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<h1 id="113-bubble-sort">11.3 &nbsp; Bubble sort<a class="headerlink" href="#113-bubble-sort" title="Permanent link">&para;</a></h1>
<p><u>Bubble sort</u> achieves sorting by continuously comparing and swapping adjacent elements. This process resembles bubbles rising from the bottom to the top, hence the name bubble sort.</p>
<p>As shown in the following figures, the bubbling process can be simulated using element swap operations: starting from the leftmost end of the array and moving right, sequentially compare the size of adjacent elements. If "left element &gt; right element," then swap them. After the traversal, the largest element will be moved to the far right end of the array.</p>
<p>As shown in Figure 11-4, the bubbling process can be simulated using element swap operations: starting from the leftmost end of the array and moving right, sequentially compare the size of adjacent elements. If "left element &gt; right element," then swap them. After the traversal, the largest element will be moved to the far right end of the array.</p>
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<p align="center"> Figure 11-4 &nbsp; Simulating bubble process using element swap </p>
<h2 id="1131-algorithm-process">11.3.1 &nbsp; Algorithm process<a class="headerlink" href="#1131-algorithm-process" title="Permanent link">&para;</a></h2>
<p>Assuming the length of the array is <span class="arithmatex">\(n\)</span>, the steps of bubble sort are shown below.</p>
<p>Assuming the length of the array is <span class="arithmatex">\(n\)</span>, the steps of bubble sort are shown in Figure 11-5.</p>
<ol>
<li>First, perform a "bubble" on <span class="arithmatex">\(n\)</span> elements, <strong>swapping the largest element to its correct position</strong>.</li>
<li>Next, perform a "bubble" on the remaining <span class="arithmatex">\(n - 1\)</span> elements, <strong>swapping the second largest element to its correct position</strong>.</li>