deploy

2026-04-04 19:20:52 +08:00 · 2023-12-02 06:24:11 +08:00
parent 5783c402bf
commit d20d8b3ee1
107 changed files with 1685 additions and 1745 deletions
--- a/chapter_stack_and_queue/deque/index.html
+++ b/chapter_stack_and_queue/deque/index.html
@@ -3436,7 +3436,7 @@

 <!-- Page content -->
 <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 double-ended queue」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>在队列中，我们仅能删除头部元素或在尾部添加元素。如图 5-7 所示，「双向队列 double-ended queue」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><a class="glightbox" href="../deque.assets/deque_operations.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="双向队列的操作" class="animation-figure" src="../deque.assets/deque_operations.png" /></a></p>
 <p align="center"> 图 5-7 &nbsp; 双向队列的操作 </p>

@@ -3487,33 +3487,35 @@
 </tbody>
 </table>
 </div>
-<p>同样地，我们可以直接使用编程语言中已实现的双向队列类。</p>
+<p>同样地，我们可以直接使用编程语言中已实现的双向队列类：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="1:12"><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" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Zig</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
-<div class="highlight"><span class="filename">deque.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 初始化双向队列</span>
-<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">deque</span><span class="p">:</span> <span class="n">deque</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="n">collections</span><span class="o">.</span><span class="n">deque</span><span class="p">()</span>
-<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
-<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># 元素入队</span>
-<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="n">deque</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>      <span class="c1"># 添加至队尾</span>
-<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">deque</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
-<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">deque</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
-<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">deque</span><span class="o">.</span><span class="n">appendleft</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>  <span class="c1"># 添加至队首</span>
-<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">deque</span><span class="o">.</span><span class="n">appendleft</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
-<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>
-<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="c1"># 访问元素</span>
-<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="n">front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deque</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># 队首元素</span>
-<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="n">rear</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deque</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>  <span class="c1"># 队尾元素</span>
-<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>
-<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="c1"># 元素出队</span>
-<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="n">pop_front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deque</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>  <span class="c1"># 队首元素出队</span>
-<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="n">pop_rear</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deque</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>       <span class="c1"># 队尾元素出队</span>
-<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>
-<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="c1"># 获取双向队列的长度</span>
-<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deque</span><span class="p">)</span>
-<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>
-<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="c1"># 判断双向队列是否为空</span>
-<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deque</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span>
+<div class="highlight"><span class="filename">deque.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">deque</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 初始化双向队列</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="n">deque</span><span class="p">:</span> <span class="n">deque</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="n">deque</span><span class="p">()</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="c1"># 元素入队</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">deque</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>      <span class="c1"># 添加至队尾</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">deque</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">deque</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">deque</span><span class="o">.</span><span class="n">appendleft</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>  <span class="c1"># 添加至队首</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="n">deque</span><span class="o">.</span><span class="n">appendleft</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="c1"># 访问元素</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deque</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># 队首元素</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="n">rear</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deque</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>  <span class="c1"># 队尾元素</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># 元素出队</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">pop_front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deque</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>  <span class="c1"># 队首元素出队</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="n">pop_rear</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deque</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>       <span class="c1"># 队尾元素出队</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># 获取双向队列的长度</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deque</span><span class="p">)</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="c1"># 判断双向队列是否为空</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deque</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span>
 </code></pre></div>
 </div>
 <div class="tabbed-block">
@@ -3816,7 +3818,7 @@
 </div>
 <p align="center"> 图 5-8 &nbsp; 基于链表实现双向队列的入队出队操作 </p>

-<p>实现代码如下所示。</p>
+<p>实现代码如下所示：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="3:12"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Zig</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -3849,7 +3851,7 @@
 <a id="__codelineno-12-27" name="__codelineno-12-27" href="#__codelineno-12-27"></a>    <span class="k">def</span> <span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">is_front</span><span class="p">:</span> <span class="nb">bool</span><span class="p">):</span>
 <a id="__codelineno-12-28" name="__codelineno-12-28" href="#__codelineno-12-28"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;入队操作&quot;&quot;&quot;</span>
 <a id="__codelineno-12-29" name="__codelineno-12-29" href="#__codelineno-12-29"></a>        <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
-<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a>        <span class="c1"># 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-12-30" name="__codelineno-12-30" href="#__codelineno-12-30"></a>        <span class="c1"># 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-12-31" name="__codelineno-12-31" href="#__codelineno-12-31"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
 <a id="__codelineno-12-32" name="__codelineno-12-32" href="#__codelineno-12-32"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>
 <a id="__codelineno-12-33" name="__codelineno-12-33" href="#__codelineno-12-33"></a>        <span class="c1"># 队首入队操作</span>
@@ -3974,7 +3976,7 @@
 <a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a><span class="w">    </span><span class="cm">/* 入队操作 */</span>
 <a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">DoublyListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
 <a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a><span class="w">        </span><span class="c1">// 队首入队操作</span>
@@ -4107,7 +4109,7 @@
 <a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">    </span><span class="cm">/* 入队操作 */</span>
 <a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
 <a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">        </span><span class="c1">// 队首入队操作</span>
@@ -4234,7 +4236,7 @@
 <a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="cm">/* 入队操作 */</span>
 <a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="k">void</span><span class="w"> </span><span class="nf">Push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
@@ -4450,7 +4452,7 @@
 <a id="__codelineno-17-32" name="__codelineno-17-32" href="#__codelineno-17-32"></a>    <span class="cm">/* 入队操作 */</span>
 <a id="__codelineno-17-33" name="__codelineno-17-33" href="#__codelineno-17-33"></a>    <span class="kd">private</span> <span class="kd">func</span> <span class="nf">push</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">Int</span><span class="p">,</span> <span class="n">isFront</span><span class="p">:</span> <span class="nb">Bool</span><span class="p">)</span> <span class="p">{</span>
 <a id="__codelineno-17-34" name="__codelineno-17-34" href="#__codelineno-17-34"></a>        <span class="kd">let</span> <span class="nv">node</span> <span class="p">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">val</span><span class="p">:</span> <span class="n">num</span><span class="p">)</span>
-<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a>        <span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-17-35" name="__codelineno-17-35" href="#__codelineno-17-35"></a>        <span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-17-36" name="__codelineno-17-36" href="#__codelineno-17-36"></a>        <span class="k">if</span> <span class="bp">isEmpty</span><span class="p">()</span> <span class="p">{</span>
 <a id="__codelineno-17-37" name="__codelineno-17-37" href="#__codelineno-17-37"></a>            <span class="n">front</span> <span class="p">=</span> <span class="n">node</span>
 <a id="__codelineno-17-38" name="__codelineno-17-38" href="#__codelineno-17-38"></a>            <span class="n">rear</span> <span class="p">=</span> <span class="n">node</span>
@@ -4576,7 +4578,7 @@
 <a id="__codelineno-18-26" name="__codelineno-18-26" href="#__codelineno-18-26"></a><span class="w">    </span><span class="cm">/* 队尾入队操作 */</span>
 <a id="__codelineno-18-27" name="__codelineno-18-27" href="#__codelineno-18-27"></a><span class="w">    </span><span class="nx">pushLast</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-18-28" name="__codelineno-18-28" href="#__codelineno-18-28"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
-<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-18-29" name="__codelineno-18-29" href="#__codelineno-18-29"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-18-30" name="__codelineno-18-30" href="#__codelineno-18-30"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-18-31" name="__codelineno-18-31" href="#__codelineno-18-31"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
 <a id="__codelineno-18-32" name="__codelineno-18-32" href="#__codelineno-18-32"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
@@ -4592,7 +4594,7 @@
 <a id="__codelineno-18-42" name="__codelineno-18-42" href="#__codelineno-18-42"></a><span class="w">    </span><span class="cm">/* 队首入队操作 */</span>
 <a id="__codelineno-18-43" name="__codelineno-18-43" href="#__codelineno-18-43"></a><span class="w">    </span><span class="nx">pushFirst</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-18-44" name="__codelineno-18-44" href="#__codelineno-18-44"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
-<a id="__codelineno-18-45" name="__codelineno-18-45" href="#__codelineno-18-45"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-18-45" name="__codelineno-18-45" href="#__codelineno-18-45"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-18-46" name="__codelineno-18-46" href="#__codelineno-18-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-18-47" name="__codelineno-18-47" href="#__codelineno-18-47"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
 <a id="__codelineno-18-48" name="__codelineno-18-48" href="#__codelineno-18-48"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="err">#</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
@@ -4701,7 +4703,7 @@
 <a id="__codelineno-19-26" name="__codelineno-19-26" href="#__codelineno-19-26"></a><span class="w">    </span><span class="cm">/* 队尾入队操作 */</span>
 <a id="__codelineno-19-27" name="__codelineno-19-27" href="#__codelineno-19-27"></a><span class="w">    </span><span class="nx">pushLast</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-28" name="__codelineno-19-28" href="#__codelineno-19-28"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
-<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-19-29" name="__codelineno-19-29" href="#__codelineno-19-29"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-19-30" name="__codelineno-19-30" href="#__codelineno-19-30"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-31" name="__codelineno-19-31" href="#__codelineno-19-31"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
 <a id="__codelineno-19-32" name="__codelineno-19-32" href="#__codelineno-19-32"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
@@ -4717,7 +4719,7 @@
 <a id="__codelineno-19-42" name="__codelineno-19-42" href="#__codelineno-19-42"></a><span class="w">    </span><span class="cm">/* 队首入队操作 */</span>
 <a id="__codelineno-19-43" name="__codelineno-19-43" href="#__codelineno-19-43"></a><span class="w">    </span><span class="nx">pushFirst</span><span class="p">(</span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-44" name="__codelineno-19-44" href="#__codelineno-19-44"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="nx">val</span><span class="p">);</span>
-<a id="__codelineno-19-45" name="__codelineno-19-45" href="#__codelineno-19-45"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-19-45" name="__codelineno-19-45" href="#__codelineno-19-45"></a><span class="w">        </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-19-46" name="__codelineno-19-46" href="#__codelineno-19-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="nx">queSize</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-19-47" name="__codelineno-19-47" href="#__codelineno-19-47"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
 <a id="__codelineno-19-48" name="__codelineno-19-48" href="#__codelineno-19-48"></a><span class="w">            </span><span class="k">this</span><span class="p">.</span><span class="nx">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">node</span><span class="p">;</span>
@@ -4976,7 +4978,7 @@
 <a id="__codelineno-21-48" name="__codelineno-21-48" href="#__codelineno-21-48"></a><span class="w">        </span><span class="c1">// 队首入队操作</span>
 <a id="__codelineno-21-49" name="__codelineno-21-49" href="#__codelineno-21-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">is_front</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-21-50" name="__codelineno-21-50" href="#__codelineno-21-50"></a><span class="w">            </span><span class="k">match</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="p">.</span><span class="n">take</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-51" name="__codelineno-21-51" href="#__codelineno-21-51"></a><span class="w">                </span><span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-21-51" name="__codelineno-21-51" href="#__codelineno-21-51"></a><span class="w">                </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-21-52" name="__codelineno-21-52" href="#__codelineno-21-52"></a><span class="w">                </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-21-53" name="__codelineno-21-53" href="#__codelineno-21-53"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
 <a id="__codelineno-21-54" name="__codelineno-21-54" href="#__codelineno-21-54"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
@@ -4992,7 +4994,7 @@
 <a id="__codelineno-21-64" name="__codelineno-21-64" href="#__codelineno-21-64"></a><span class="w">        </span><span class="c1">// 队尾入队操作</span>
 <a id="__codelineno-21-65" name="__codelineno-21-65" href="#__codelineno-21-65"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-21-66" name="__codelineno-21-66" href="#__codelineno-21-66"></a><span class="w">            </span><span class="k">match</span><span class="w"> </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="p">.</span><span class="n">take</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
-<a id="__codelineno-21-67" name="__codelineno-21-67" href="#__codelineno-21-67"></a><span class="w">                </span><span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-21-67" name="__codelineno-21-67" href="#__codelineno-21-67"></a><span class="w">                </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-21-68" name="__codelineno-21-68" href="#__codelineno-21-68"></a><span class="w">                </span><span class="nb">None</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-21-69" name="__codelineno-21-69" href="#__codelineno-21-69"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
 <a id="__codelineno-21-70" name="__codelineno-21-70" href="#__codelineno-21-70"></a><span class="w">                    </span><span class="bp">self</span><span class="p">.</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
@@ -5153,7 +5155,7 @@
 <a id="__codelineno-22-59" name="__codelineno-22-59" href="#__codelineno-22-59"></a><span class="cm">/* 入队 */</span>
 <a id="__codelineno-22-60" name="__codelineno-22-60" href="#__codelineno-22-60"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="n">LinkedListDeque</span><span class="w"> </span><span class="o">*</span><span class="n">deque</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-22-61" name="__codelineno-22-61" href="#__codelineno-22-61"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newDoublyListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-22-62" name="__codelineno-22-62" href="#__codelineno-22-62"></a><span class="w">    </span><span class="c1">// 若链表为空，则令 front, rear 都指向node</span>
+<a id="__codelineno-22-62" name="__codelineno-22-62" href="#__codelineno-22-62"></a><span class="w">    </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向node</span>
 <a id="__codelineno-22-63" name="__codelineno-22-63" href="#__codelineno-22-63"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">empty</span><span class="p">(</span><span class="n">deque</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-22-64" name="__codelineno-22-64" href="#__codelineno-22-64"></a><span class="w">        </span><span class="n">deque</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">deque</span><span class="o">-&gt;</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-22-65" name="__codelineno-22-65" href="#__codelineno-22-65"></a><span class="w">    </span><span class="p">}</span>
@@ -5313,7 +5315,7 @@
 <a id="__codelineno-23-58" name="__codelineno-23-58" href="#__codelineno-23-58"></a><span class="w">        </span><span class="kr">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="p">,</span><span class="w"> </span><span class="n">is_front</span><span class="o">:</span><span class="w"> </span><span class="kt">bool</span><span class="p">)</span><span class="w"> </span><span class="o">!</span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-23-59" name="__codelineno-23-59" href="#__codelineno-23-59"></a><span class="w">            </span><span class="kr">var</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">try</span><span class="w"> </span><span class="n">self</span><span class="p">.</span><span class="n">mem_allocator</span><span class="p">.</span><span class="n">create</span><span class="p">(</span><span class="n">ListNode</span><span class="p">(</span><span class="n">T</span><span class="p">));</span>
 <a id="__codelineno-23-60" name="__codelineno-23-60" href="#__codelineno-23-60"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="n">init</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
-<a id="__codelineno-23-61" name="__codelineno-23-61" href="#__codelineno-23-61"></a><span class="w">            </span><span class="c1">// 若链表为空，则令 front, rear 都指向 node</span>
+<a id="__codelineno-23-61" name="__codelineno-23-61" href="#__codelineno-23-61"></a><span class="w">            </span><span class="c1">// 若链表为空，则令 front 和 rear 都指向 node</span>
 <a id="__codelineno-23-62" name="__codelineno-23-62" href="#__codelineno-23-62"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">self</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
 <a id="__codelineno-23-63" name="__codelineno-23-63" href="#__codelineno-23-63"></a><span class="w">                </span><span class="n">self</span><span class="p">.</span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
 <a id="__codelineno-23-64" name="__codelineno-23-64" href="#__codelineno-23-64"></a><span class="w">                </span><span class="n">self</span><span class="p">.</span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
@@ -5435,7 +5437,7 @@
 </div>
 <p align="center"> 图 5-9 &nbsp; 基于数组实现双向队列的入队出队操作 </p>

-<p>在队列的实现基础上，仅需增加“队首入队”和“队尾出队”的方法。</p>
+<p>在队列的实现基础上，仅需增加“队首入队”和“队尾出队”的方法：</p>
 <div class="tabbed-set tabbed-alternate" data-tabs="5:12"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Zig</label></div>
 <div class="tabbed-content">
 <div class="tabbed-block">
@@ -6618,7 +6620,7 @@
 </div>
 <h2 id="533">5.3.3 &nbsp; 双向队列应用<a class="headerlink" href="#533" title="Permanent link">&para;</a></h2>
 <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>
+<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（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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