deploy

chapter_sorting/bubble_sort/index.html

@@ -3461,7 +3461,7 @@
 <li>首先，对 <span class="arithmatex">\(n\)</span> 个元素执行“冒泡”，<strong>将数组的最大元素交换至正确位置</strong>，</li>
 <li>接下来，对剩余 <span class="arithmatex">\(n - 1\)</span> 个元素执行“冒泡”，<strong>将第二大元素交换至正确位置</strong>。</li>
 <li>以此类推，经过 <span class="arithmatex">\(n - 1\)</span> 轮“冒泡”后，<strong>前 <span class="arithmatex">\(n - 1\)</span> 大的元素都被交换至正确位置</strong>。</li>
-<li>仅剩的一个元素必定是最小元素，无需排序，因此数组排序完成。</li>
+<li>仅剩的一个元素必定是最小元素，无须排序，因此数组排序完成。</li>
 </ol>
 <p><img alt="冒泡排序流程" src="../bubble_sort.assets/bubble_sort_overview.png" /></p>
 <p align="center"> 图：冒泡排序流程 </p>

chapter_sorting/heap_sort/index.html

@@ -3488,7 +3488,7 @@
 <a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
 <a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">r</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span>
 <a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
 <a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="w">        </span><span class="c1">// 交换两节点</span>
@@ -3530,7 +3530,7 @@
 <a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
 <a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
 <a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
-<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="p">}</span>
@@ -3569,7 +3569,7 @@
 <a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a>            <span class="n">ma</span> <span class="o">=</span> <span class="n">l</span>
 <a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>        <span class="k">if</span> <span class="n">r</span> <span class="o">&lt;</span> <span class="n">n</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
 <a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a>            <span class="n">ma</span> <span class="o">=</span> <span class="n">r</span>
-<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a>        <span class="c1"># 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a>        <span class="c1"># 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>        <span class="k">if</span> <span class="n">ma</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
 <a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a>            <span class="k">break</span>
 <a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a>        <span class="c1"># 交换两节点</span>
@@ -3604,7 +3604,7 @@
 <a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">r</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">nums</span><span class="p">)[</span><span class="nx">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="w">            </span><span class="nx">ma</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">r</span>
 <a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">            </span><span class="k">break</span>
 <a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">        </span><span class="p">}</span>
@@ -3645,7 +3645,7 @@
 <a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">            </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
 <a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">        </span><span class="p">}</span>
@@ -3686,7 +3686,7 @@
 <a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">ma</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="w">            </span><span class="nx">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">r</span><span class="p">;</span>
 <a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">ma</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="nx">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="w">        </span><span class="p">}</span>
@@ -3725,7 +3725,7 @@
 <a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
 <a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
 <a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
-<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="w">        </span><span class="p">}</span>
@@ -3768,7 +3768,7 @@
 <a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
 <a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
 <a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
-<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
 <a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="w">        </span><span class="c1">// 交换两节点</span>
@@ -3809,7 +3809,7 @@
 <a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a>        <span class="k">if</span> <span class="n">r</span> <span class="o">&lt;</span> <span class="n">n</span><span class="p">,</span> <span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span> <span class="p">{</span>
 <a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a>            <span class="n">ma</span> <span class="p">=</span> <span class="n">r</span>
 <a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a>        <span class="p">}</span>
-<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a>        <span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a>        <span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a>        <span class="k">if</span> <span class="n">ma</span> <span class="p">==</span> <span class="n">i</span> <span class="p">{</span>
 <a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a>            <span class="k">break</span>
 <a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a>        <span class="p">}</span>
@@ -3852,7 +3852,7 @@
 <a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
 <a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
 <a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
-<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="c1">// 交换两节点</span>
 <a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
@@ -3895,7 +3895,7 @@
 <a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
 <a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a><span class="w">        </span><span class="p">}</span>
-<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无需继续堆化，跳出</span>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="w">        </span><span class="c1">// 若节点 i 最大或索引 l, r 越界，则无须继续堆化，跳出</span>
 <a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
 <a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="w">        </span><span class="p">}</span>

chapter_sorting/insertion_sort/index.html

@@ -3652,7 +3652,7 @@
 </ul>
 <h2 id="1143">11.4.3 &nbsp; 插入排序优势<a class="headerlink" href="#1143" title="Permanent link">&para;</a></h2>
 <p>插入排序的时间复杂度为 <span class="arithmatex">\(O(n^2)\)</span> ，而我们即将学习的快速排序的时间复杂度为 <span class="arithmatex">\(O(n \log n)\)</span> 。尽管插入排序的时间复杂度相比快速排序更高，<strong>但在数据量较小的情况下，插入排序通常更快</strong>。</p>
-<p>这个结论与线性查找和二分查找的适用情况的结论类似。快速排序这类 <span class="arithmatex">\(O(n \log n)\)</span> 的算法属于基于分治的排序算法，往往包含更多单元计算操作。而在数据量较小时，<span class="arithmatex">\(n^2\)</span> 和 <span class="arithmatex">\(n \log n\)</span> 的数值比较接近，复杂度不占主导作用；每轮中的单元计算操作数量起到决定性因素。</p>
+<p>这个结论与线性查找和二分查找的适用情况的结论类似。快速排序这类 <span class="arithmatex">\(O(n \log n)\)</span> 的算法属于基于分治的排序算法，往往包含更多单元计算操作。而在数据量较小时，<span class="arithmatex">\(n^2\)</span> 和 <span class="arithmatex">\(n \log n\)</span> 的数值比较接近，复杂度不占主导作用；每轮中的单元操作数量起到决定性因素。</p>
 <p>实际上，许多编程语言（例如 Java）的内置排序函数都采用了插入排序，大致思路为：对于长数组，采用基于分治的排序算法，例如快速排序；对于短数组，直接使用插入排序。</p>
 <p>虽然冒泡排序、选择排序和插入排序的时间复杂度都为 <span class="arithmatex">\(O(n^2)\)</span> ，但在实际情况中，<strong>插入排序的使用频率显著高于冒泡排序和选择排序</strong>。这是因为：</p>
 <ul>

chapter_sorting/merge_sort/index.html

@@ -4037,7 +4037,7 @@
 <h2 id="1163">11.6.3 &nbsp; 链表排序 *<a class="headerlink" href="#1163" title="Permanent link">&para;</a></h2>
 <p>归并排序在排序链表时具有显著优势，空间复杂度可以优化至 <span class="arithmatex">\(O(1)\)</span> ，原因如下：</p>
 <ul>
-<li>由于链表仅需改变指针就可实现节点的增删操作，因此合并阶段（将两个短有序链表合并为一个长有序链表）无需创建辅助链表。</li>
+<li>由于链表仅需改变指针就可实现节点的增删操作，因此合并阶段（将两个短有序链表合并为一个长有序链表）无须创建辅助链表。</li>
 <li>通过使用“迭代划分”替代“递归划分”，可省去递归使用的栈帧空间。</li>
 </ul>
 <p>具体实现细节比较复杂，有兴趣的同学可以查阅相关资料进行学习。</p>

chapter_sorting/selection_sort/index.html

@@ -3405,7 +3405,7 @@
 <li>选取区间 <span class="arithmatex">\([0, n-1]\)</span> 中的最小元素，将其与索引 <span class="arithmatex">\(0\)</span> 处元素交换。完成后，数组前 1 个元素已排序。</li>
 <li>选取区间 <span class="arithmatex">\([1, n-1]\)</span> 中的最小元素，将其与索引 <span class="arithmatex">\(1\)</span> 处元素交换。完成后，数组前 2 个元素已排序。</li>
 <li>以此类推。经过 <span class="arithmatex">\(n - 1\)</span> 轮选择与交换后，数组前 <span class="arithmatex">\(n - 1\)</span> 个元素已排序。</li>
-<li>仅剩的一个元素必定是最大元素，无需排序，因此数组排序完成。</li>
+<li>仅剩的一个元素必定是最大元素，无须排序，因此数组排序完成。</li>
 </ol>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:11"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label><label for="__tabbed_1_10">&lt;10&gt;</label><label for="__tabbed_1_11">&lt;11&gt;</label></div>
 <div class="tabbed-content">

chapter_sorting/sorting_algorithm/index.html

@@ -3419,7 +3419,7 @@
 
 <h2 id="1111">11.1.1 &nbsp; 评价维度<a class="headerlink" href="#1111" title="Permanent link">&para;</a></h2>
 <p><strong>运行效率</strong>：我们期望排序算法的时间复杂度尽量低，且总体操作数量较少（即时间复杂度中的常数项降低）。对于大数据量情况，运行效率显得尤为重要。</p>
-<p><strong>就地性</strong>：顾名思义，「原地排序」通过在原数组上直接操作实现排序，无需借助额外的辅助数组，从而节省内存。通常情况下，原地排序的数据搬运操作较少，运行速度也更快。</p>
+<p><strong>就地性</strong>：顾名思义，「原地排序」通过在原数组上直接操作实现排序，无须借助额外的辅助数组，从而节省内存。通常情况下，原地排序的数据搬运操作较少，运行速度也更快。</p>
 <p><strong>稳定性</strong>：「稳定排序」在完成排序后，相等元素在数组中的相对顺序不发生改变。稳定排序是优良特性，也是多级排序场景的必要条件。</p>
 <p>假设我们有一个存储学生信息的表格，第 1, 2 列分别是姓名和年龄。在这种情况下，「非稳定排序」可能导致输入数据的有序性丧失。</p>
 <div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 输入数据是按照姓名排序好的</span>