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<h1 id="117-heap-sort">11.7 &nbsp; Heap sort<a class="headerlink" href="#117-heap-sort" title="Permanent link">&para;</a></h1>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>Before reading this section, please make sure you have completed the "Heap" chapter.</p>
<p>Before reading this section, please ensure you have completed the "Heap" chapter.</p>
</div>
<p><u>Heap sort</u> is an efficient sorting algorithm based on the heap data structure. We can implement heap sort using the "heap creation" and "element extraction" operations we have already learned.</p>
<ol>
<li>Input the array and establish a min-heap, where the smallest element is at the heap's top.</li>
<li>Continuously perform the extraction operation, recording the extracted elements in sequence to obtain a sorted list from smallest to largest.</li>
<li>Input the array and construct a min-heap, where the smallest element is at the top of the heap.</li>
<li>Continuously perform the extraction operation, record the extracted elements sequentially to obtain a sorted list from smallest to largest.</li>
</ol>
<p>Although the above method is feasible, it requires an additional array to save the popped elements, which is somewhat space-consuming. In practice, we usually use a more elegant implementation.</p>
<p>Although the above method is feasible, it requires an additional array to store the popped elements, which is somewhat space-consuming. In practice, we usually use a more elegant implementation.</p>
<h2 id="1171-algorithm-flow">11.7.1 &nbsp; Algorithm flow<a class="headerlink" href="#1171-algorithm-flow" title="Permanent link">&para;</a></h2>
<p>Suppose the array length is <span class="arithmatex">\(n\)</span>, the heap sort process is as follows.</p>
<ol>
<li>Input the array and establish a max-heap. After completion, the largest element is at the heap's top.</li>
<li>Swap the top element of the heap (the first element) with the heap's bottom element (the last element). After the swap, reduce the heap's length by <span class="arithmatex">\(1\)</span> and increase the sorted elements count by <span class="arithmatex">\(1\)</span>.</li>
<li>Input the array and establish a max-heap. After this step, the largest element is positioned at the top of the heap.</li>
<li>Swap the top element of the heap (the first element) with the heap's bottom element (the last element). Following this swap, reduce the heap's length by <span class="arithmatex">\(1\)</span> and increase the sorted elements count by <span class="arithmatex">\(1\)</span>.</li>
<li>Starting from the heap top, perform the sift-down operation from top to bottom. After the sift-down, the heap's property is restored.</li>
<li>Repeat steps <code>2.</code> and <code>3.</code> Loop for <span class="arithmatex">\(n - 1\)</span> rounds to complete the sorting of the array.</li>
</ol>
<div class="admonition tip">
<p class="admonition-title">Tip</p>
<p>In fact, the element extraction operation also includes steps <code>2.</code> and <code>3.</code>, with the addition of a popping element step.</p>
<p>In fact, the element extraction operation also includes steps <code>2.</code> and <code>3.</code>, with an additional step to pop (remove) the extracted element from the heap.</p>
</div>
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