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<h1 id="53">5.3 &nbsp; 双向队列<a class="headerlink" href="#53" title="Permanent link">&para;</a></h1>
<p>在队列中，我们仅能在头部删除或在尾部添加元素。如图 5-7 所示，「双向队列 deque」提供了更高的灵活性，允许在头部和尾部执行元素的添加或删除操作。</p>
<p><img alt="双向队列的操作" src="../deque.assets/deque_operations.png" /></p>
@@ -6701,11 +6733,73 @@
<p>双向队列兼具栈与队列的逻辑，<strong>因此它可以实现这两者的所有应用场景，同时提供更高的自由度</strong>。</p>
<p>我们知道，软件的“撤销”功能通常使用栈来实现：系统将每次更改操作 <code>push</code> 到栈中，然后通过 <code>pop</code> 实现撤销。然而，考虑到系统资源的限制，软件通常会限制撤销的步数（例如仅允许保存 <span class="arithmatex">\(50\)</span> 步）。当栈的长度超过 <span class="arithmatex">\(50\)</span> 时，软件需要在栈底（即队首）执行删除操作。<strong>但栈无法实现该功能，此时就需要使用双向队列来替代栈</strong>。请注意，“撤销”的核心逻辑仍然遵循栈的先入后出原则，只是双向队列能够更加灵活地实现一些额外逻辑。</p>
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<h1 id="5">第 5 章 &nbsp; 栈与队列<a class="headerlink" href="#5" title="Permanent link">&para;</a></h1>
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<h1 id="52">5.2 &nbsp; 队列<a class="headerlink" href="#52" title="Permanent link">&para;</a></h1>
<p>「队列 queue」是一种遵循先入先出规则的线性数据结构。顾名思义，队列模拟了排队现象，即新来的人不断加入队列的尾部，而位于队列头部的人逐个离开。</p>
<p>如图 5-4 所示，我们将队列的头部称为“队首”，尾部称为“队尾”，将把元素加入队尾的操作称为“入队”，删除队首元素的操作称为“出队”。</p>
@@ -4570,7 +4602,7 @@
<a id="__codelineno-22-75" name="__codelineno-22-75" href="#__codelineno-22-75"></a><span class="w"> </span><span class="c1">// 拷贝链表中的数据到数组</span>
<a id="__codelineno-22-76" name="__codelineno-22-76" href="#__codelineno-22-76"></a><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
<a id="__codelineno-22-77" name="__codelineno-22-77" href="#__codelineno-22-77"></a><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
<a id="__codelineno-22-78" name="__codelineno-22-78" href="#__codelineno-22-78"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-78" name="__codelineno-22-78" href="#__codelineno-22-78"></a><span class="w"> </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queue</span><span class="o">-&gt;</span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
<a id="__codelineno-22-79" name="__codelineno-22-79" href="#__codelineno-22-79"></a><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
<a id="__codelineno-22-80" name="__codelineno-22-80" href="#__codelineno-22-80"></a><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
<a id="__codelineno-22-81" name="__codelineno-22-81" href="#__codelineno-22-81"></a><span class="w"> </span><span class="p">}</span>
@@ -5574,11 +5606,73 @@
<li><strong>各类待办事项</strong>。任何需要实现“先来后到”功能的场景，例如打印机的任务队列、餐厅的出餐队列等。队列在这些场景中可以有效地维护处理顺序。</li>
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@@ -5170,11 +5202,73 @@
<li><strong>程序内存管理</strong>。每次调用函数时，系统都会在栈顶添加一个栈帧，用于记录函数的上下文信息。在递归函数中，向下递推阶段会不断执行入栈操作，而向上回溯阶段则会执行出栈操作。</li>
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