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</style></head> <body> <header> <div> <a href="/" id="logo">&gt; _</a> <nav> <a href="https://code.evalyte.net" target="_blank">Repositories</a> <!--<a href="/devlog">Devlog</a>--> <a href="/notes">Notes</a> <!--<a href="/utilities">Utilities</a>--> <!--<a href="/services">Services</a>--> <a href="/about">About</a> </nav> </div> </header> <main data-astro-cid-hhdr4bp3> <div style="display:flex;flex-direction:column;gap:var(--default-gap);justify-content:center;align-items:start"> <div style="display:flex;flex-direction:column;gap:var(--default-gap);justify-content:center;align-items:start"> <h1 data-astro-cid-hhdr4bp3>Quick Sort algorithm</h1> </div> <div style="flex:1"> <p data-astro-cid-hhdr4bp3> <p>To explain the Quick Sort algorithm, let’s take a simple example:</p>
<p>We have an array of number (integer) in random order, but we want them in ascending order, so we have to sort them, here comes the Quick Sort algorithm.</p>
<p><em>Note: The range of the numbers and the length of the array have no importance for the algorithm itself, but it will have a performance cost.</em></p>
<h2 id="algorithm">Algorithm</h2>
<p>Select a number, called “pivot”, chosen arbritrary from the array itself, put all the numbers lower than the pivot before it and all the numbers greater after it, split the current partition into 2 new partitions (the ones before and after the pivot), and repeat the procedure for each partition until there is no partition left (when the array length is 1).</p>
<p>The Quick Sort algorithm steps are:</p>
<ul>
<li>Select a pivot value from the partition and move it at the end of the partition (P, the pivot value).</li>
<li>Remember the start index of the current partition (S, the start index).</li>
<li>for each element (E), if E is lower or equal than P, then swap value E with the value at index S, then increment S.</li>
<li>Use the pivot P to divide the partition into 2 new partitions.</li>
<li>Repeat the algorithm for the 2 newly created partitions until there is no partition left.</li>
</ul>
<h2 id="implementation">Implementation</h2>
<h4 id="go">Go</h4>
<pre class="astro-code github-dark" style="background-color:#24292e;color:#e1e4e8; overflow-x: auto;" tabindex="0" data-language="go"><code><span class="line"><span style="color:#F97583">func</span><span style="color:#B392F0"> Swap</span><span style="color:#E1E4E8">(</span><span style="color:#FFAB70">partition</span><span style="color:#E1E4E8"> []</span><span style="color:#F97583">int</span><span style="color:#E1E4E8">, </span><span style="color:#FFAB70">i</span><span style="color:#F97583"> int</span><span style="color:#E1E4E8">, </span><span style="color:#FFAB70">j</span><span style="color:#F97583"> int</span><span style="color:#E1E4E8">) {</span></span>
<span class="line"><span style="color:#E1E4E8"> partition[i], partition[j] </span><span style="color:#F97583">=</span><span style="color:#E1E4E8"> partition[j], partition[i]</span></span>
<span class="line"><span style="color:#E1E4E8">}</span></span>
<span class="line"></span>
<span class="line"><span style="color:#F97583">func</span><span style="color:#B392F0"> QuickSort</span><span style="color:#E1E4E8">(</span><span style="color:#FFAB70">partition</span><span style="color:#E1E4E8"> []</span><span style="color:#F97583">int</span><span style="color:#E1E4E8">) {</span></span>
<span class="line"><span style="color:#B392F0"> Swap</span><span style="color:#E1E4E8">(partition, </span><span style="color:#B392F0">len</span><span style="color:#E1E4E8">(partition) </span><span style="color:#F97583">/</span><span style="color:#79B8FF"> 2</span><span style="color:#E1E4E8">, </span><span style="color:#B392F0">len</span><span style="color:#E1E4E8">(partition) </span><span style="color:#F97583">-</span><span style="color:#79B8FF"> 1</span><span style="color:#E1E4E8">) </span><span style="color:#6A737D">// Select the pivot from the middle (arbitrary) of the partition and swap it with the last element</span></span>
<span class="line"></span>
<span class="line"><span style="color:#E1E4E8"> startIndex </span><span style="color:#F97583">:=</span><span style="color:#79B8FF"> 0</span></span>
<span class="line"><span style="color:#E1E4E8"> pivot </span><span style="color:#F97583">:=</span><span style="color:#E1E4E8"> partition[</span><span style="color:#B392F0">len</span><span style="color:#E1E4E8">(partition) </span><span style="color:#F97583">-</span><span style="color:#79B8FF"> 1</span><span style="color:#E1E4E8">] </span><span style="color:#6A737D">// Since we already swapped the pivot, we get the value directly from the end of the partition</span></span>
<span class="line"></span>
<span class="line"><span style="color:#F97583"> for</span><span style="color:#E1E4E8"> i </span><span style="color:#F97583">:=</span><span style="color:#E1E4E8"> startIndex; i </span><span style="color:#F97583">&#x3C;</span><span style="color:#B392F0"> len</span><span style="color:#E1E4E8">(partition); i</span><span style="color:#F97583">++</span><span style="color:#E1E4E8"> {</span></span>
<span class="line"><span style="color:#F97583"> if</span><span style="color:#E1E4E8"> partition[i] </span><span style="color:#F97583">&#x3C;=</span><span style="color:#E1E4E8"> pivot {</span></span>
<span class="line"><span style="color:#B392F0"> Swap</span><span style="color:#E1E4E8">(partition, i, startIndex)</span></span>
<span class="line"><span style="color:#E1E4E8"> startIndex</span><span style="color:#F97583">++</span></span>
<span class="line"><span style="color:#E1E4E8"> }</span></span>
<span class="line"><span style="color:#E1E4E8"> }</span></span>
<span class="line"></span>
<span class="line"><span style="color:#6A737D"> // startIndex now point at the first element of the values greater or equal than the pivot</span></span>
<span class="line"><span style="color:#F97583"> if</span><span style="color:#E1E4E8"> startIndex </span><span style="color:#F97583">></span><span style="color:#79B8FF"> 1</span><span style="color:#E1E4E8"> {</span></span>
<span class="line"><span style="color:#B392F0"> QuickSort</span><span style="color:#E1E4E8">(partition[:startIndex </span><span style="color:#F97583">-</span><span style="color:#79B8FF"> 1</span><span style="color:#E1E4E8">])</span></span>
<span class="line"><span style="color:#E1E4E8"> }</span></span>
<span class="line"></span>
<span class="line"><span style="color:#F97583"> if</span><span style="color:#B392F0"> len</span><span style="color:#E1E4E8">(partition) </span><span style="color:#F97583">-</span><span style="color:#E1E4E8"> startIndex </span><span style="color:#F97583">></span><span style="color:#79B8FF"> 1</span><span style="color:#E1E4E8"> {</span></span>
<span class="line"><span style="color:#B392F0"> QuickSort</span><span style="color:#E1E4E8">(partition[startIndex:])</span></span>
<span class="line"><span style="color:#E1E4E8"> }</span></span>
<span class="line"><span style="color:#E1E4E8">}</span></span></code></pre>
<h2 id="performance-speed">Performance (speed)</h2>
<p>Average: O(n*log(n))<br>
Best case: O(n*log(n))<br>
Worst case: O(n²)</p>
<h2 id="sources">Sources</h2>
<p><a href="https://fr.wikipedia.org/wiki/Tri_rapide">https://fr.wikipedia.org/wiki/Tri_rapide</a> (fr)<br>
<a href="https://en.wikipedia.org/wiki/Quicksort">https://en.wikipedia.org/wiki/Quicksort</a> (en)<br>
My experience.</p> </p> </div> </div> </main> <footer>© 2024 Evalyte</footer> </body></html>
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