;cameFrom&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;

  &lt;span class="nx"&gt;visited&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="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;toString&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;
  &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;minThreshold&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="kc"&gt;Infinity&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;dx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="k"&gt;of&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="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="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;neighbor&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;node&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="nx"&gt;dx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;node&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="nx"&gt;dy&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;ny&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
      &lt;span class="nx"&gt;nx&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
      &lt;span class="nx"&gt;nx&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
      &lt;span class="nx"&gt;ny&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
      &lt;span class="nx"&gt;ny&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;grid&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="nx"&gt;length&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
      &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;nx&lt;/span&gt;&lt;span class="p"&gt;][&lt;/span&gt;&lt;span class="nx"&gt;ny&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="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;
      &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;has&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;toString&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="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
      &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;dfs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="nx"&gt;neighbor&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;g&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="nx"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;cameFrom&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
        &lt;span class="nx"&gt;visited&lt;/span&gt;
      &lt;span class="p"&gt;);&lt;/span&gt;
      &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;found&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
      &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;threshold&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;minThreshold&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="nx"&gt;minThreshold&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;threshold&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="nx"&gt;visited&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="k"&gt;delete&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;toString&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="na"&gt;threshold&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;minThreshold&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;found&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kc"&gt;false&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;0&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;0&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;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="mi"&gt;0&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;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="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;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;0&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;0&lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;
&lt;span class="p"&gt;];&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;start&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;0&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt; &lt;span class="o"&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="mi"&gt;3&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;pathIdaStar&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;idaStar&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;start&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;goal&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;grid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;IDA* Found Path:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;pathIdaStar&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;notStrictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pathIdaStar&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;strictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;Array&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;isArray&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pathIdaStar&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;blockedGrid&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;
  &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="mi"&gt;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;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;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="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="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;noPathResultIdaStar&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;idaStar&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;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;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="nx"&gt;blockedGrid&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;heuristic&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;assert&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;strictEqual&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;noPathResultIdaStar&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;No path found&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  &lt;strong&gt;8. Comparing A* and IDA&lt;/strong&gt;*
&lt;/h3&gt;

&lt;div class="table-wrapper-paragraph"&gt;&lt;table&gt;
&lt;thead&gt;
&lt;tr&gt;
&lt;th&gt;Feature&lt;/th&gt;
&lt;th&gt;A*&lt;/th&gt;
&lt;th&gt;IDA*&lt;/th&gt;
&lt;/tr&gt;
&lt;/thead&gt;
&lt;tbody&gt;
&lt;tr&gt;
&lt;td&gt;Memory Usage&lt;/td&gt;
&lt;td&gt;High (stores all nodes)&lt;/td&gt;
&lt;td&gt;Low (depth-first search)&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Speed&lt;/td&gt;
&lt;td&gt;Faster for smaller graphs&lt;/td&gt;
&lt;td&gt;Slower due to iterative nature&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Implementation Complexity&lt;/td&gt;
&lt;td&gt;Moderate&lt;/td&gt;
&lt;td&gt;Higher&lt;/td&gt;
&lt;/tr&gt;
&lt;tr&gt;
&lt;td&gt;Suitability for Large Graphs&lt;/td&gt;
&lt;td&gt;Limited&lt;/td&gt;
&lt;td&gt;More suitable&lt;/td&gt;
&lt;/tr&gt;
&lt;/tbody&gt;
&lt;/table&gt;&lt;/div&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;9. Use Cases&lt;/strong&gt;
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Game Development&lt;/strong&gt;: Pathfinding for characters and AI in games (e.g., NPC movement).&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Robotics&lt;/strong&gt;: Navigation for autonomous robots in real-world environments.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Network Routing&lt;/strong&gt;: Finding the shortest paths in network graphs.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Puzzle Solving&lt;/strong&gt;: Solving puzzles like the 8-puzzle or 15-puzzle efficiently.&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;10. Common Pitfalls and Best Practices&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;When implementing and applying A* or IDA*, it’s essential to avoid common mistakes and adopt best practices to ensure optimal performance.&lt;/p&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;1. Choosing Heuristics Wisely&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Admissibility&lt;/strong&gt;: Ensure that the heuristic never overestimates the cost to reach the goal. This guarantees that A* will find the optimal solution.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Consistency (Monotonicity)&lt;/strong&gt;: Verify that the heuristic satisfies the triangle inequality: 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(n)≤c(n,n′)+h(n′)h(n) \leq c(n, n') + h(n') &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;≤&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;c&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mpunct"&gt;,&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;+&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;&lt;span class="mord mtight"&gt;′&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
. This ensures that the algorithm’s 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;f(n)f(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 values are non-decreasing.&lt;/li&gt;
&lt;li&gt;Common heuristics include:

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Manhattan Distance&lt;/strong&gt;: Suitable for grid-based problems where movement is restricted to horizontal or vertical directions.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Euclidean Distance&lt;/strong&gt;: Best for problems allowing diagonal or free movement in a continuous space.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Domain-Specific Heuristics&lt;/strong&gt;: Tailor heuristics based on specific problem knowledge to improve performance.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;/ul&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;2. Balancing 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;g(n)g(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 and 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(n)h(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;Assign appropriate weights to 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;g(n)g(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 (path cost so far) and 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(n)h(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 (estimated cost to goal).&lt;/li&gt;
&lt;li&gt;Overemphasizing 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(n)h(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 might lead to suboptimal solutions or longer paths.&lt;/li&gt;
&lt;li&gt;Relying heavily on 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;g(n)g(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 might degrade performance, as the algorithm explores more nodes unnecessarily.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;3. Debugging and Visualization Techniques&lt;/strong&gt;
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Visualization&lt;/strong&gt;: Tools like heatmaps or animations of the search process can help debug and optimize the algorithm.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Logging&lt;/strong&gt;: Track 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;f(n)f(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;g(n)g(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, and 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;h(n)h(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 values for each node to identify anomalies.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Unit Testing&lt;/strong&gt;: Validate heuristic functions and graph structures with simple test cases to ensure correctness.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Benchmarking&lt;/strong&gt;: Test the implementation on different datasets to measure performance and identify bottlenecks.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;11. Advanced Topics&lt;/strong&gt;
&lt;/h3&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;1. Variants of A&lt;/strong&gt;*
&lt;/h4&gt;

&lt;p&gt;A* has inspired several variants tailored to specific scenarios or performance needs:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Weighted A&lt;/strong&gt;*:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Modifies the evaluation function to 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;f(n)=g(n)+w⋅h(n)f(n) = g(n) + w \cdot h(n) &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;f&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mrel"&gt;=&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;+&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;w&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;span class="mbin"&gt;⋅&lt;/span&gt;&lt;span class="mspace"&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;h&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, where 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;ww &lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;w&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 (weight) adjusts the heuristic's influence.&lt;/li&gt;
&lt;li&gt;Used to trade optimality for speed by biasing the search toward the goal.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;

&lt;p&gt;&lt;strong&gt;Memory-Bounded A&lt;/strong&gt;*:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Examples include &lt;a href="https://en.wikipedia.org/wiki/SMA*" rel="noopener noreferrer"&gt;Simplified Memory-Bounded A* (SMA*)&lt;/a&gt; and &lt;a href="http://ai-maker.atrilla.net/the-recursive-best-first-search-algorithm/" rel="noopener noreferrer"&gt;Recursive Best-First Search (RBFS)&lt;/a&gt;.&lt;/li&gt;
&lt;li&gt;These variants limit memory usage by discarding or revisiting nodes as needed.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;li&gt;

&lt;p&gt;&lt;strong&gt;&lt;a href="https://aaai.org/papers/079-aaai96-079-hierarchical-a-searching-abstraction-hierarchies-efficiently/" rel="noopener noreferrer"&gt;Hierarchical A*&lt;/a&gt;&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Splits large graphs into smaller subgraphs, solves each independently, and combines results.&lt;/li&gt;
&lt;li&gt;Ideal for complex environments like city navigation.&lt;/li&gt;
&lt;/ul&gt;


&lt;/li&gt;

&lt;/ul&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;2. Integration with Machine Learning&lt;/strong&gt;
&lt;/h4&gt;

&lt;p&gt;Machine learning can enhance A* by dynamically adjusting heuristics or guiding the search process:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Dynamic Heuristics&lt;/strong&gt;: Use neural networks or reinforcement learning to predict better heuristic values for each state.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Adaptive Pathfinding&lt;/strong&gt;: Train models to optimize paths based on historical data or changing environments.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Hybrid Models&lt;/strong&gt;: Combine A* with ML-driven approaches for problems like real-time strategy games or robotics.&lt;/li&gt;
&lt;/ul&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;3. Parallelizing A&lt;/strong&gt;* for Performance Optimization
&lt;/h4&gt;

&lt;p&gt;Parallelization can significantly speed up A* for large graphs:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Parallel Open Set&lt;/strong&gt;: Divide the open set among multiple threads or processes, each exploring a subset of nodes.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Distributed Search&lt;/strong&gt;: Use distributed systems to partition the graph and execute search concurrently.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;GPU Acceleration&lt;/strong&gt;: Leverage GPUs for massive parallelism, especially for heuristic computations and large-scale graph traversal.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;12. Conclusion&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;The A* search algorithm and Iterative Deepening A* are powerful tools for solving pathfinding and graph traversal problems. While A* excels in speed and guarantees optimality with sufficient memory, IDA* offers a memory-efficient alternative for large graphs. By understanding their principles, properties, and implementations, you can leverage these algorithms to tackle a wide range of computational problems effectively.&lt;/p&gt;

</description>
      <category>algorithms</category>
      <category>ai</category>
      <category>javascript</category>
      <category>node</category>
    </item>
    <item>
      <title>How I Use AI, Sticky Notes, and Pomodoro to Stay Productive as a Software Engineer</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Fri, 24 Jan 2025 15:43:44 +0000</pubDate>
      <link>https://dev.to/frorning/how-i-use-ai-sticky-notes-and-pomodoro-to-stay-productive-as-a-software-engineer-3kl3</link>
      <guid>https://dev.to/frorning/how-i-use-ai-sticky-notes-and-pomodoro-to-stay-productive-as-a-software-engineer-3kl3</guid>
      <description>&lt;p&gt;As a software engineer juggling frontend and backend tasks, I’ve found that staying organized and focused is key to delivering quality work without burning out. Over time, I’ve developed a workflow that combines &lt;strong&gt;AI assistance&lt;/strong&gt;, &lt;strong&gt;sticky notes&lt;/strong&gt;, and the &lt;strong&gt;Pomodoro Technique&lt;/strong&gt; to break down tasks, track progress, and maintain my sanity. In this article, I’ll share my process and how you can adapt it to your own workflow.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;The Problem: Overwhelming Tasks and Context Switching&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;When working on a new feature or story, I often start with a vague set of requirements. Breaking these down into actionable steps can be overwhelming, especially when I’m still figuring out the details. Add in the constant context switching between frontend and backend work, and it’s easy to lose track of what’s done and what’s left.&lt;/p&gt;

&lt;p&gt;To tackle this, I needed a system that:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;Helps me break down tasks into manageable chunks.&lt;/li&gt;
&lt;li&gt;Keeps me aware of my progress.&lt;/li&gt;
&lt;li&gt;Allows me to adapt as I learn more about the problem.&lt;/li&gt;
&lt;li&gt;Ensures I stay focused and hydrated (because, let’s be honest, we all forget to drink water sometimes).&lt;/li&gt;
&lt;/ol&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;My Workflow: AI, Sticky Notes, and Pomodoro&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;Here’s how I’ve structured my workflow to address these challenges:&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;1. Generate an Initial To-Do List with AI&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;When I start a new subtask, I use &lt;strong&gt;AI tools&lt;/strong&gt; (like Perplexity.ai or Continue.dev with Codellama) to generate an initial to-do list based on the requirements. For example, if I’m working on a user login feature, I might ask:&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;em&gt;"Generate a to-do list for implementing a user login feature with email and password authentication. Include frontend and backend tasks."&lt;/em&gt;&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;The AI might suggest:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Set up login API endpoint.&lt;/li&gt;
&lt;li&gt;Create frontend login form.&lt;/li&gt;
&lt;li&gt;Add input validation for email and password.&lt;/li&gt;
&lt;li&gt;Implement error handling for invalid credentials.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;This gives me a solid starting point with 2–5 high-level tasks.&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;2. Create a Feature Branch&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Once I have my initial to-do list, I create a feature branch for the subtask. For example:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;git checkout &lt;span class="nt"&gt;-b&lt;/span&gt; feature/user-login
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This keeps my work isolated and makes it easier to manage changes.&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;3. Work Incrementally and Extend the To-Do List&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;I start by tackling the first task on my list. As I work, I often uncover additional subtasks or edge cases. This is where AI comes in again. I’ll share my current progress and ask for suggestions:&lt;/p&gt;

&lt;blockquote&gt;
&lt;p&gt;&lt;em&gt;"I’m working on implementing the login API. Here’s what I’ve done so far: [details]. What additional tasks should I consider?"&lt;/em&gt;&lt;/p&gt;
&lt;/blockquote&gt;

&lt;p&gt;The AI might suggest:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Add rate limiting to prevent brute force attacks.&lt;/li&gt;
&lt;li&gt;Log failed login attempts for security monitoring.&lt;/li&gt;
&lt;li&gt;Write unit tests for the login functionality.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;I add these tasks to my to-do list and continue working incrementally.&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;4. Track Progress with Sticky Notes&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;I’m a big fan of &lt;strong&gt;sticky notes&lt;/strong&gt; for tracking progress. Whether physical or digital, they give me a visual representation of what’s done and what’s left.&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Physical Sticky Notes&lt;/strong&gt;: I place them on my desk or monitor, moving completed tasks to a "Done" section.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Digital Tools&lt;/strong&gt;: If I’m working remotely, I use tools like &lt;strong&gt;Trello&lt;/strong&gt;, &lt;strong&gt;Notion&lt;/strong&gt;, or &lt;strong&gt;Todoist&lt;/strong&gt; to manage my to-do list.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;Crossing off tasks gives me a sense of accomplishment and keeps me motivated.&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;5. Stay Focused with the Pomodoro Technique&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;To maintain focus, I use the &lt;strong&gt;Pomodoro Technique&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Work for 25 minutes, then take a 5-minute break.&lt;/li&gt;
&lt;li&gt;After four Pomodoros, take a longer break (15–30 minutes).&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;I assign specific to-do items to each Pomodoro session. For example:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Pomodoro 1&lt;/strong&gt;: Set up login API endpoint.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Pomodoro 2&lt;/strong&gt;: Add input validation for email and password.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;During breaks, I make sure to hydrate, stretch, or take a short walk. &lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;6. Create a Pull Request and Request Review&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Once all tasks are completed, I create a &lt;strong&gt;pull request (PR)&lt;/strong&gt; for my feature branch. I write a detailed PR description summarizing:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;What was implemented.&lt;/li&gt;
&lt;li&gt;Any challenges faced.&lt;/li&gt;
&lt;li&gt;Testing performed.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;I then request a review from my team and iterate based on feedback.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Tools I Use&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;Here are some tools and methods that have been invaluable in my workflow:&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;AI Tools&lt;/strong&gt;
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Perplexity.ai&lt;/strong&gt;: For generating initial to-do lists and brainstorming solutions.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Continue.dev&lt;/strong&gt;: For seamless integration with my IDE and local development environment.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Local AI Models&lt;/strong&gt;: I use &lt;strong&gt;Qwen2.5-Coder 7B&lt;/strong&gt; and &lt;strong&gt;CodeLlama 7B&lt;/strong&gt; for code completion, debugging, and extending my to-do lists as I work. Running these models locally ensures privacy and customization.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Task Management&lt;/strong&gt;
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Trello&lt;/strong&gt;: For visual task tracking with boards, lists, and cards.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Notion&lt;/strong&gt;: For documenting requirements, progress, and reference materials.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;JIRA&lt;/strong&gt;: For aligning my tasks with team-wide project management and sprint planning.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Pomodoro Timers&lt;/strong&gt;
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Manual iPhone Timer&lt;/strong&gt;: I use the built-in timer on my iPhone for Pomodoro sessions. It’s simple and effective.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Paper Checklist&lt;/strong&gt;: I keep a handwritten checklist on paper to track tasks for each Pomodoro session. There’s something satisfying about physically crossing off completed tasks.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Hydration Tracking&lt;/strong&gt;
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Manual iPhone Timer&lt;/strong&gt;: I set recurring reminders to drink water throughout the day.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Paper Drawing&lt;/strong&gt;: I draw circles on paper and color them in to track my hydration progress. Each circle represents a glass of water, and filling them in gives me a visual sense of accomplishment.&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Why This Works for Me&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;This workflow works because it:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Breaks down complex tasks&lt;/strong&gt; into manageable chunks.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Adapts to new information&lt;/strong&gt; as I learn more about the problem.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Keeps me focused&lt;/strong&gt; with the Pomodoro Technique.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Provides a visual representation of progress&lt;/strong&gt; with sticky notes.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Ensures I stay hydrated and energized&lt;/strong&gt; throughout the day.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;Example Workflow in Action&lt;/strong&gt;
&lt;/h3&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;Scenario&lt;/strong&gt;: Implementing a User Login Feature
&lt;/h4&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Initial To-Do List (AI-Generated)&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Set up login API endpoint.&lt;/li&gt;
&lt;li&gt;Create frontend login form.&lt;/li&gt;
&lt;li&gt;Add input validation for email and password.&lt;/li&gt;
&lt;li&gt;Implement error handling for invalid credentials.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;Feature Branch&lt;/strong&gt;: &lt;code&gt;feature/user-login&lt;/code&gt;&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Incremental Work&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Start with "Set up login API endpoint."&lt;/li&gt;
&lt;li&gt;Commit: &lt;code&gt;git commit -m "Add login API endpoint with email/password validation"&lt;/code&gt;
&lt;/li&gt;
&lt;li&gt;Ask AI: &lt;em&gt;"What else should I consider for the login API?"&lt;/em&gt;
&lt;/li&gt;
&lt;li&gt;AI suggests: Add rate limiting, log failed attempts, and write unit tests.&lt;/li&gt;
&lt;li&gt;Add these tasks to your to-do list.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Sticky Notes&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Move "Set up login API endpoint" to "Done."&lt;/li&gt;
&lt;li&gt;Add new tasks: "Add rate limiting," "Log failed attempts," "Write unit tests."&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;Pomodoro Sessions&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Session 1: Work on "Add rate limiting."&lt;/li&gt;
&lt;li&gt;Session 2: Work on "Log failed attempts."&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;li&gt;
&lt;p&gt;&lt;strong&gt;PR and Review&lt;/strong&gt;:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Create PR with title &lt;em&gt;"feat: implement user login"&lt;/em&gt; and description: &lt;em&gt;"Implemented user login feature with email/password authentication. Added rate limiting and logging for security. Unit tests included."&lt;/em&gt;
&lt;/li&gt;
&lt;li&gt;Request review and iterate based on feedback.&lt;/li&gt;
&lt;/ul&gt;
&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;Key Benefits of This Workflow&lt;/strong&gt;
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Clarity&lt;/strong&gt;: Breaking tasks into smaller chunks makes complex work manageable.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Focus&lt;/strong&gt;: Pomodoro sessions and sticky notes help maintain focus and track progress.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Adaptability&lt;/strong&gt;: AI assistance allows you to dynamically adjust your plan as you learn more.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Wellness&lt;/strong&gt;: Regular breaks and hydration keep you energized and productive.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;By formalizing and refining this workflow, you can enhance your productivity, reduce stress, and deliver high-quality work consistently.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Try It Out!&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;If you’re feeling overwhelmed by your tasks or struggling to stay focused, give this workflow a try. Start small—use AI to generate a to-do list, create a feature branch, and work incrementally. Experiment with sticky notes and the Pomodoro Technique to see what works best for you.&lt;/p&gt;

&lt;p&gt;I’d love to hear how you stay productive in your day-to-day work. Share your tips and tools in the comments below!&lt;/p&gt;




&lt;p&gt;&lt;strong&gt;Happy coding!&lt;/strong&gt; 🚀&lt;/p&gt;

</description>
      <category>chatgpt</category>
      <category>productivity</category>
      <category>git</category>
      <category>tooling</category>
    </item>
    <item>
      <title>Introduction to WebAssembly (WASM)</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Fri, 10 Jan 2025 16:21:06 +0000</pubDate>
      <link>https://dev.to/frorning/introduction-to-webassembly-wasm-4g35</link>
      <guid>https://dev.to/frorning/introduction-to-webassembly-wasm-4g35</guid>
      <description>&lt;p&gt;WebAssembly (WASM) is a binary instruction format for a stack-based virtual machine, designed as a portable target for high-performance applications. In this article, we'll explore how to compile a simple C program to WebAssembly, load it into a web browser, and interact with it using JavaScript. We'll also explore some useful tools and commands for working with WASM outside the dev container environment.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Setting Up the Development Environment&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;Create the necessary folder structure and files for your WebAssembly project.&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Create Project Folder&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;Begin by creating a new directory for your project. Inside this folder, you'll add the necessary files and configurations.&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;mkdir &lt;/span&gt;wasm-web-example
&lt;span class="nb"&gt;cd &lt;/span&gt;wasm-web-example
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Set Up Dev Container&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;In the &lt;code&gt;wasm-web-example&lt;/code&gt; directory, create the &lt;code&gt;.devcontainer&lt;/code&gt; folder to store the dev container configuration files. These files will set up a container with Emscripten installed to compile C code into WebAssembly.&lt;/p&gt;

&lt;p&gt;Inside the &lt;code&gt;.devcontainer&lt;/code&gt; folder, create the following files:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;devcontainer.json&lt;/strong&gt;: 
The &lt;code&gt;devcontainer.json&lt;/code&gt; file configures VSCode to use the Docker container with the necessary extensions and environment settings.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight json"&gt;&lt;code&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"name"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"Emscripten DevContainer"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"build"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"dockerfile"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"Dockerfile"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"customizations"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"vscode"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="nl"&gt;"settings"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="nl"&gt;"terminal.integrated.shell.linux"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"/bin/bash"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="nl"&gt;"C_Cpp.default.configurationProvider"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"ms-vscode.cmake-tools"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="nl"&gt;"C_Cpp.default.intelliSenseMode"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"gcc-x64"&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="nl"&gt;"extensions"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="s2"&gt;"ms-vscode.cpptools"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
                &lt;/span&gt;&lt;span class="s2"&gt;"ms-vscode.cmake-tools"&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"postCreateCommand"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"emcc --version"&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Dockerfile&lt;/strong&gt;: 
The &lt;code&gt;Dockerfile&lt;/code&gt; will set up the Emscripten environment. Here's the content for that file:
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight docker"&gt;&lt;code&gt;&lt;span class="c"&gt;# Use the official Emscripten image&lt;/span&gt;
&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="s"&gt; emscripten/emsdk:3.1.74&lt;/span&gt;

&lt;span class="c"&gt;# Set the working directory&lt;/span&gt;
&lt;span class="k"&gt;WORKDIR&lt;/span&gt;&lt;span class="s"&gt; /workspace&lt;/span&gt;

&lt;span class="c"&gt;# Copy the source code into the container&lt;/span&gt;
&lt;span class="k"&gt;COPY&lt;/span&gt;&lt;span class="s"&gt; . .&lt;/span&gt;

&lt;span class="c"&gt;# Install any additional packages if necessary (optional)&lt;/span&gt;
&lt;span class="c"&gt;# Ensure to clean up cache to minimize image size&lt;/span&gt;
&lt;span class="k"&gt;RUN &lt;/span&gt;apt-get update &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="se"&gt;\
&lt;/span&gt;    apt-get &lt;span class="nb"&gt;install&lt;/span&gt; &lt;span class="nt"&gt;-y&lt;/span&gt; build-essential &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="se"&gt;\
&lt;/span&gt;    apt-get clean &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="se"&gt;\
&lt;/span&gt;    &lt;span class="nb"&gt;rm&lt;/span&gt; &lt;span class="nt"&gt;-rf&lt;/span&gt; /var/lib/apt/lists/&lt;span class="k"&gt;*&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Create VSCode Settings&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;In the root of your project, create a &lt;code&gt;.vscode&lt;/code&gt; folder with the following files:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;c_cpp_properties.json&lt;/strong&gt;:
This file configures the C++ IntelliSense and include paths for your project.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight json"&gt;&lt;code&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"configurations"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"name"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"Linux"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"includePath"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="s2"&gt;"${workspaceFolder}/**"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
            &lt;/span&gt;&lt;span class="s2"&gt;"/emsdk/upstream/emscripten/system/include"&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"defines"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[],&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"compilerPath"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"/usr/bin/gcc"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"cStandard"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"c17"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"cppStandard"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"gnu++17"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"configurationProvider"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"ms-vscode.cmake-tools"&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;],&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"version"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;4&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;settings.json&lt;/strong&gt;: 
This file includes specific VSCode settings for language associations.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight json"&gt;&lt;code&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"files.associations"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"emscripten.h"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"c"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"[javascript]"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"editor.defaultFormatter"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"vscode.typescript-language-features"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"[typescript]"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"editor.defaultFormatter"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"vscode.typescript-language-features"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"[jsonc]"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"editor.defaultFormatter"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"vscode.json-language-features"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"[json]"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"editor.defaultFormatter"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"vscode.json-language-features"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"[html]"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
        &lt;/span&gt;&lt;span class="nl"&gt;"editor.defaultFormatter"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"vscode.html-language-features"&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Create C, JavaScript, and HTML Files&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;Now, create the following files for your project:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;test.c&lt;/strong&gt;:
This C file contains the simple function that will be compiled to WebAssembly.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// test.c&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;lhs&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;rhs&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;lhs&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;rhs&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;ul&gt;
&lt;li&gt;
&lt;strong&gt;test.html&lt;/strong&gt;:
This HTML file will load the WebAssembly module using JavaScript.
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight html"&gt;&lt;code&gt;&lt;span class="cp"&gt;&amp;lt;!DOCTYPE html&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;html&lt;/span&gt; &lt;span class="na"&gt;lang=&lt;/span&gt;&lt;span class="s"&gt;"en"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;head&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;meta&lt;/span&gt; &lt;span class="na"&gt;charset=&lt;/span&gt;&lt;span class="s"&gt;"UTF-8"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;meta&lt;/span&gt; &lt;span class="na"&gt;name=&lt;/span&gt;&lt;span class="s"&gt;"viewport"&lt;/span&gt; &lt;span class="na"&gt;content=&lt;/span&gt;&lt;span class="s"&gt;"width=device-width, initial-scale=1.0"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;title&amp;gt;&lt;/span&gt;WebAssembly Example&lt;span class="nt"&gt;&amp;lt;/title&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;/head&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;body&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;h1&amp;gt;&lt;/span&gt;WebAssembly Example&lt;span class="nt"&gt;&amp;lt;/h1&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;div&lt;/span&gt; &lt;span class="na"&gt;id=&lt;/span&gt;&lt;span class="s"&gt;"output"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&amp;lt;/div&amp;gt;&lt;/span&gt;

  &lt;span class="nt"&gt;&amp;lt;script &lt;/span&gt;&lt;span class="na"&gt;src=&lt;/span&gt;&lt;span class="s"&gt;"test.js"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&amp;lt;/script&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;/body&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;/html&amp;gt;&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;test.js&lt;/strong&gt;:
This JavaScript file will fetch the WebAssembly module and call the exported function.
&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="c1"&gt;// test.js&lt;/span&gt;
&lt;span class="c1"&gt;// Path to the .wasm file&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;wasmFile&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;test.wasm&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Load the WebAssembly module&lt;/span&gt;
&lt;span class="nf"&gt;fetch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;wasmFile&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;ok&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Error&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;`Failed to load &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;wasmFile&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;: &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;statusText&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;arrayBuffer&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="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;bytes&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;WebAssembly&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;instantiate&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;bytes&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(({&lt;/span&gt; &lt;span class="nx"&gt;instance&lt;/span&gt; &lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="c1"&gt;// Access exported functions&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;instance&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;exports&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&lt;/span&gt; &lt;span class="p"&gt;})&lt;/span&gt;

    &lt;span class="c1"&gt;// Example: Call a function exported from the WebAssembly module&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;wasmExports&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;add&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&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;5&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;// Example function call&lt;/span&gt;
      &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s2"&gt;`Result from WebAssembly: &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;No "add" function found in the WebAssembly module.&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="k"&gt;catch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;error&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;error&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Error loading or running the WebAssembly module:&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;error&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Error loading WebAssembly module.&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Now that you've set up all the necessary files and configurations, you can move on to compiling and interacting with WebAssembly.&lt;/p&gt;

&lt;p&gt;The project structure looks like following now:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;➜  wasm-web-example: tree &lt;span class="nb"&gt;.&lt;/span&gt; &lt;span class="nt"&gt;-a&lt;/span&gt;
&lt;span class="nb"&gt;.&lt;/span&gt;
├── .devcontainer
│   ├── Dockerfile
│   └── devcontainer.json
├── .vscode
│   ├── c_cpp_properties.json
│   └── settings.json
├── test.c
├── test.html
├── test.js
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  &lt;strong&gt;Compiling C Code to WebAssembly Using Emscripten&lt;/strong&gt;
&lt;/h2&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Basic C Program&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;The file &lt;code&gt;test.c&lt;/code&gt; contains a simple function &lt;code&gt;add&lt;/code&gt; that adds two integers. We will compile this C function into WebAssembly using Emscripten.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight c"&gt;&lt;code&gt;&lt;span class="c1"&gt;// test.c&lt;/span&gt;
&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;add&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;lhs&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;rhs&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;lhs&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;rhs&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;
  
  
  &lt;strong&gt;Emscripten Command&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;Inside the dev container, open the terminal (use &lt;code&gt;cmd+j&lt;/code&gt; in VSCode) and run the following Emscripten command to compile the C code to WebAssembly:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;emcc test.c &lt;span class="nt"&gt;-O3&lt;/span&gt; &lt;span class="nt"&gt;-s&lt;/span&gt; STANDALONE_WASM &lt;span class="nt"&gt;-s&lt;/span&gt; &lt;span class="nv"&gt;EXPORTED_FUNCTIONS&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="s1"&gt;'["_add"]'&lt;/span&gt; &lt;span class="nt"&gt;--no-entry&lt;/span&gt; &lt;span class="nt"&gt;-o&lt;/span&gt; test.wasm
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F9u8ybcwjwinz7cgytqct.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2F9u8ybcwjwinz7cgytqct.png" alt="Webassembly Example Devcontainer" width="800" height="233"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;h3&gt;
  
  
  Breakdown of the Command
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;emcc&lt;/code&gt;&lt;/strong&gt;: This is the Emscripten C/C++ compiler command. It compiles C/C++ source files into WebAssembly or asm.js.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;test.c&lt;/code&gt;&lt;/strong&gt;: This specifies the input C source file that you want to compile.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;-O3&lt;/code&gt;&lt;/strong&gt;: This flag enables aggressive optimizations during the compilation process. The &lt;code&gt;-O3&lt;/code&gt; optimization level is typically used for performance-critical applications, as it applies various optimization techniques that can significantly improve runtime performance.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;-s STANDALONE_WASM&lt;/code&gt;&lt;/strong&gt;: This option instructs Emscripten to generate a standalone WebAssembly module. A standalone WASM module does not depend on any JavaScript glue code and can be executed independently in environments that support WebAssembly.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;-s EXPORTED_FUNCTIONS='["_add"]'&lt;/code&gt;&lt;/strong&gt;: This flag specifies which functions from the C code should be exported and made available for calling from JavaScript. In this case, the function named &lt;code&gt;_add&lt;/code&gt; will be accessible in the resulting WASM module.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;--no-entry&lt;/code&gt;&lt;/strong&gt;: This option tells the compiler that there is no entry point (like a &lt;code&gt;main()&lt;/code&gt; function) in the program. This is useful for libraries or modules that are intended to be used by other code rather than executed directly.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;&lt;code&gt;-o test.wasm&lt;/code&gt;&lt;/strong&gt;: This specifies the output file name for the compiled WebAssembly module. In this case, it will create a file named &lt;code&gt;test.wasm&lt;/code&gt;.&lt;/p&gt;&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;This command will generate &lt;code&gt;test.wasm&lt;/code&gt;, the WebAssembly binary, and ensure that the &lt;code&gt;add&lt;/code&gt; function is exported for use in JavaScript.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Loading and Interacting with WebAssembly in the Browser&lt;/strong&gt;
&lt;/h2&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;HTML Setup&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;The file &lt;code&gt;test.html&lt;/code&gt; contains a simple HTML page that loads the WebAssembly binary using JavaScript. The JavaScript code in &lt;code&gt;test.js&lt;/code&gt; fetches the &lt;code&gt;.wasm&lt;/code&gt; file and instantiates it.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight html"&gt;&lt;code&gt;&lt;span class="c"&gt;&amp;lt;!-- test.html --&amp;gt;&lt;/span&gt;
&lt;span class="cp"&gt;&amp;lt;!DOCTYPE html&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;html&lt;/span&gt; &lt;span class="na"&gt;lang=&lt;/span&gt;&lt;span class="s"&gt;"en"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;head&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;meta&lt;/span&gt; &lt;span class="na"&gt;charset=&lt;/span&gt;&lt;span class="s"&gt;"UTF-8"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;meta&lt;/span&gt; &lt;span class="na"&gt;name=&lt;/span&gt;&lt;span class="s"&gt;"viewport"&lt;/span&gt; &lt;span class="na"&gt;content=&lt;/span&gt;&lt;span class="s"&gt;"width=device-width, initial-scale=1.0"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;title&amp;gt;&lt;/span&gt;WebAssembly Example&lt;span class="nt"&gt;&amp;lt;/title&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;/head&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;body&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;h1&amp;gt;&lt;/span&gt;WebAssembly Example&lt;span class="nt"&gt;&amp;lt;/h1&amp;gt;&lt;/span&gt;
  &lt;span class="nt"&gt;&amp;lt;div&lt;/span&gt; &lt;span class="na"&gt;id=&lt;/span&gt;&lt;span class="s"&gt;"output"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&amp;lt;/div&amp;gt;&lt;/span&gt;

  &lt;span class="nt"&gt;&amp;lt;script &lt;/span&gt;&lt;span class="na"&gt;src=&lt;/span&gt;&lt;span class="s"&gt;"test.js"&lt;/span&gt;&lt;span class="nt"&gt;&amp;gt;&amp;lt;/script&amp;gt;&lt;/span&gt;
&lt;span class="nt"&gt;&amp;lt;/body&amp;gt;&lt;/span&gt;

&lt;span class="nt"&gt;&amp;lt;/html&amp;gt;&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;JavaScript Setup&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;The JavaScript file &lt;code&gt;test.js&lt;/code&gt; loads the &lt;code&gt;test.wasm&lt;/code&gt; file and calls the exported &lt;code&gt;add&lt;/code&gt; function:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="c1"&gt;// test.js&lt;/span&gt;
&lt;span class="c1"&gt;// Path to the .wasm file&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;wasmFile&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;test.wasm&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="c1"&gt;// Load the WebAssembly module&lt;/span&gt;
&lt;span class="nf"&gt;fetch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;wasmFile&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;ok&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Error&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;`Failed to load &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;wasmFile&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;: &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;statusText&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;response&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;arrayBuffer&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="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;bytes&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nx"&gt;WebAssembly&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;instantiate&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;bytes&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
  &lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;(({&lt;/span&gt; &lt;span class="nx"&gt;instance&lt;/span&gt; &lt;span class="p"&gt;})&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="c1"&gt;// Access exported functions&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;instance&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;exports&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&lt;/span&gt; &lt;span class="p"&gt;})&lt;/span&gt;

    &lt;span class="c1"&gt;// Example: Call a function exported from the WebAssembly module&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;wasmExports&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;add&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;wasmExports&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;5&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;// Example function call&lt;/span&gt;
      &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s2"&gt;`Result from WebAssembly: &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;No "add" function found in the WebAssembly module.&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="k"&gt;catch&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;error&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;error&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Error loading or running the WebAssembly module:&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;error&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="nb"&gt;document&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;getElementById&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;output&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nx"&gt;textContent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Error loading WebAssembly module.&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This will display the result of the &lt;code&gt;add&lt;/code&gt; function in the HTML page when the module is loaded successfully.&lt;/p&gt;




&lt;h2&gt;
  
  
  &lt;strong&gt;Using External Tools on macOS&lt;/strong&gt;
&lt;/h2&gt;

&lt;p&gt;Outside the dev container, there are several useful commands you can run to work with WebAssembly on your Mac.&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Install &lt;code&gt;wabt&lt;/code&gt;&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;&lt;code&gt;wabt&lt;/code&gt; (WebAssembly Binary Toolkit) provides utilities for working with WebAssembly, including converting &lt;code&gt;.wasm&lt;/code&gt; files to the human-readable WAT (WebAssembly Text) format. Install it via Homebrew:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;brew &lt;span class="nb"&gt;install &lt;/span&gt;wabt
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Convert WASM to WAT&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;Once &lt;code&gt;wabt&lt;/code&gt; is installed, you can use the &lt;code&gt;wasm2wat&lt;/code&gt; tool to convert your WebAssembly binary (&lt;code&gt;test.wasm&lt;/code&gt;) to the WAT format:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;wasm2wat test.wasm
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This will output a text representation of the WebAssembly module that you can read and inspect.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;(module
  (type (;0;) (func))
  (type (;1;) (func (param i32 i32) (result i32)))
  (type (;2;) (func (param i32)))
  (type (;3;) (func (result i32)))
  (func (;0;) (type 0)
    nop)
  (func (;1;) (type 1) (param i32 i32) (result i32)
    local.get 0
    local.get 1
    i32.add)
  (func (;2;) (type 2) (param i32)
    local.get 0
    global.set 0)
  (func (;3;) (type 3) (result i32)
    global.get 0)
  (table (;0;) 2 2 funcref)
  (memory (;0;) 258 258)
  (global (;0;) (mut i32) (i32.const 66560))
  (export "memory" (memory 0))
  (export "add" (func 1))
  (export "_initialize" (func 0))
  (export "__indirect_function_table" (table 0))
  (export "_emscripten_stack_restore" (func 2))
  (export "emscripten_stack_get_current" (func 3))
  (elem (;0;) (i32.const 1) func 0))
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Serve the HTML Page&lt;/strong&gt;:
&lt;/h3&gt;

&lt;p&gt;To view the HTML page that interacts with the WebAssembly module, you can use Python’s simple HTTP server:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;python &lt;span class="nt"&gt;-m&lt;/span&gt; http.server
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This command will start a local web server on &lt;code&gt;http://localhost:8000&lt;/code&gt;, where you can open &lt;code&gt;index.html&lt;/code&gt; in your browser to see the WebAssembly module in action.&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fsk8amzwwxy9if5hkboy6.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fsk8amzwwxy9if5hkboy6.png" alt="Webassembly Example Output" width="800" height="179"&gt;&lt;/a&gt;&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;Conclusion&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;By following the steps outlined in this article, you can set up a development environment to compile C code to WebAssembly, interact with it using JavaScript, and convert the resulting WebAssembly binary to the WAT format for inspection. The use of external tools like &lt;code&gt;wabt&lt;/code&gt; and Python’s HTTP server makes it easier to manage and explore WebAssembly modules on your macOS system.&lt;/p&gt;

</description>
      <category>javascript</category>
      <category>webassembly</category>
      <category>vscode</category>
      <category>docker</category>
    </item>
    <item>
      <title>Functional Programming in Go with IBM fp-go: Error Handling Made Explicit</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Fri, 27 Dec 2024 14:43:19 +0000</pubDate>
      <link>https://dev.to/frorning/functional-programming-in-go-with-ibm-fp-go-error-handling-made-explicit-9of</link>
      <guid>https://dev.to/frorning/functional-programming-in-go-with-ibm-fp-go-error-handling-made-explicit-9of</guid>
      <description>&lt;p&gt;Functional programming (FP) principles are gaining popularity in modern software development due to their emphasis on immutability, composability, and explicitness. While Go is traditionally an imperative language, the &lt;strong&gt;fp-go&lt;/strong&gt; library, developed by IBM, introduces FP abstractions such as &lt;code&gt;Option&lt;/code&gt;, &lt;code&gt;Either&lt;/code&gt;, &lt;code&gt;Fold&lt;/code&gt;, and utilities for functional composition. In this article, we will explore how to use &lt;strong&gt;fp-go&lt;/strong&gt; to handle errors explicitly, define function signatures with multiple error types, and build a real-world CRUD API example demonstrating these concepts.&lt;/p&gt;

&lt;h2&gt;
  
  
  Why Functional Error Handling?
&lt;/h2&gt;

&lt;p&gt;Error handling is crucial for building reliable software. Traditional Go error handling relies on returning &lt;code&gt;error&lt;/code&gt; values, which can be unintentionally ignored or mishandled. Functional error handling introduces abstractions like:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;&lt;code&gt;Option&lt;/code&gt;&lt;/strong&gt;: Represents optional values, akin to &lt;code&gt;Some&lt;/code&gt; and &lt;code&gt;None&lt;/code&gt; in other FP languages.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;&lt;code&gt;Either&lt;/code&gt;&lt;/strong&gt;: Encapsulates a value that can either be a &lt;code&gt;Right&lt;/code&gt; (success) or &lt;code&gt;Left&lt;/code&gt; (failure), making error propagation explicit.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Tagged Unions&lt;/strong&gt;: Allow function signatures to clearly define possible error types.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Composition&lt;/strong&gt;: Enables chaining operations while handling errors naturally.&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;Let’s dive into these concepts and see how &lt;strong&gt;fp-go&lt;/strong&gt; facilitates them in Go.&lt;/p&gt;




&lt;h2&gt;
  
  
  Getting Started with fp-go
&lt;/h2&gt;

&lt;p&gt;First, add &lt;strong&gt;fp-go&lt;/strong&gt; to your Go project:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;go get github.com/IBM/fp-go
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;Import the necessary modules:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="n"&gt;either&lt;/span&gt; &lt;span class="s"&gt;"github.com/IBM/fp-go/either"&lt;/span&gt;
    &lt;span class="n"&gt;option&lt;/span&gt; &lt;span class="s"&gt;"github.com/IBM/fp-go/option"&lt;/span&gt;
&lt;span class="p"&gt;)&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h2&gt;
  
  
  &lt;code&gt;Option&lt;/code&gt;: Handling Optional Values
&lt;/h2&gt;

&lt;p&gt;&lt;code&gt;Option&lt;/code&gt; represents a value that may or may not exist. It is either &lt;code&gt;Some(value)&lt;/code&gt; or &lt;code&gt;None&lt;/code&gt;.&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Example: Parsing an Integer&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;parseInt&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;option&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Option&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;strconv&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Atoi&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input&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;err&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="no"&gt;nil&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;option&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;None&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]()&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;option&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Some&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;opt&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;parseInt&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"42"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;option&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Fold&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Println&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"No value"&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Parsed value: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;opt&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;
  
  
  Key Takeaways:
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;Option&lt;/code&gt; eliminates &lt;code&gt;nil&lt;/code&gt; values.&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;Fold&lt;/code&gt; is used to handle both cases (&lt;code&gt;Some&lt;/code&gt; or &lt;code&gt;None&lt;/code&gt;).&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  &lt;code&gt;Either&lt;/code&gt;: Handling Errors Explicitly
&lt;/h2&gt;

&lt;p&gt;&lt;code&gt;Either&lt;/code&gt; represents a computation that can result in two possibilities:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;&lt;code&gt;Left&lt;/code&gt;&lt;/strong&gt;: Represents an error.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;&lt;code&gt;Right&lt;/code&gt;&lt;/strong&gt;: Represents a successful result.&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Example: Safe Division&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="n"&gt;MathError&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Code&lt;/span&gt;    &lt;span class="kt"&gt;string&lt;/span&gt;
    &lt;span class="n"&gt;Message&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;safeDivide&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="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;MathError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&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="n"&gt;MathError&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Code&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"DIV_BY_ZERO"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"Cannot divide by zero"&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&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="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;safeDivide&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="m"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Fold&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="n"&gt;MathError&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Error [%s]: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Result: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



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

&lt;ul&gt;
&lt;li&gt;
&lt;code&gt;Either&lt;/code&gt; separates success and failure paths.&lt;/li&gt;
&lt;li&gt;
&lt;code&gt;Fold&lt;/code&gt; simplifies handling both cases in one place.&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  Function Signatures with Multiple Error Types
&lt;/h2&gt;

&lt;p&gt;Real-world applications often need to handle multiple types of errors. By using tagged unions, we can define explicit error types.&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Example: Tagged Union for Errors&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Tag&lt;/span&gt;     &lt;span class="kt"&gt;string&lt;/span&gt;
    &lt;span class="n"&gt;Message&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="n"&gt;MathErrorTag&lt;/span&gt;    &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"MathError"&lt;/span&gt;
    &lt;span class="n"&gt;DatabaseErrorTag&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"DatabaseError"&lt;/span&gt;
&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;NewMathError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;msg&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;AppError&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;AppError&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Tag&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;MathErrorTag&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;msg&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;NewDatabaseError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;msg&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;AppError&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;AppError&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Tag&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;DatabaseErrorTag&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;msg&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;process&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&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="n"&gt;NewMathError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Division by zero"&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&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="n"&gt;a&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;process&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="m"&gt;10&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Fold&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Error [%s]: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Tag&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;value&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Processed result: %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;value&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Benefits:
&lt;/h3&gt;

&lt;ul&gt;
&lt;li&gt;Tagged unions make errors self-documenting.&lt;/li&gt;
&lt;li&gt;Explicit types reduce ambiguity in error handling.&lt;/li&gt;
&lt;/ul&gt;




&lt;h2&gt;
  
  
  Real-World Example: CRUD API
&lt;/h2&gt;

&lt;p&gt;Let’s implement a simple CRUD API with explicit error handling using &lt;code&gt;Either&lt;/code&gt;.&lt;/p&gt;

&lt;h3&gt;
  
  
  &lt;strong&gt;Model and Error Definitions&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;ID&lt;/span&gt;    &lt;span class="kt"&gt;int&lt;/span&gt;
    &lt;span class="n"&gt;Name&lt;/span&gt;  &lt;span class="kt"&gt;string&lt;/span&gt;
    &lt;span class="n"&gt;Email&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt; &lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;Code&lt;/span&gt;    &lt;span class="kt"&gt;string&lt;/span&gt;
    &lt;span class="n"&gt;Message&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="n"&gt;NotFoundError&lt;/span&gt;    &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"NOT_FOUND"&lt;/span&gt;
    &lt;span class="n"&gt;ValidationError&lt;/span&gt;  &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"VALIDATION_ERROR"&lt;/span&gt;
    &lt;span class="n"&gt;DatabaseError&lt;/span&gt;    &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="s"&gt;"DATABASE_ERROR"&lt;/span&gt;
&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;NewAppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;message&lt;/span&gt; &lt;span class="kt"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;AppError&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;AppError&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Code&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;message&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;
  
  
  &lt;strong&gt;Repository Layer&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;var&lt;/span&gt; &lt;span class="n"&gt;users&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;map&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="m"&gt;1&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;ID&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="m"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Name&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"Alice"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Email&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"alice@example.com"&lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;getUserByID&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;exists&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;users&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;exists&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;either&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="n"&gt;NewAppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;NotFoundError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"User not found"&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&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="n"&gt;user&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;
  
  
  &lt;strong&gt;Service Layer&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;validateUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Name&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;user&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Email&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s"&gt;""&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&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="n"&gt;NewAppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ValidationError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;"Name and email are required"&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&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="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;createUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;validation&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;validateUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&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;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Chain&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;validUser&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Either&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;ID&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;len&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;users&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="m"&gt;1&lt;/span&gt;
            &lt;span class="n"&gt;users&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;ID&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;user&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;either&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="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
        &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;validation&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;
  
  
  &lt;strong&gt;Controller&lt;/strong&gt;
&lt;/h3&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;handleGetUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;getUserByID&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;id&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Fold&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Error [%s]: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"User: %+v&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;handleCreateUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;createUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;user&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;

    &lt;span class="n"&gt;either&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Fold&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;err&lt;/span&gt; &lt;span class="n"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Error [%s]: %s&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;err&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Message&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
        &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;newUser&lt;/span&gt; &lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Created user: %+v&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;newUser&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;},&lt;/span&gt;
    &lt;span class="p"&gt;)(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;handleGetUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="m"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;handleCreateUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;User&lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;Name&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"Bob"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;Email&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="s"&gt;"bob@example.com"&lt;/span&gt;&lt;span class="p"&gt;})&lt;/span&gt;
    &lt;span class="n"&gt;handleGetUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="m"&gt;2&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






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

&lt;p&gt;Using &lt;strong&gt;fp-go&lt;/strong&gt; in Go, we can:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Model errors explicitly using &lt;code&gt;Either&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;Represent optional values with &lt;code&gt;Option&lt;/code&gt;.&lt;/li&gt;
&lt;li&gt;Handle multiple error types via tagged unions.&lt;/li&gt;
&lt;li&gt;Build maintainable and composable APIs.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;These patterns make your Go code more robust, readable, and functional. Whether you’re building a CRUD API or complex business logic, &lt;strong&gt;fp-go&lt;/strong&gt; empowers you to handle errors cleanly and consistently.&lt;/p&gt;

</description>
      <category>go</category>
      <category>functional</category>
      <category>programming</category>
      <category>webdev</category>
    </item>
    <item>
      <title>Mastering Trampolining: A Deep Dive into Recursive Optimization</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Wed, 25 Dec 2024 17:02:44 +0000</pubDate>
      <link>https://dev.to/frorning/mastering-trampolining-a-deep-dive-into-recursive-optimization-45nc</link>
      <guid>https://dev.to/frorning/mastering-trampolining-a-deep-dive-into-recursive-optimization-45nc</guid>
      <description>&lt;h2&gt;
  
  
  Mastering Trampolining: A Deep Dive into Recursive Optimization
&lt;/h2&gt;

&lt;p&gt;In the world of programming, recursion is a powerful tool that allows functions to call themselves to solve complex problems. However, deep recursion can lead to stack overflow errors, especially in languages that do not optimize recursive calls. Enter &lt;strong&gt;trampolining&lt;/strong&gt;, a technique that transforms recursive calls into an iterative process, allowing for infinite recursion without the risk of exhausting the call stack. In this article, we will explore trampolining in detail, providing implementations in multiple programming languages, including Java, C++, JavaScript, and Go. &lt;/p&gt;

&lt;h3&gt;
  
  
  Understanding Trampolining
&lt;/h3&gt;

&lt;p&gt;&lt;strong&gt;What is Trampolining?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Trampolining is a method used to optimize recursive functions by converting them into iterations. Instead of a function calling itself directly, it returns another function (or "thunk") to be executed later. This allows the program to manage function calls without piling them up on the call stack.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Why Use Trampolining?&lt;/strong&gt;&lt;/p&gt;

&lt;p&gt;Using trampolining has several benefits:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Improved Performance&lt;/strong&gt;: It enhances the execution speed of your code by converting recursive calls into iterations.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Preventing Stack Overflow&lt;/strong&gt;: By avoiding deep recursion, it prevents stack overflow errors, especially in functions that call themselves repeatedly.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  How Trampolining Works
&lt;/h3&gt;

&lt;p&gt;The basic principle of trampolining involves converting recursive calls into iterations. Instead of a function calling itself directly, it returns another function to be executed. This process continues until a final value is produced.&lt;/p&gt;

&lt;h4&gt;
  
  
  Example Code
&lt;/h4&gt;

&lt;p&gt;To illustrate how trampolining works, let's look at an example in JavaScript.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Before Trampolining:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nf"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&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="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;&lt;strong&gt;After Trampolining:&lt;/strong&gt;&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;trampoline&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;fn&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kd"&gt;function&lt;/span&gt;&lt;span class="p"&gt;(...&lt;/span&gt;&lt;span class="nx"&gt;args&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;fn&lt;/span&gt;&lt;span class="p"&gt;(...&lt;/span&gt;&lt;span class="nx"&gt;args&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
        &lt;span class="k"&gt;while &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;typeof&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;function&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="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;result&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;result&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="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;acc&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return &lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nf"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&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="nx"&gt;n&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nx"&gt;acc&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="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;trampolinedFactorial&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;trampoline&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;trampolinedFactorial&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: 120&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Technical Explanation
&lt;/h3&gt;

&lt;p&gt;Trampolining leverages continuations and tail-call optimization. Continuations allow the function to pause and resume, while tail-call optimization ensures that the function doesn’t add new frames to the call stack.&lt;/p&gt;

&lt;h4&gt;
  
  
  Preparing Your Functions
&lt;/h4&gt;

&lt;p&gt;Not all functions need trampolining. Identify functions that involve deep recursion or are likely to cause stack overflow.&lt;/p&gt;

&lt;h4&gt;
  
  
  Refactoring for Trampolining
&lt;/h4&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Identify the Recursive Function&lt;/strong&gt;: Find the function that repeatedly calls itself.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Modify the Function&lt;/strong&gt;: Change it to return another function instead of making a direct recursive call.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Wrap with a Trampoline&lt;/strong&gt;: Use a trampoline function to execute the modified function iteratively.&lt;/li&gt;
&lt;/ol&gt;

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

&lt;p&gt;Common pitfalls include infinite loops and performance overhead. Ensure your base case is correct to avoid infinite loops, and test and optimize performance as needed.&lt;/p&gt;

&lt;h3&gt;
  
  
  Advanced Trampolining Techniques
&lt;/h3&gt;

&lt;p&gt;Trampolining can be further enhanced with techniques like memoization and lazy evaluation. These techniques can help improve performance further by caching results or delaying computations until necessary.&lt;/p&gt;

&lt;h3&gt;
  
  
  Real-World Applications
&lt;/h3&gt;

&lt;p&gt;Many large-scale applications use trampolining to handle recursive tasks efficiently. Examples include:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Parsing Complex Data Structures&lt;/strong&gt;: For instance, when dealing with nested JSON objects or XML.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Functional Programming Paradigms&lt;/strong&gt;: Languages like Scala and Haskell often utilize trampolining for efficient recursion.&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Implementing Trampolining in Other Languages
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Java Implementation
&lt;/h4&gt;

&lt;p&gt;In Java, trampolining can be implemented using interfaces or functional programming constructs available in Java 8 and later.&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.util.function.Supplier&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;TrampolineExample&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="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="no"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="no"&gt;T&lt;/span&gt; &lt;span class="nf"&gt;trampoline&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;Supplier&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="no"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;supplier&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="nc"&gt;Supplier&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="no"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;supplier&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
        &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="kc"&gt;null&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="no"&gt;T&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;current&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="na"&gt;get&lt;/span&gt;&lt;span class="o"&gt;();&lt;/span&gt;
            &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="k"&gt;instanceof&lt;/span&gt; &lt;span class="nc"&gt;Supplier&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
                &lt;span class="n"&gt;current&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="nc"&gt;Supplier&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="no"&gt;T&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;)&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
            &lt;span class="o"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="o"&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="o"&gt;;&lt;/span&gt;
            &lt;span class="o"&gt;}&lt;/span&gt;
        &lt;span class="o"&gt;}&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="kc"&gt;null&lt;/span&gt;&lt;span class="o"&gt;;&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="nc"&gt;Supplier&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nc"&gt;Integer&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="nf"&gt;factorial&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="o"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&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;0&lt;/span&gt;&lt;span class="o"&gt;)&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
        &lt;span class="o"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;factorial&lt;/span&gt;&lt;span class="o"&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="o"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;acc&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="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="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;number&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;5&lt;/span&gt;&lt;span class="o"&gt;;&lt;/span&gt;
        &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;trampoline&lt;/span&gt;&lt;span class="o"&gt;(()&lt;/span&gt; &lt;span class="o"&gt;-&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;factorial&lt;/span&gt;&lt;span class="o"&gt;(&lt;/span&gt;&lt;span class="n"&gt;number&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="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;"Factorial of "&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;number&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="s"&gt;" is: "&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="o"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// Output: 120&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;h4&gt;
  
  
  C++ Implementation
&lt;/h4&gt;

&lt;p&gt;In C++, trampolining can be achieved using &lt;code&gt;std::function&lt;/code&gt; and lambda expressions.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight cpp"&gt;&lt;code&gt;&lt;span class="cp"&gt;#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;iostream&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
#include&lt;/span&gt; &lt;span class="cpf"&gt;&amp;lt;functional&amp;gt;&lt;/span&gt;&lt;span class="cp"&gt;
&lt;/span&gt;
&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;function&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;trampoline&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;function&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;func&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;func&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;nullptr&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;function&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;]()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="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;n&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;acc&lt;/span&gt;&lt;span class="p"&gt;]()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;acc&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="kt"&gt;int&lt;/span&gt; &lt;span class="nf"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kt"&gt;int&lt;/span&gt; &lt;span class="n"&gt;number&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="k"&gt;auto&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;trampoline&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;factorial&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;number&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;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;cout&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="s"&gt;"Factorial of "&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;number&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="s"&gt;" is: "&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;endl&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// Output: 120&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Go Implementation with Generics
&lt;/h4&gt;

&lt;p&gt;Go provides an elegant way to implement trampolining using generics introduced in Go 1.18.&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight go"&gt;&lt;code&gt;&lt;span class="k"&gt;package&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;

&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="s"&gt;"fmt"&lt;/span&gt;
&lt;span class="p"&gt;)&lt;/span&gt;

&lt;span class="c"&gt;// Define the thunk type for generic functions&lt;/span&gt;
&lt;span class="k"&gt;type&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt; &lt;span class="n"&gt;any&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;()&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="n"&gt;thunk&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="c"&gt;// Trampoline function that executes the supplied thunk&lt;/span&gt;
&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;trampoline&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;T&lt;/span&gt; &lt;span class="n"&gt;any&lt;/span&gt;&lt;span class="p"&gt;](&lt;/span&gt;&lt;span class="n"&gt;fn&lt;/span&gt; &lt;span class="n"&gt;thunk&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="n"&gt;T&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&gt;fn&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;next&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="no"&gt;nil&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="c"&gt;// Final result&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
        &lt;span class="n"&gt;fn&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;next&lt;/span&gt; &lt;span class="c"&gt;// Continue with the next thunk&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="c"&gt;// Fibonacci function using trampolining with generics&lt;/span&gt;
&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&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="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;curr&lt;/span&gt; &lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="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;==&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="no"&gt;nil&lt;/span&gt; &lt;span class="c"&gt;// Return final accumulated value&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="m"&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="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
            &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;curr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="no"&gt;nil&lt;/span&gt; &lt;span class="c"&gt;// Return final accumulated value&lt;/span&gt;
        &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;func&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;thunk&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="kt"&gt;int&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
        &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="m"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&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="m"&gt;1&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;curr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;curr&lt;/span&gt;&lt;span class="o"&gt;+&lt;/span&gt;&lt;span class="n"&gt;prev&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;// Return next step as a thunk&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="k"&gt;func&lt;/span&gt; &lt;span class="n"&gt;main&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="n"&gt;n&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="m"&gt;10&lt;/span&gt; &lt;span class="c"&gt;// fib(10) == 55&lt;/span&gt;
    &lt;span class="n"&gt;fibThunk&lt;/span&gt; &lt;span class="o"&gt;:=&lt;/span&gt; &lt;span class="n"&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="m"&gt;0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="m"&gt;1&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="c"&gt;// Initialize with starting values&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;trampoline&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;fibThunk&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
    &lt;span class="n"&gt;fmt&lt;/span&gt;&lt;span class="o"&gt;.&lt;/span&gt;&lt;span class="n"&gt;Printf&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s"&gt;"Fibonacci(%d) = %d&lt;/span&gt;&lt;span class="se"&gt;\n&lt;/span&gt;&lt;span class="s"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;n&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="c"&gt;// Output: 55&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  Conclusion
&lt;/h3&gt;

&lt;p&gt;Trampolining is a powerful technique for optimizing recursive functions across various programming languages. It improves performance and prevents stack overflow errors by transforming recursive calls into an iterative process. By mastering this technique and implementing it in your codebase—whether in JavaScript, Java, C++, or Go—you can enhance the robustness and efficiency of your applications.&lt;/p&gt;

&lt;p&gt;As you explore more complex algorithms and data structures in your programming journey, consider incorporating trampolining where appropriate. This approach not only helps manage recursion effectively but also encourages cleaner and more maintainable code.&lt;/p&gt;

&lt;p&gt;Happy coding!&lt;/p&gt;

&lt;p&gt;Citations:&lt;br&gt;
[1] &lt;a href="https://rdinnager.github.io/trampoline/" rel="noopener noreferrer"&gt;https://rdinnager.github.io/trampoline/&lt;/a&gt;&lt;br&gt;
[2] &lt;a href="https://www.geeksforgeeks.org/es6-trampoline-function/" rel="noopener noreferrer"&gt;https://www.geeksforgeeks.org/es6-trampoline-function/&lt;/a&gt;&lt;br&gt;
[3] &lt;a href="https://gcc.gnu.org/onlinedocs/gccint/Trampolines.html" rel="noopener noreferrer"&gt;https://gcc.gnu.org/onlinedocs/gccint/Trampolines.html&lt;/a&gt;&lt;/p&gt;

</description>
      <category>javascript</category>
      <category>java</category>
      <category>go</category>
      <category>cpp</category>
    </item>
    <item>
      <title>Mastering Quick Sort: A Fundamental Algorithm in Computer Science</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Wed, 25 Dec 2024 13:46:12 +0000</pubDate>
      <link>https://dev.to/frorning/mastering-quick-sort-a-fundamental-algorithm-in-computer-science-15bi</link>
      <guid>https://dev.to/frorning/mastering-quick-sort-a-fundamental-algorithm-in-computer-science-15bi</guid>
      <description>&lt;h2&gt;
  
  
  Introduction to Quick Sort
&lt;/h2&gt;

&lt;p&gt;In the vast world of algorithms and data structures, Quick Sort stands as one of the most elegant and efficient sorting methods. Its simplicity and effectiveness make it a favorite among developers and researchers alike. Whether you're working on optimizing code or just curious about how modern computing systems handle large datasets, understanding Quick Sort is invaluable.&lt;/p&gt;

&lt;h2&gt;
  
  
  The Essence of Quick Sort
&lt;/h2&gt;

&lt;p&gt;Quick Sort is based on the divide-and-conquer strategy, which involves breaking down a complex problem into smaller sub-problems that are easier to solve. &lt;br&gt;
In the context of sorting algorithms, this means dividing an array or list of elements into two parts, such that the left part contains elements less than a chosen pivot and the right part contains elements greater than the pivot.&lt;/p&gt;
&lt;h3&gt;
  
  
  How It Works
&lt;/h3&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Choose a Pivot&lt;/strong&gt;: Select an element from the array as the pivot.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Partitioning&lt;/strong&gt;: Rearrange the array so that all elements with values less than the pivot come before it, while all elements with values greater than the pivot come after it. The pivot is now in its final position.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Recursively Apply to Sub-arrays&lt;/strong&gt;: Repeat the process for both sub-arrays formed by partitioning.&lt;/li&gt;
&lt;/ol&gt;
&lt;h2&gt;
  
  
  Implementing Quick Sort
&lt;/h2&gt;

&lt;p&gt;Here’s a basic Python implementation of Quick Sort:&lt;br&gt;
&lt;/p&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;quick_sort&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="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;&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;arr&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;pivot&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;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;2&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
        &lt;span class="n"&gt;left&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="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="n"&gt;arr&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;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;middle&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="n"&gt;arr&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="n"&gt;pivot&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="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="n"&gt;arr&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;pivot&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;quick_sort&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;middle&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="nf"&gt;quick_sort&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;# Example usage
&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;6&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;10&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;1&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="nf"&gt;quick_sort&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;p&gt;This implementation is straightforward and leverages list comprehensions for simplicity. However, it's important to note that in practice, the choice of pivot can significantly impact performance.&lt;/p&gt;

&lt;h2&gt;
  
  
  Performance Analysis
&lt;/h2&gt;

&lt;p&gt;The efficiency of Quick Sort varies based on the chosen pivot:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Average Case&lt;/strong&gt;: 

&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;O(nlogn)O(n log n)&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mord mathnormal"&gt;l&lt;/span&gt;&lt;span class="mord mathnormal"&gt;o&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, where n is the number of elements.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Best Case&lt;/strong&gt;: 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;O(nlogn)O(n log n)&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mord mathnormal"&gt;l&lt;/span&gt;&lt;span class="mord mathnormal"&gt;o&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Worst Case&lt;/strong&gt;: 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;O(n2)O(n^2)&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord"&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="msupsub"&gt;&lt;span class="vlist-t"&gt;&lt;span class="vlist-r"&gt;&lt;span class="vlist"&gt;&lt;span&gt;&lt;span class="pstrut"&gt;&lt;/span&gt;&lt;span class="sizing reset-size6 size3 mtight"&gt;&lt;span class="mord mtight"&gt;2&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
, which occurs when the smallest or largest element is always chosen as the pivot.&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The worst-case scenario can be mitigated by choosing a good pivot, such as the median-of-three method (choosing the median of the first, middle, and last elements).&lt;/p&gt;

&lt;h2&gt;
  
  
  Applications
&lt;/h2&gt;

&lt;p&gt;Quick Sort is widely used in real-world applications due to its efficiency. It's particularly useful for:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Sorting Large Datasets&lt;/strong&gt;: Quick Sort handles large datasets well, making it suitable for big data processing.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Memory Usage&lt;/strong&gt;: It uses 
&lt;span class="katex-element"&gt;
  &lt;span class="katex"&gt;&lt;span class="katex-mathml"&gt;O(logn)O(log n)&lt;/span&gt;&lt;span class="katex-html"&gt;&lt;span class="base"&gt;&lt;span class="strut"&gt;&lt;/span&gt;&lt;span class="mord mathnormal"&gt;O&lt;/span&gt;&lt;span class="mopen"&gt;(&lt;/span&gt;&lt;span class="mord mathnormal"&gt;l&lt;/span&gt;&lt;span class="mord mathnormal"&gt;o&lt;/span&gt;&lt;span class="mord mathnormal"&gt;g&lt;/span&gt;&lt;span class="mord mathnormal"&gt;n&lt;/span&gt;&lt;span class="mclose"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;
&lt;/span&gt;
 extra space if implemented with recursion.&lt;/li&gt;
&lt;/ul&gt;

&lt;h2&gt;
  
  
  Practical Examples
&lt;/h2&gt;

&lt;p&gt;Imagine you have a dataset of millions of records that need to be sorted. By leveraging the quick sort algorithm, you can efficiently manage and sort this data in a way that minimizes memory usage and processing time.&lt;/p&gt;

&lt;h3&gt;
  
  
  Example: Sorting Financial Data
&lt;/h3&gt;

&lt;p&gt;In a financial application, where transactions are processed in real-time, Quick Sort can help quickly process and analyze large volumes of transaction data to identify trends or anomalies.&lt;/p&gt;

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

&lt;p&gt;Quick Sort is an essential algorithm for any programmer or computer scientist. Its elegance lies not only in its simplicity but also in its ability to handle complex datasets efficiently. Whether you're optimizing code, analyzing algorithms, or just curious about the underlying principles, mastering Quick Sort provides a solid foundation in computational thinking and problem-solving.&lt;/p&gt;

</description>
      <category>python</category>
      <category>algorithms</category>
      <category>programming</category>
      <category>beginners</category>
    </item>
    <item>
      <title>Functional Programming with fp-ts in Node.js</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Sun, 22 Dec 2024 10:26:06 +0000</pubDate>
      <link>https://dev.to/frorning/functional-programming-with-fp-ts-in-nodejs-3239</link>
      <guid>https://dev.to/frorning/functional-programming-with-fp-ts-in-nodejs-3239</guid>
      <description>&lt;h4&gt;
  
  
  Introduction
&lt;/h4&gt;

&lt;p&gt;Functional programming (FP) has gained popularity for its composability, testability, and robustness. In the JavaScript ecosystem, libraries like &lt;strong&gt;fp-ts&lt;/strong&gt; bring powerful FP concepts to TypeScript, allowing you to write cleaner and more reliable code.&lt;/p&gt;

&lt;p&gt;This article explores &lt;strong&gt;fp-ts&lt;/strong&gt; concepts like &lt;code&gt;Option&lt;/code&gt;, &lt;code&gt;Either&lt;/code&gt;, &lt;code&gt;Task&lt;/code&gt;, &lt;code&gt;Reader&lt;/code&gt;, and &lt;code&gt;ReaderTaskEither&lt;/code&gt;. We’ll build a basic CRUD app using &lt;strong&gt;fp-ts&lt;/strong&gt;, &lt;strong&gt;pg&lt;/strong&gt; (PostgreSQL client), and &lt;strong&gt;Express.js&lt;/strong&gt; to see how these abstractions shine in real-world applications.&lt;/p&gt;




&lt;h3&gt;
  
  
  Key Concepts
&lt;/h3&gt;

&lt;p&gt;Before diving into the app, let’s briefly discuss the main concepts:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Option&lt;/strong&gt;: Models the presence or absence of a value (&lt;code&gt;Some&lt;/code&gt; or &lt;code&gt;None&lt;/code&gt;).&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Either&lt;/strong&gt;: Represents computations that can succeed (&lt;code&gt;Right&lt;/code&gt;) or fail (&lt;code&gt;Left&lt;/code&gt;).&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Task&lt;/strong&gt;: Represents lazy asynchronous computations.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Reader&lt;/strong&gt;: Injects dependencies into computations.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;ReaderTaskEither&lt;/strong&gt;: Combines Reader, Task, and Either for async operations with dependencies and error handling.&lt;/li&gt;
&lt;/ol&gt;




&lt;h3&gt;
  
  
  Setting Up the Project
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Initialize the Project
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="nb"&gt;mkdir &lt;/span&gt;fp-ts-crud &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="nb"&gt;cd &lt;/span&gt;fp-ts-crud
npm init &lt;span class="nt"&gt;-y&lt;/span&gt;
npm &lt;span class="nb"&gt;install &lt;/span&gt;express pg fp-ts io-ts
npm &lt;span class="nb"&gt;install&lt;/span&gt; &lt;span class="nt"&gt;--save-dev&lt;/span&gt; typescript @types/express ts-node-dev jest @types/jest ts-jest
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Setup TypeScript
&lt;/h4&gt;

&lt;p&gt;Create a &lt;code&gt;tsconfig.json&lt;/code&gt;:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight json"&gt;&lt;code&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="nl"&gt;"compilerOptions"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"target"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"ES2020"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"module"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"CommonJS"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"outDir"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"dist"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"strict"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
    &lt;/span&gt;&lt;span class="nl"&gt;"esModuleInterop"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="kc"&gt;true&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="p"&gt;},&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="nl"&gt;"include"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="s2"&gt;"src/**/*"&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Project Structure
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;src/
  index.ts        # Entry point
  db.ts           # Database setup
  models/         # Data models and validation
  services/       # Business logic
  controllers/    # CRUD operations
  utils/          # fp-ts utilities
  errors/         # Custom error classes
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  Implementing the CRUD App
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Database Setup (&lt;code&gt;db.ts&lt;/code&gt;)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;Pool&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;pg&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;export&lt;/span&gt; &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;pool&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Pool&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;
  &lt;span class="na"&gt;user&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;postgres&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="na"&gt;host&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;localhost&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="na"&gt;database&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;fp_ts_crud&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="na"&gt;password&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;password&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="na"&gt;port&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="mi"&gt;5432&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
&lt;span class="p"&gt;});&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Define Models and Validation (&lt;code&gt;models/User.ts&lt;/code&gt;)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="nx"&gt;t&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;io-ts&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;isRight&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;fp-ts/Either&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="k"&gt;export&lt;/span&gt; &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;User&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;t&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;type&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;
  &lt;span class="na"&gt;id&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;t&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="kr"&gt;number&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="nx"&gt;t&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="kr"&gt;string&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
  &lt;span class="na"&gt;email&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;t&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="kr"&gt;string&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
&lt;span class="p"&gt;});&lt;/span&gt;

&lt;span class="k"&gt;export&lt;/span&gt; &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;validateUser&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;unknown&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt; &lt;span class="nx"&gt;t&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;TypeOf&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="k"&gt;typeof&lt;/span&gt; &lt;span class="nx"&gt;User&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;|&lt;/span&gt; &lt;span class="kc"&gt;null&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;User&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;decode&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;data&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;isRight&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kc"&gt;null&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="p"&gt;};&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Custom Error Handling (&lt;code&gt;errors/AppError.ts&lt;/code&gt;)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="k"&gt;export&lt;/span&gt; &lt;span class="kd"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;AppError&lt;/span&gt; &lt;span class="kd"&gt;extends&lt;/span&gt; &lt;span class="nc"&gt;Error&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="nf"&gt;constructor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;public&lt;/span&gt; &lt;span class="nx"&gt;statusCode&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kr"&gt;number&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;public&lt;/span&gt; &lt;span class="nx"&gt;code&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kr"&gt;string&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;public&lt;/span&gt; &lt;span class="nx"&gt;message&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kr"&gt;string&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;super&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;message&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;name&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;AppError&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="k"&gt;export&lt;/span&gt; &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;createAppError&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;statusCode&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kr"&gt;number&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;code&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kr"&gt;string&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;message&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kr"&gt;string&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt; &lt;span class="nx"&gt;AppError&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;statusCode&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;message&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;};&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Service Layer (&lt;code&gt;services/UserService.ts&lt;/code&gt;)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;pool&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;../db&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;ReaderTaskEither&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;left&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;fp-ts/ReaderTaskEither&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;pipe&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;fp-ts/function&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;createAppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;AppError&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;../errors/AppError&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;validateUser&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;../models/User&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kd"&gt;type&lt;/span&gt; &lt;span class="nx"&gt;Dependencies&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;db&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="k"&gt;typeof&lt;/span&gt; &lt;span class="nx"&gt;pool&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
&lt;span class="kd"&gt;type&lt;/span&gt; &lt;span class="nx"&gt;User&lt;/span&gt; &lt;span class="o"&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="kr"&gt;string&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nl"&gt;email&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kr"&gt;string&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;

&lt;span class="k"&gt;export&lt;/span&gt; &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;createUser&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;
  &lt;span class="nx"&gt;user&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;User&lt;/span&gt;
&lt;span class="p"&gt;):&lt;/span&gt; &lt;span class="nx"&gt;ReaderTaskEither&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nx"&gt;Dependencies&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kr"&gt;string&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;deps&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="k"&gt;async &lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="c1"&gt;// Validate the incoming user data&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;validatedUser&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;validateUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;user&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

  &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="nx"&gt;validatedUser&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;createAppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;400&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;INVALID_USER_DATA&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Invalid user data provided&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="k"&gt;try&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;await&lt;/span&gt; &lt;span class="nx"&gt;deps&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;db&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;query&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
      &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;INSERT INTO users (name, email) VALUES ($1, $2) RETURNING id&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;
      &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;validatedUser&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;validatedUser&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;email&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt;
    &lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;`User created with ID: &lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;rows&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="nx"&gt;id&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;catch &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;error&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nf"&gt;left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;createAppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;USER_CREATION_FAILED&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Failed to create user&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="k"&gt;export&lt;/span&gt; &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;getUser&lt;/span&gt; &lt;span class="o"&gt;=&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="kr"&gt;number&lt;/span&gt;
&lt;span class="p"&gt;):&lt;/span&gt; &lt;span class="nx"&gt;ReaderTaskEither&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="nx"&gt;Dependencies&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;id&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kr"&gt;number&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nl"&gt;name&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kr"&gt;string&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nl"&gt;email&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="kr"&gt;string&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;deps&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="k"&gt;async &lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="k"&gt;try&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;await&lt;/span&gt; &lt;span class="nx"&gt;deps&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;db&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;query&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;SELECT * FROM users WHERE id = $1&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="nx"&gt;id&lt;/span&gt;&lt;span class="p"&gt;]);&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;rows&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="nf"&gt;right&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;rows&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="nf"&gt;left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;createAppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;404&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;USER_NOT_FOUND&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;User not found&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="k"&gt;catch&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;left&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;createAppError&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;USER_FETCH_FAILED&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Failed to fetch user&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  CRUD Operations (&lt;code&gt;controllers/UserController.ts&lt;/code&gt;)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;pipe&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;fp-ts/function&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;createUser&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;getUser&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;../services/UserService&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;pool&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;../db&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;AppError&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;../errors/AppError&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;errorHandler&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;err&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;unknown&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;res&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;express&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;Response&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt; &lt;span class="k"&gt;void&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;err&lt;/span&gt; &lt;span class="k"&gt;instanceof&lt;/span&gt; &lt;span class="nx"&gt;AppError&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;res&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;status&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;err&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;statusCode&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;json&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;error&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;code&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;err&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;code&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;message&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;err&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;message&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="p"&gt;});&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;res&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;status&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;500&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;json&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;error&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="na"&gt;code&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;UNKNOWN_ERROR&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;message&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;An unexpected error occurred&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="k"&gt;export&lt;/span&gt; &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;createUserHandler&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;req&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;express&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;Request&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;res&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;express&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;Response&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt; &lt;span class="k"&gt;void&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="nf"&gt;pipe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="nf"&gt;createUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;req&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;body&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt;
    &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;task&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nf"&gt;task&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;db&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pool&lt;/span&gt; &lt;span class="p"&gt;}),&lt;/span&gt;
    &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;promise&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;
      &lt;span class="nx"&gt;promise&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;
        &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;_tag&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Left&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;
          &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nf"&gt;errorHandler&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;res&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
          &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;res&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;json&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;message&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt; &lt;span class="p"&gt;})&lt;/span&gt;
      &lt;span class="p"&gt;)&lt;/span&gt;
  &lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;};&lt;/span&gt;

&lt;span class="k"&gt;export&lt;/span&gt; &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;getUserHandler&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;req&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;express&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;Request&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;res&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;express&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;Response&lt;/span&gt;&lt;span class="p"&gt;):&lt;/span&gt; &lt;span class="k"&gt;void&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="nf"&gt;pipe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;
    &lt;span class="nf"&gt;getUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nf"&gt;parseInt&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;req&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;params&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="mi"&gt;10&lt;/span&gt;&lt;span class="p"&gt;)),&lt;/span&gt;
    &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;task&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="nf"&gt;task&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;db&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pool&lt;/span&gt; &lt;span class="p"&gt;}),&lt;/span&gt;
    &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;promise&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;
      &lt;span class="nx"&gt;promise&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;then&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt;
        &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;_tag&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Left&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;
          &lt;span class="p"&gt;?&lt;/span&gt; &lt;span class="nf"&gt;errorHandler&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;res&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
          &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;res&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;json&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;
      &lt;span class="p"&gt;)&lt;/span&gt;
  &lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="p"&gt;};&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Express API (&lt;code&gt;index.ts&lt;/code&gt;)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="nx"&gt;express&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;express&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;createUserHandler&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;getUserHandler&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;./controllers/UserController&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;app&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;express&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
&lt;span class="nx"&gt;app&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;use&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;express&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;json&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;

&lt;span class="c1"&gt;// Routes&lt;/span&gt;
&lt;span class="nx"&gt;app&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;post&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;/users&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;createUserHandler&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;app&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="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;/users/:id&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;getUserHandler&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// Start Server&lt;/span&gt;
&lt;span class="nx"&gt;app&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;listen&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;3000&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Server running on http://localhost:3000&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  Running the App with Docker and Docker Compose
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Dockerfile
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight docker"&gt;&lt;code&gt;&lt;span class="c"&gt;# Stage 1: Build&lt;/span&gt;
&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;node:22&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s"&gt;builder&lt;/span&gt;
&lt;span class="k"&gt;WORKDIR&lt;/span&gt;&lt;span class="s"&gt; /app&lt;/span&gt;
&lt;span class="k"&gt;COPY&lt;/span&gt;&lt;span class="s"&gt; package*.json .&lt;/span&gt;
&lt;span class="k"&gt;RUN &lt;/span&gt;npm &lt;span class="nb"&gt;install&lt;/span&gt;
&lt;span class="k"&gt;COPY&lt;/span&gt;&lt;span class="s"&gt; . .&lt;/span&gt;
&lt;span class="k"&gt;RUN &lt;/span&gt;npm run build

&lt;span class="c"&gt;# Stage 2: Run&lt;/span&gt;
&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="s"&gt; node:22&lt;/span&gt;
&lt;span class="k"&gt;WORKDIR&lt;/span&gt;&lt;span class="s"&gt; /app&lt;/span&gt;
&lt;span class="k"&gt;COPY&lt;/span&gt;&lt;span class="s"&gt; --from=builder /app/dist ./dist&lt;/span&gt;
&lt;span class="k"&gt;COPY&lt;/span&gt;&lt;span class="s"&gt; package*.json ./&lt;/span&gt;
&lt;span class="k"&gt;RUN &lt;/span&gt;npm &lt;span class="nb"&gt;install&lt;/span&gt; &lt;span class="nt"&gt;--production&lt;/span&gt;
&lt;span class="k"&gt;CMD&lt;/span&gt;&lt;span class="s"&gt; ["node", "dist/index.js"]&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  docker-compose.yml
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight yaml"&gt;&lt;code&gt;&lt;span class="na"&gt;version&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s1"&gt;'&lt;/span&gt;&lt;span class="s"&gt;3.8'&lt;/span&gt;
&lt;span class="na"&gt;services&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
  &lt;span class="na"&gt;db&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
    &lt;span class="na"&gt;image&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;postgres:15&lt;/span&gt;
    &lt;span class="na"&gt;environment&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
      &lt;span class="na"&gt;POSTGRES_USER&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;postgres&lt;/span&gt;
      &lt;span class="na"&gt;POSTGRES_PASSWORD&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;password&lt;/span&gt;
      &lt;span class="na"&gt;POSTGRES_DB&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt; &lt;span class="s"&gt;fp_ts_crud&lt;/span&gt;
    &lt;span class="na"&gt;ports&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
      &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="s"&gt;5432:5432"&lt;/span&gt;
    &lt;span class="na"&gt;volumes&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
      &lt;span class="pi"&gt;-&lt;/span&gt; &lt;span class="s"&gt;db_data:/var/lib/postgresql/data&lt;/span&gt;
&lt;span class="na"&gt;volumes&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
  &lt;span class="na"&gt;db_data&lt;/span&gt;&lt;span class="pi"&gt;:&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Run the App - Development Mode
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Start the database&lt;/span&gt;
docker-compose up &lt;span class="nt"&gt;-d&lt;/span&gt;

&lt;span class="c"&gt;# Run the app&lt;/span&gt;
npx ts-node-dev src/index.ts
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Run the App - Production Mode
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="c"&gt;# Build the docker image&lt;/span&gt;
docker build &lt;span class="nt"&gt;-t&lt;/span&gt; fp-ts-crud-app &lt;span class="nb"&gt;.&lt;/span&gt;

&lt;span class="c"&gt;# Start the database&lt;/span&gt;
docker-compose up &lt;span class="nt"&gt;-d&lt;/span&gt;

&lt;span class="c"&gt;# Run the container&lt;/span&gt;
docker run &lt;span class="nt"&gt;-p&lt;/span&gt; 3000:3000 fp-ts-crud-app
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  Writing Tests
&lt;/h3&gt;

&lt;h4&gt;
  
  
  Setup Jest
&lt;/h4&gt;

&lt;p&gt;Update &lt;code&gt;package.json&lt;/code&gt; scripts:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight json"&gt;&lt;code&gt;&lt;span class="nl"&gt;"scripts"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="nl"&gt;"test"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"jest"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt;
  &lt;/span&gt;&lt;span class="nl"&gt;"test:watch"&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s2"&gt;"jest --watch"&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;span class="w"&gt;
&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  Example Test (&lt;code&gt;__tests__/UserService.test.ts&lt;/code&gt;)
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight typescript"&gt;&lt;code&gt;&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;createUser&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;getUser&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;../services/UserService&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
&lt;span class="k"&gt;import&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="nx"&gt;pool&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt; &lt;span class="k"&gt;from&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;../db&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;

&lt;span class="nx"&gt;jest&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;mock&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;../db&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="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;({&lt;/span&gt;
  &lt;span class="na"&gt;pool&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="na"&gt;query&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;jest&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;fn&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="nf"&gt;describe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;UserService&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="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="nf"&gt;afterEach&lt;/span&gt;&lt;span class="p"&gt;(()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;jest&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;clearAllMocks&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;
  &lt;span class="p"&gt;});&lt;/span&gt;

  &lt;span class="nf"&gt;it&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;should create a user&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;async &lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pool&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;query&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="nx"&gt;jest&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;Mock&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;mockResolvedValueOnce&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="p"&gt;[{&lt;/span&gt; &lt;span class="na"&gt;id&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="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;await&lt;/span&gt; &lt;span class="nf"&gt;createUser&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="s1"&gt;Alice&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;email&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;alice@example.com&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt; &lt;span class="p"&gt;})({&lt;/span&gt; &lt;span class="na"&gt;db&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pool&lt;/span&gt; &lt;span class="p"&gt;})();&lt;/span&gt;

    &lt;span class="nf"&gt;expect&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;_tag&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;toBe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Right&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;_tag&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Right&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="nf"&gt;expect&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;right&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;toBe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;User created with ID: 1&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="nf"&gt;it&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;should return error if user not found&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;async &lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;pool&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;query&lt;/span&gt; &lt;span class="k"&gt;as&lt;/span&gt; &lt;span class="nx"&gt;jest&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;Mock&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;mockResolvedValueOnce&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt; &lt;span class="na"&gt;rows&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="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;await&lt;/span&gt; &lt;span class="nf"&gt;getUser&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="na"&gt;db&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pool&lt;/span&gt; &lt;span class="p"&gt;})();&lt;/span&gt;

    &lt;span class="nf"&gt;expect&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;_tag&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;toBe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Left&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;_tag&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Left&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="nf"&gt;expect&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;message&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;toBe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;User not found&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="nf"&gt;it&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;should return error for invalid user data during creation&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;async &lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;invalidData&lt;/span&gt; &lt;span class="o"&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="mi"&gt;123&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="na"&gt;email&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;invalid-email&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt; &lt;span class="p"&gt;};&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;await&lt;/span&gt; &lt;span class="nf"&gt;createUser&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;invalidData&lt;/span&gt;&lt;span class="p"&gt;)({&lt;/span&gt; &lt;span class="na"&gt;db&lt;/span&gt;&lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="nx"&gt;pool&lt;/span&gt; &lt;span class="p"&gt;})();&lt;/span&gt;
    &lt;span class="nf"&gt;expect&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;_tag&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;toBe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Left&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;_tag&lt;/span&gt; &lt;span class="o"&gt;===&lt;/span&gt; &lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Left&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="nf"&gt;expect&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;left&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;message&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;toBe&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;'&lt;/span&gt;&lt;span class="s1"&gt;Invalid user data provided&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






&lt;h3&gt;
  
  
  Conclusion
&lt;/h3&gt;

&lt;p&gt;By leveraging &lt;strong&gt;fp-ts&lt;/strong&gt;, Docker, and robust error handling, we built a functional, scalable, and maintainable Node.js CRUD application. Using functional programming patterns makes your code more predictable and reliable, especially when handling asynchronous workflows.&lt;/p&gt;

</description>
      <category>javascript</category>
      <category>webdev</category>
      <category>node</category>
      <category>postgres</category>
    </item>
    <item>
      <title>Building a Basic Testing Framework in Bash 🐚</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Sat, 21 Dec 2024 17:21:40 +0000</pubDate>
      <link>https://dev.to/frorning/building-a-basic-testing-framework-in-bash-5c4i</link>
      <guid>https://dev.to/frorning/building-a-basic-testing-framework-in-bash-5c4i</guid>
      <description>&lt;p&gt;In the world of software development, testing is crucial for ensuring that your code behaves as expected. In this article, we'll explore a simple yet effective Bash script that serves as a basic testing framework. This framework will help you track test results, log outcomes, and summarize the results of your tests. Let's dive in! 🚀&lt;/p&gt;

&lt;h2&gt;
  
  
  Overview of the Script
&lt;/h2&gt;

&lt;p&gt;The script consists of several components that work together to facilitate testing:&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;Variables for Tracking Test Results&lt;/strong&gt;: These variables keep count of the total tests, passed tests, and failed tests.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Logging Function&lt;/strong&gt;: A function to log the results of each test.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Assertion Functions&lt;/strong&gt;: Functions to check for equality and command success.&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;Summary Function&lt;/strong&gt;: A function to display the overall results after running the tests.&lt;/li&gt;
&lt;/ol&gt;

&lt;h3&gt;
  
  
  Breakdown of the Script
&lt;/h3&gt;

&lt;h4&gt;
  
  
  1. Variables for Tracking Test Results
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;&lt;span class="nv"&gt;total_tests&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;0
&lt;span class="nv"&gt;passed_tests&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;0
&lt;span class="nv"&gt;failed_tests&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;0
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;These variables initialize counters for tracking how many tests have been run, how many have passed, and how many have failed.&lt;/p&gt;

&lt;h4&gt;
  
  
  2. Logging Function
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;log_result&lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
    &lt;span class="nb"&gt;local &lt;/span&gt;&lt;span class="nv"&gt;status&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="nv"&gt;$1&lt;/span&gt;
    &lt;span class="nb"&gt;local &lt;/span&gt;&lt;span class="nv"&gt;message&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="nv"&gt;$2&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;[&lt;/span&gt; &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$status&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt; &lt;span class="nt"&gt;-eq&lt;/span&gt; 0 &lt;span class="o"&gt;]&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="k"&gt;then
        &lt;/span&gt;&lt;span class="nb"&gt;echo&lt;/span&gt; &lt;span class="s2"&gt;"✅ PASS: &lt;/span&gt;&lt;span class="nv"&gt;$message&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;
        &lt;span class="o"&gt;((&lt;/span&gt;passed_tests++&lt;span class="o"&gt;))&lt;/span&gt;
    &lt;span class="k"&gt;else
        &lt;/span&gt;&lt;span class="nb"&gt;echo&lt;/span&gt; &lt;span class="s2"&gt;"❌ FAIL: &lt;/span&gt;&lt;span class="nv"&gt;$message&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;
        &lt;span class="o"&gt;((&lt;/span&gt;failed_tests++&lt;span class="o"&gt;))&lt;/span&gt;
    &lt;span class="k"&gt;fi&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;The &lt;code&gt;log_result&lt;/code&gt; function takes a status code and a message. If the status is &lt;code&gt;0&lt;/code&gt;, it logs a pass; otherwise, it logs a failure and increments the respective counters.&lt;/p&gt;

&lt;h4&gt;
  
  
  3. Assertion Functions
&lt;/h4&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Assert Equality&lt;/strong&gt;
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;assert_equal&lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
    &lt;span class="nb"&gt;local &lt;/span&gt;&lt;span class="nv"&gt;expected&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="nv"&gt;$1&lt;/span&gt;
    &lt;span class="nb"&gt;local &lt;/span&gt;&lt;span class="nv"&gt;actual&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="nv"&gt;$2&lt;/span&gt;
    &lt;span class="nb"&gt;local &lt;/span&gt;&lt;span class="nv"&gt;test_name&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="nv"&gt;$3&lt;/span&gt;

    &lt;span class="o"&gt;((&lt;/span&gt;total_tests++&lt;span class="o"&gt;))&lt;/span&gt;
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;[&lt;/span&gt; &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$expected&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$actual&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt; &lt;span class="o"&gt;]&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="k"&gt;then
        &lt;/span&gt;log_result 0 &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$test_name&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;
    &lt;span class="k"&gt;else
        &lt;/span&gt;log_result 1 &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$test_name&lt;/span&gt;&lt;span class="s2"&gt; (Expected: '&lt;/span&gt;&lt;span class="nv"&gt;$expected&lt;/span&gt;&lt;span class="s2"&gt;', Got: '&lt;/span&gt;&lt;span class="nv"&gt;$actual&lt;/span&gt;&lt;span class="s2"&gt;')"&lt;/span&gt;
    &lt;span class="k"&gt;fi&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This function checks if two values are equal. It logs the result and updates the total test count.&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;Assert Command Success&lt;/strong&gt;
&lt;/li&gt;
&lt;/ul&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;assert_command_success&lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
    &lt;span class="nb"&gt;local command&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$1&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;
    &lt;span class="nb"&gt;local &lt;/span&gt;&lt;span class="nv"&gt;test_name&lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="nv"&gt;$2&lt;/span&gt;

    &lt;span class="o"&gt;((&lt;/span&gt;total_tests++&lt;span class="o"&gt;))&lt;/span&gt;
    &lt;span class="nb"&gt;eval&lt;/span&gt; &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$command&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt; &amp;amp;&amp;gt; /dev/null
    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;[&lt;/span&gt; &lt;span class="nv"&gt;$?&lt;/span&gt; &lt;span class="nt"&gt;-eq&lt;/span&gt; 0 &lt;span class="o"&gt;]&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="k"&gt;then
        &lt;/span&gt;log_result 0 &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$test_name&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;
    &lt;span class="k"&gt;else
        &lt;/span&gt;log_result 1 &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$test_name&lt;/span&gt;&lt;span class="s2"&gt; (Command failed)"&lt;/span&gt;
    &lt;span class="k"&gt;fi&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;This function runs a command and checks its exit status. If the command succeeds, it logs a pass; otherwise, it logs a failure.&lt;/p&gt;

&lt;h4&gt;
  
  
  4. Summary Function
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight shell"&gt;&lt;code&gt;summary&lt;span class="o"&gt;()&lt;/span&gt; &lt;span class="o"&gt;{&lt;/span&gt;
    &lt;span class="nb"&gt;echo
    echo&lt;/span&gt; &lt;span class="s2"&gt;"Total Tests: &lt;/span&gt;&lt;span class="nv"&gt;$total_tests&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;
    &lt;span class="nb"&gt;echo&lt;/span&gt; &lt;span class="s2"&gt;"Passed: &lt;/span&gt;&lt;span class="nv"&gt;$passed_tests&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;
    &lt;span class="nb"&gt;echo&lt;/span&gt; &lt;span class="s2"&gt;"Failed: &lt;/span&gt;&lt;span class="nv"&gt;$failed_tests&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt;

    &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="o"&gt;[&lt;/span&gt; &lt;span class="s2"&gt;"&lt;/span&gt;&lt;span class="nv"&gt;$failed_tests&lt;/span&gt;&lt;span class="s2"&gt;"&lt;/span&gt; &lt;span class="nt"&gt;-eq&lt;/span&gt; 0 &lt;span class="o"&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;"🎉 All tests passed!"&lt;/span&gt;
    &lt;span class="k"&gt;else
        &lt;/span&gt;&lt;span class="nb"&gt;echo&lt;/span&gt; &lt;span class="s2"&gt;"⚠️ Some tests failed."&lt;/span&gt;
    &lt;span class="k"&gt;fi&lt;/span&gt;
&lt;span class="o"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;After all tests are executed, this function summarizes the results, indicating how many tests passed or failed.&lt;/p&gt;

&lt;h3&gt;
  
  
  Example Usage
&lt;/h3&gt;

&lt;p&gt;Below is an example of how to use this testing framework:&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;echo&lt;/span&gt; &lt;span class="s2"&gt;"Running Tests..."&lt;/span&gt;
assert_equal &lt;span class="s2"&gt;"hello"&lt;/span&gt; &lt;span class="s2"&gt;"hello"&lt;/span&gt; &lt;span class="s2"&gt;"Check if strings are equal"&lt;/span&gt;
assert_equal &lt;span class="s2"&gt;"1"&lt;/span&gt; &lt;span class="s2"&gt;"2"&lt;/span&gt; &lt;span class="s2"&gt;"Check if integers are equal"&lt;/span&gt;
assert_command_success &lt;span class="s2"&gt;"ls /"&lt;/span&gt; &lt;span class="s2"&gt;"Check if 'ls /' command succeeds"&lt;/span&gt;
assert_command_success &lt;span class="s2"&gt;"invalid_command"&lt;/span&gt; &lt;span class="s2"&gt;"Check if invalid command fails"&lt;/span&gt;

&lt;span class="c"&gt;# Display the summary&lt;/span&gt;
summary
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;p&gt;In this example:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;We check string equality.&lt;/li&gt;
&lt;li&gt;We validate integer equality (which will fail).&lt;/li&gt;
&lt;li&gt;We run a valid command (&lt;code&gt;ls /&lt;/code&gt;) and an invalid command (&lt;code&gt;invalid_command&lt;/code&gt;).&lt;/li&gt;
&lt;/ul&gt;

&lt;h3&gt;
  
  
  Conclusion 🎊
&lt;/h3&gt;

&lt;p&gt;This basic testing framework in Bash provides a simple way to automate your testing process. By using functions to assert conditions and log results, you can easily track the health of your scripts. Feel free to expand upon this framework by adding more complex assertions or incorporating additional features as needed!&lt;/p&gt;

&lt;p&gt;Happy scripting! 🖥️✨&lt;/p&gt;

</description>
      <category>bash</category>
      <category>linux</category>
      <category>testing</category>
      <category>beginners</category>
    </item>
    <item>
      <title>🚀 Unlocking Sprint Success with Jira Versions: A Strategic Guide</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Sat, 21 Dec 2024 16:41:21 +0000</pubDate>
      <link>https://dev.to/frorning/unlocking-sprint-success-with-jira-versions-a-strategic-guide-47ge</link>
      <guid>https://dev.to/frorning/unlocking-sprint-success-with-jira-versions-a-strategic-guide-47ge</guid>
      <description>&lt;p&gt;&lt;a href="https://www.atlassian.com/agile/tutorials/versions" rel="noopener noreferrer"&gt;Jira versions&lt;/a&gt; are powerful tools that help teams organize and track project milestones more effectively. Here's a comprehensive breakdown of leveraging versions for sprint success:&lt;/p&gt;

&lt;p&gt;&lt;a href="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fmj3qbhzeeig07wln630c.png" class="article-body-image-wrapper"&gt;&lt;img src="https://media2.dev.to/dynamic/image/width=800%2Cheight=%2Cfit=scale-down%2Cgravity=auto%2Cformat=auto/https%3A%2F%2Fdev-to-uploads.s3.amazonaws.com%2Fuploads%2Farticles%2Fmj3qbhzeeig07wln630c.png" alt="Jira versions" width="800" height="507"&gt;&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;🎯 What Are Versions?&lt;/strong&gt;&lt;br&gt;
Versions represent specific points-in-time for a project, serving as external milestones that focus on customer-facing outputs. Unlike sprints, which are internal time-boxes, versions help teams prioritize and organize work with a clear end goal.&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;🌟 Key Benefits of Using Versions&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;
&lt;strong&gt;📍 Milestone Tracking&lt;/strong&gt;: Create clear project checkpoints&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;🏷️ Issue Organization&lt;/strong&gt;: Assign and prioritize tasks within specific releases&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;📊 Progress Monitoring&lt;/strong&gt;: Visualize project advancement through version timelines&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;&lt;strong&gt;🛠️ Overcoming Common Challenges&lt;/strong&gt;&lt;/p&gt;

&lt;ol&gt;
&lt;li&gt;
&lt;strong&gt;🧩 Complexity&lt;/strong&gt;: Start simple and gradually customize your version workflow&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;📚 Training&lt;/strong&gt;: Invest time in understanding Jira's version management features&lt;/li&gt;
&lt;li&gt;
&lt;strong&gt;🧹 Maintenance&lt;/strong&gt;: Regularly review and clean up outdated versions&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;&lt;strong&gt;💡 Pro Tips for Effective Version Management&lt;/strong&gt;&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Use versions to align team efforts towards specific project goals&lt;/li&gt;
&lt;li&gt;Integrate versions with sprint planning for seamless workflow&lt;/li&gt;
&lt;li&gt;Leverage Jira's reporting tools to track version progress&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;By embracing Jira versions, teams can transform their project management approach, delivering more structured and focused increments with greater efficiency. 💪✨&lt;/p&gt;

</description>
      <category>beginners</category>
      <category>agile</category>
      <category>productivity</category>
      <category>devops</category>
    </item>
    <item>
      <title>Precise Allocations with Big.js: Handling Rounding and Leftover Redistribution</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Sat, 21 Dec 2024 16:34:29 +0000</pubDate>
      <link>https://dev.to/frorning/precise-allocations-with-bigjs-handling-rounding-and-leftover-redistribution-4iol</link>
      <guid>https://dev.to/frorning/precise-allocations-with-bigjs-handling-rounding-and-leftover-redistribution-4iol</guid>
      <description>&lt;p&gt;When dealing with fractional allocations of large amounts, rounding errors and leftover redistributions become significant challenges. These problems are not confined to financial calculations; they can occur in other domains like resource distribution, task scheduling, or budget allocation. In this article, we demonstrate a verified and tested method using the &lt;code&gt;big.js&lt;/code&gt; library in JavaScript to achieve precise allocations while handling rounding and leftover redistribution effectively.&lt;/p&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;Problem: Allocating Funds Among Stocks&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Imagine a scenario where you need to allocate a very large amount of money among multiple stocks based on their respective percentages. For example:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Stock A: 50.5%&lt;/li&gt;
&lt;li&gt;Stock B: 30.3%&lt;/li&gt;
&lt;li&gt;Stock C: 19.2%&lt;/li&gt;
&lt;/ul&gt;

&lt;p&gt;The requirements are:&lt;/p&gt;

&lt;ul&gt;
&lt;li&gt;Perform calculations in cents to avoid floating-point errors.&lt;/li&gt;
&lt;li&gt;Distribute leftover cents fairly after initial rounding.&lt;/li&gt;
&lt;li&gt;Convert the final allocations back to dollars with two decimal places.&lt;/li&gt;
&lt;/ul&gt;




&lt;h3&gt;
  
  
  &lt;strong&gt;The Solution&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Using the &lt;code&gt;big.js&lt;/code&gt; library, we can handle these challenges with arbitrary-precision arithmetic. Here is the complete solution:&lt;/p&gt;

&lt;h4&gt;
  
  
  &lt;strong&gt;1. Initialize Inputs and Convert Percentages to Ratios&lt;/strong&gt;
&lt;/h4&gt;



&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;Big&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;require&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;big.js&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="kd"&gt;function&lt;/span&gt; &lt;span class="nf"&gt;allocateMoney&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;amount&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;allocations&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="c1"&gt;// Step 1: Convert percentages to rational numbers&lt;/span&gt;
  &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;totalPercent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="k"&gt;in&lt;/span&gt; &lt;span class="nx"&gt;allocations&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;totalPercent&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;totalPercent&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;plus&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;allocations&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]));&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;allocationRatios&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;
  &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="k"&gt;in&lt;/span&gt; &lt;span class="nx"&gt;allocations&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;allocationRatios&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;allocations&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]).&lt;/span&gt;&lt;span class="nf"&gt;div&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;totalPercent&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  &lt;strong&gt;2. Calculate Initial Allocation in Cents&lt;/strong&gt;
&lt;/h4&gt;

&lt;p&gt;Convert the total amount to cents and perform initial rounding:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;totalCents&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;amount&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;times&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;toFixed&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;// Convert amount to cents&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;allocatedCents&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;
  &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="k"&gt;in&lt;/span&gt; &lt;span class="nx"&gt;allocationRatios&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;allocatedCents&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;allocationRatios&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nf"&gt;times&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;totalCents&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;toFixed&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;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt; &lt;span class="c1"&gt;// Convert to int (round down)&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  &lt;strong&gt;3. Redistribute Remaining Cents&lt;/strong&gt;
&lt;/h4&gt;

&lt;p&gt;Calculate the leftover cents and distribute them fairly based on fractional remainders:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;  &lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;distributedTotal&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
  &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="k"&gt;in&lt;/span&gt; &lt;span class="nx"&gt;allocatedCents&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;distributedTotal&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;distributedTotal&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;plus&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;allocatedCents&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]));&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;remainingCents&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;totalCents&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;minus&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;distributedTotal&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;toFixed&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;// Sort allocations by fractional remainder descending for redistribution&lt;/span&gt;
  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;fractionalRemainders&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;
  &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="k"&gt;in&lt;/span&gt; &lt;span class="nx"&gt;allocationRatios&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;allocated&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;allocationRatios&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nf"&gt;times&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;totalCents&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;fractionalPart&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;allocated&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;minus&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;allocated&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;toFixed&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="nx"&gt;fractionalRemainders&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;fractionalPart&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;sortedKeys&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;Object&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="nx"&gt;fractionalRemainders&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="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;=&amp;gt;&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;fractionalRemainders&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nf"&gt;gt&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;fractionalRemainders&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;if &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;fractionalRemainders&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;b&lt;/span&gt;&lt;span class="p"&gt;].&lt;/span&gt;&lt;span class="nf"&gt;lt&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;fractionalRemainders&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;a&lt;/span&gt;&lt;span class="p"&gt;]))&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
      &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
    &lt;span class="p"&gt;}&lt;/span&gt;
    &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;
  &lt;span class="p"&gt;});&lt;/span&gt;

  &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="nx"&gt;remainingCents&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="nx"&gt;i&lt;/span&gt;&lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;sortedKeys&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;i&lt;/span&gt; &lt;span class="o"&gt;%&lt;/span&gt; &lt;span class="nx"&gt;sortedKeys&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nx"&gt;length&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;
    &lt;span class="nx"&gt;allocatedCents&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;allocatedCents&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]).&lt;/span&gt;&lt;span class="nf"&gt;plus&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;toFixed&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;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h4&gt;
  
  
  &lt;strong&gt;4. Convert Back to Dollars&lt;/strong&gt;
&lt;/h4&gt;

&lt;p&gt;Finally, convert the allocations back to dollars:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;  &lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;allocatedDollars&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;{};&lt;/span&gt;
  &lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="k"&gt;in&lt;/span&gt; &lt;span class="nx"&gt;allocatedCents&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
    &lt;span class="nx"&gt;allocatedDollars&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;allocatedCents&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]).&lt;/span&gt;&lt;span class="nf"&gt;div&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;100&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="nf"&gt;toFixed&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;// Convert cents to dollars with 2 decimals&lt;/span&gt;
  &lt;span class="p"&gt;}&lt;/span&gt;

  &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nx"&gt;allocatedDollars&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;
  
  
  &lt;strong&gt;Example Usage&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;Here’s how you can use the &lt;code&gt;allocateMoney&lt;/code&gt; function to allocate funds among stocks:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight javascript"&gt;&lt;code&gt;&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;totalAmount&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;1234567890123456.78&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;// A very large total amount&lt;/span&gt;
&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;stockAllocations&lt;/span&gt; &lt;span class="o"&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;Stock A&lt;/span&gt;&lt;span class="dl"&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;50.5&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="c1"&gt;// 50.5%&lt;/span&gt;
  &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Stock B&lt;/span&gt;&lt;span class="dl"&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;30.3&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="c1"&gt;// 30.3%&lt;/span&gt;
  &lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Stock C&lt;/span&gt;&lt;span class="dl"&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;19.2&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="c1"&gt;// 19.2%&lt;/span&gt;
&lt;span class="p"&gt;};&lt;/span&gt;

&lt;span class="kd"&gt;const&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nf"&gt;allocateMoney&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;totalAmount&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nx"&gt;stockAllocations&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="s2"&gt;Allocation:&lt;/span&gt;&lt;span class="dl"&gt;"&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;

&lt;span class="c1"&gt;// Calculate total allocated&lt;/span&gt;
&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;totalAllocated&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;span class="k"&gt;for &lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="kd"&gt;let&lt;/span&gt; &lt;span class="nx"&gt;key&lt;/span&gt; &lt;span class="k"&gt;in&lt;/span&gt; &lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;
  &lt;span class="nx"&gt;totalAllocated&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nx"&gt;totalAllocated&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;plus&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;new&lt;/span&gt; &lt;span class="nc"&gt;Big&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nx"&gt;result&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="nx"&gt;key&lt;/span&gt;&lt;span class="p"&gt;]));&lt;/span&gt;
&lt;span class="p"&gt;}&lt;/span&gt;

&lt;span class="nx"&gt;console&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="s2"&gt;`Total Allocated: $&lt;/span&gt;&lt;span class="p"&gt;${&lt;/span&gt;&lt;span class="nx"&gt;totalAllocated&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nf"&gt;toFixed&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="s2"&gt;`&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;



&lt;h3&gt;
  
  
  &lt;strong&gt;Output for the Example&lt;/strong&gt;
&lt;/h3&gt;

&lt;p&gt;For the given inputs, the output is:&lt;br&gt;
&lt;/p&gt;

&lt;div class="highlight js-code-highlight"&gt;
&lt;pre class="highlight plaintext"&gt;&lt;code&gt;Allocation:
{
  'Stock A': '623456784512345.67',
  'Stock B': '374074070707407.41',
  'Stock C': '237037034903703.70'
}
Total Allocated: $1234567890123456.78
&lt;/code&gt;&lt;/pre&gt;

&lt;/div&gt;






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

&lt;ol&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;Precise Arithmetic with &lt;code&gt;big.js&lt;/code&gt;:&lt;/strong&gt;&lt;br&gt;
The &lt;code&gt;big.js&lt;/code&gt; library ensures accuracy by avoiding floating-point errors.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;Handle Leftovers Fairly:&lt;/strong&gt;&lt;br&gt;
Use fractional remainders to distribute leftover units deterministically and fairly.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;Reconcile Totals:&lt;/strong&gt;&lt;br&gt;
After all adjustments, ensure that the total allocation matches the original amount.&lt;/p&gt;&lt;/li&gt;
&lt;li&gt;&lt;p&gt;&lt;strong&gt;Scalable for Large Values:&lt;/strong&gt;&lt;br&gt;
This approach works seamlessly for very large amounts, making it suitable for financial and resource allocation problems.&lt;/p&gt;&lt;/li&gt;
&lt;/ol&gt;

&lt;p&gt;By following this method, you can achieve precise and fair allocations in any scenario requiring high numerical accuracy.&lt;/p&gt;

</description>
      <category>programming</category>
      <category>algorithms</category>
      <category>node</category>
      <category>javascript</category>
    </item>
    <item>
      <title>Embedding vs. Referencing - A Strategic Choice!</title>
      <dc:creator>Piyush Chauhan</dc:creator>
      <pubDate>Sat, 21 Dec 2024 14:34:11 +0000</pubDate>
      <link>https://dev.to/frorning/-i1m</link>
      <guid>https://dev.to/frorning/-i1m</guid>
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  &lt;a href="https://dev.to/frorning/mongodb-data-modeling-embedding-vs-referencing-a-strategic-choice-53np" class="ltag__link__link"&gt;
    &lt;div class="ltag__link__content"&gt;
      &lt;h2&gt;🔍 MongoDB Data Modeling: Embedding vs. Referencing - A Strategic Choice!&lt;/h2&gt;
      &lt;h3&gt;Piyush Chauhan ・ Dec 21 '24&lt;/h3&gt;
      &lt;div class="ltag__link__taglist"&gt;
        &lt;span class="ltag__link__tag"&gt;#mongodb&lt;/span&gt;
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  &lt;/a&gt;
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