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-    Chapter 1. Encounter With Algorithms
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 <!-- Page content -->
 <h1 id="112-selection-sort">11.2 &nbsp; Selection Sort<a class="headerlink" href="#112-selection-sort" title="Permanent link">&para;</a></h1>
-<p><u>Selection sort (selection sort)</u> works very simply: it opens a loop, and in each round, selects the smallest element from the unsorted interval and places it at the end of the sorted interval.</p>
-<p>Assume the array has length <span class="arithmatex">\(n\)</span>. The algorithm flow of selection sort is shown in Figure 11-2.</p>
+<p><u>Selection sort</u> works very simply: in each round, it selects the smallest element from the unsorted interval and places it at the end of the sorted interval.</p>
+<p>Assume the array has length <span class="arithmatex">\(n\)</span>. The procedure of selection sort is shown in Figure 11-2.</p>
 <ol>
 <li>Initially, all elements are unsorted, i.e., the unsorted (index) interval is <span class="arithmatex">\([0, n-1]\)</span>.</li>
 <li>Select the smallest element in the interval <span class="arithmatex">\([0, n-1]\)</span> and swap it with the element at index <span class="arithmatex">\(0\)</span>. After completion, the first element of the array is sorted.</li>
 <li>Select the smallest element in the interval <span class="arithmatex">\([1, n-1]\)</span> and swap it with the element at index <span class="arithmatex">\(1\)</span>. After completion, the first 2 elements of the array are sorted.</li>
 <li>And so on. After <span class="arithmatex">\(n - 1\)</span> rounds of selection and swapping, the first <span class="arithmatex">\(n - 1\)</span> elements of the array are sorted.</li>
-<li>The only remaining element must be the largest element, requiring no sorting, so the array sorting is complete.</li>
+<li>The only remaining element must be the largest, so no further sorting is needed and the array is sorted.</li>
 </ol>
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 <p align="center"> Figure 11-2 &nbsp; Selection sort steps </p>
 
-<p>In the code, we use <span class="arithmatex">\(k\)</span> to record the smallest element within the unsorted interval:</p>
+<p>In the code, we use <span class="arithmatex">\(k\)</span> to track the smallest element within the unsorted interval:</p>
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 <h2 id="1121-algorithm-characteristics">11.2.1 &nbsp; Algorithm Characteristics<a class="headerlink" href="#1121-algorithm-characteristics" title="Permanent link">&para;</a></h2>
 <ul>
-<li><strong>Time complexity of <span class="arithmatex">\(O(n^2)\)</span>, non-adaptive sorting</strong>: The outer loop has <span class="arithmatex">\(n - 1\)</span> rounds in total. The length of the unsorted interval in the first round is <span class="arithmatex">\(n\)</span>, and the length of the unsorted interval in the last round is <span class="arithmatex">\(2\)</span>. That is, each round of the outer loop contains <span class="arithmatex">\(n\)</span>, <span class="arithmatex">\(n - 1\)</span>, <span class="arithmatex">\(\dots\)</span>, <span class="arithmatex">\(3\)</span>, <span class="arithmatex">\(2\)</span> inner loop iterations, summing to <span class="arithmatex">\(\frac{(n - 1)(n + 2)}{2}\)</span>.</li>
-<li><strong>Space complexity of <span class="arithmatex">\(O(1)\)</span>, in-place sorting</strong>: Pointers <span class="arithmatex">\(i\)</span> and <span class="arithmatex">\(j\)</span> use a constant amount of extra space.</li>
-<li><strong>Non-stable sorting</strong>: As shown in Figure 11-3, element <code>nums[i]</code> may be swapped to the right of an element equal to it, causing a change in their relative order.</li>
+<li><strong>Time complexity <span class="arithmatex">\(O(n^2)\)</span>, non-adaptive sorting</strong>: The outer loop has <span class="arithmatex">\(n - 1\)</span> rounds in total. The length of the unsorted interval in the first round is <span class="arithmatex">\(n\)</span>, and the length of the unsorted interval in the last round is <span class="arithmatex">\(2\)</span>. That is, the rounds of the outer loop contain inner loops with <span class="arithmatex">\(n\)</span>, <span class="arithmatex">\(n - 1\)</span>, <span class="arithmatex">\(\dots\)</span>, <span class="arithmatex">\(3\)</span>, and <span class="arithmatex">\(2\)</span> iterations, summing to <span class="arithmatex">\(\frac{(n - 1)(n + 2)}{2}\)</span>.</li>
+<li><strong>Space complexity <span class="arithmatex">\(O(1)\)</span>, in-place sorting</strong>: Pointers <span class="arithmatex">\(i\)</span> and <span class="arithmatex">\(j\)</span> use a constant amount of extra space.</li>
+<li><strong>Unstable sorting</strong>: As shown in Figure 11-3, element <code>nums[i]</code> may be swapped to the right of an element equal to it, causing a change in their relative order.</li>
 </ul>
 <p><img alt="Selection sort non-stability example" class="animation-figure" src="../selection_sort.assets/selection_sort_instability.png" /></p>
 <p align="center"> Figure 11-3 &nbsp; Selection sort non-stability example </p>
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