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<!-- Page content -->
<h1 id="53-double-ended-queue">5.3 &nbsp; Double-Ended Queue<a class="headerlink" href="#53-double-ended-queue" title="Permanent link">&para;</a></h1>
<p>In a regular queue, we can only delete elements from the head or add elements to the tail. As shown in the Figure 5-7 , a "double-ended queue (deque)" offers more flexibility, allowing the addition or removal of elements at both the head and the tail.</p>
<p>In a queue, we can only delete elements from the head or add elements to the tail. As shown in the following diagram, a "double-ended queue (deque)" offers more flexibility, allowing the addition or removal of elements at both the head and the tail.</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="Operations in Double-Ended Queue" class="animation-figure" src="../deque.assets/deque_operations.png" /></a></p>
<p align="center"> Figure 5-7 &nbsp; Operations in Double-Ended Queue </p>
<h2 id="531-common-operations-in-double-ended-queue">5.3.1 &nbsp; Common Operations in Double-Ended Queue<a class="headerlink" href="#531-common-operations-in-double-ended-queue" title="Permanent link">&para;</a></h2>
<p>The common operations in a double-ended queue are listed below, and the specific method names depend on the programming language used.</p>
<p>The common operations in a double-ended queue are listed below, and the names of specific methods depend on the programming language used.</p>
<p align="center"> Table 5-3 &nbsp; Efficiency of Double-Ended Queue Operations </p>
<div class="center-table">
@ -1649,32 +1649,32 @@
<tbody>
<tr>
<td><code>pushFirst()</code></td>
<td>Add an element to the front</td>
<td>Add an element to the head</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td><code>pushLast()</code></td>
<td>Add an element to the rear</td>
<td>Add an element to the tail</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td><code>popFirst()</code></td>
<td>Remove the front element</td>
<td>Remove the first element</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td><code>popLast()</code></td>
<td>Remove the rear element</td>
<td>Remove the last element</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td><code>peekFirst()</code></td>
<td>Access the front element</td>
<td>Access the first element</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
<tr>
<td><code>peekLast()</code></td>
<td>Access the rear element</td>
<td>Access the last element</td>
<td><span class="arithmatex">\(O(1)\)</span></td>
</tr>
</tbody>
@ -1690,19 +1690,19 @@
<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"># Enqueue elements</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"># Add to the rear</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"># Add to the tail</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"># Add to the front</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"># Add to the head</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"># Access elements</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"># Front element</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"># Rear element</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"># The first element</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"># The last element</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"># Dequeue elements</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"># Front element dequeued</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"># Rear element dequeued</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"># The first element dequeued</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"># The last element dequeued</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"># Get the length of the deque</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>
@ -1716,19 +1716,19 @@
<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">deque</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">deque</span><span class="p">;</span>
<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm">/* Enqueue elements */</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the rear</span>
<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the tail</span>
<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_front</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the front</span>
<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_front</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the head</span>
<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_front</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a>
<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* Access elements */</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">int</span><span class="w"> </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="p">.</span><span class="n">front</span><span class="p">();</span><span class="w"> </span><span class="c1">// Front element</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">back</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">back</span><span class="p">();</span><span class="w"> </span><span class="c1">// Rear element</span>
<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">int</span><span class="w"> </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="p">.</span><span class="n">front</span><span class="p">();</span><span class="w"> </span><span class="c1">// The first element</span>
<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">back</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">back</span><span class="p">();</span><span class="w"> </span><span class="c1">// The last element</span>
<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a>
<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="cm">/* Dequeue elements */</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="n">deque</span><span class="p">.</span><span class="n">pop_front</span><span class="p">();</span><span class="w"> </span><span class="c1">// Front element dequeued</span>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="n">deque</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span><span class="w"> </span><span class="c1">// Rear element dequeued</span>
<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="n">deque</span><span class="p">.</span><span class="n">pop_front</span><span class="p">();</span><span class="w"> </span><span class="c1">// The first element dequeued</span>
<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="n">deque</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span><span class="w"> </span><span class="c1">// The last element dequeued</span>
<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a>
<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="cm">/* Get the length of the deque */</span>
<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
@ -1742,19 +1742,19 @@
<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Deque</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">deque</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">LinkedList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="cm">/* Enqueue elements */</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerLast</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the rear</span>
<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerLast</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the tail</span>
<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerLast</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerLast</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerFirst</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the front</span>
<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerFirst</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the head</span>
<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerFirst</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* Access elements */</span>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">peekFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// Front element</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">peekLast</span><span class="p">();</span><span class="w"> </span><span class="c1">// Rear element</span>
<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">peekFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// The first element</span>
<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">peekLast</span><span class="p">();</span><span class="w"> </span><span class="c1">// The last element</span>
<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a>
<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="cm">/* Dequeue elements */</span>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">pollFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// Front element dequeued</span>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">pollLast</span><span class="p">();</span><span class="w"> </span><span class="c1">// Rear element dequeued</span>
<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">pollFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// The first element dequeued</span>
<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">pollLast</span><span class="p">();</span><span class="w"> </span><span class="c1">// The last element dequeued</span>
<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a>
<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="cm">/* Get the length of the deque */</span>
<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
@ -1769,19 +1769,19 @@
<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">LinkedList</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="cm">/* Enqueue elements */</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddLast</span><span class="p">(</span><span class="m">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the rear</span>
<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddLast</span><span class="p">(</span><span class="m">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the tail</span>
<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddLast</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddLast</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddFirst</span><span class="p">(</span><span class="m">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the front</span>
<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddFirst</span><span class="p">(</span><span class="m">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the head</span>
<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddFirst</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a>
<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="cm">/* Access elements */</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">First</span><span class="p">.</span><span class="n">Value</span><span class="p">;</span><span class="w"> </span><span class="c1">// Front element</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">Last</span><span class="p">.</span><span class="n">Value</span><span class="p">;</span><span class="w"> </span><span class="c1">// Rear element</span>
<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">First</span><span class="p">.</span><span class="n">Value</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element</span>
<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">Last</span><span class="p">.</span><span class="n">Value</span><span class="p">;</span><span class="w"> </span><span class="c1">// The last element</span>
<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a>
<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="cm">/* Dequeue elements */</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="n">deque</span><span class="p">.</span><span class="n">RemoveFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// Front element dequeued</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="n">deque</span><span class="p">.</span><span class="n">RemoveLast</span><span class="p">();</span><span class="w"> </span><span class="c1">// Rear element dequeued</span>
<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="n">deque</span><span class="p">.</span><span class="n">RemoveFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// The first element dequeued</span>
<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="n">deque</span><span class="p">.</span><span class="n">RemoveLast</span><span class="p">();</span><span class="w"> </span><span class="c1">// The last element dequeued</span>
<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a>
<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="cm">/* Get the length of the deque */</span>
<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
@ -1796,19 +1796,19 @@
<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="nx">deque</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">list</span><span class="p">.</span><span class="nx">New</span><span class="p">()</span>
<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/* Enqueue elements */</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="c1">// Add to the rear</span>
<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="c1">// Add to the tail</span>
<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushFront</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="c1">// Add to the front</span>
<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushFront</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="c1">// Add to the head</span>
<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushFront</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* Access elements */</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="nx">front</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Front</span><span class="p">()</span><span class="w"> </span><span class="c1">// Front element</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="nx">rear</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Back</span><span class="p">()</span><span class="w"> </span><span class="c1">// Rear element</span>
<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="nx">front</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Front</span><span class="p">()</span><span class="w"> </span><span class="c1">// The first element</span>
<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="nx">rear</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Back</span><span class="p">()</span><span class="w"> </span><span class="c1">// The last element</span>
<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a>
<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="cm">/* Dequeue elements */</span>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">front</span><span class="p">)</span><span class="w"> </span><span class="c1">// Front element dequeued</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">rear</span><span class="p">)</span><span class="w"> </span><span class="c1">// Rear element dequeued</span>
<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">front</span><span class="p">)</span><span class="w"> </span><span class="c1">// The first element dequeued</span>
<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">rear</span><span class="p">)</span><span class="w"> </span><span class="c1">// The last element dequeued</span>
<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a>
<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="cm">/* Get the length of the deque */</span>
<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span>
@ -1823,20 +1823,20 @@
<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span> <span class="nv">deque</span><span class="p">:</span> <span class="p">[</span><span class="nb">Int</span><span class="p">]</span> <span class="p">=</span> <span class="p">[]</span>
<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* Enqueue elements */</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="c1">// Add to the rear</span>
<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span> <span class="c1">// Add to the tail</span>
<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">deque</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">at</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span> <span class="c1">// Add to the front</span>
<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">deque</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">at</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span> <span class="c1">// Add to the head</span>
<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="n">deque</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">at</span><span class="p">:</span> <span class="mi">0</span><span class="p">)</span>
<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* Access elements */</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">let</span> <span class="nv">peekFirst</span> <span class="p">=</span> <span class="n">deque</span><span class="p">.</span><span class="bp">first</span><span class="p">!</span> <span class="c1">// Front element</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">let</span> <span class="nv">peekLast</span> <span class="p">=</span> <span class="n">deque</span><span class="p">.</span><span class="bp">last</span><span class="p">!</span> <span class="c1">// Rear element</span>
<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">let</span> <span class="nv">peekFirst</span> <span class="p">=</span> <span class="n">deque</span><span class="p">.</span><span class="bp">first</span><span class="p">!</span> <span class="c1">// The first element</span>
<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">let</span> <span class="nv">peekLast</span> <span class="p">=</span> <span class="n">deque</span><span class="p">.</span><span class="bp">last</span><span class="p">!</span> <span class="c1">// The last element</span>
<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>
<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="cm">/* Dequeue elements */</span>
<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="c1">// Using Array, popFirst has a complexity of O(n)</span>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="kd">let</span> <span class="nv">popFirst</span> <span class="p">=</span> <span class="n">deque</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">()</span> <span class="c1">// Front element dequeued</span>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="kd">let</span> <span class="nv">popLast</span> <span class="p">=</span> <span class="n">deque</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span> <span class="c1">// Rear element dequeued</span>
<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="kd">let</span> <span class="nv">popFirst</span> <span class="p">=</span> <span class="n">deque</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">()</span> <span class="c1">// The first element dequeued</span>
<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="kd">let</span> <span class="nv">popLast</span> <span class="p">=</span> <span class="n">deque</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span> <span class="c1">// The last element dequeued</span>
<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a>
<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="cm">/* Get the length of the deque */</span>
<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="kd">let</span> <span class="nv">size</span> <span class="p">=</span> <span class="n">deque</span><span class="p">.</span><span class="bp">count</span>
@ -1859,13 +1859,13 @@
<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">unshift</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a>
<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="cm">/* Access elements */</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// Front element</span>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// Rear element</span>
<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// The first element</span>
<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// The last element</span>
<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a>
<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="cm">/* Dequeue elements */</span>
<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="c1">// Note that shift() has a time complexity of O(n) as it&#39;s an array</span>
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popFront</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span><span class="w"> </span><span class="c1">// Front element dequeued</span>
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popBack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// Rear element dequeued</span>
<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popFront</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span><span class="w"> </span><span class="c1">// The first element dequeued</span>
<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popBack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// The last element dequeued</span>
<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a>
<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="cm">/* Get the length of the deque */</span>
<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
@ -1888,13 +1888,13 @@
<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">unshift</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a>
<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="cm">/* Access elements */</span>
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekFirst</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// Front element</span>
<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekLast</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// Rear element</span>
<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekFirst</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// The first element</span>
<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekLast</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// The last element</span>
<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a>
<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="cm">/* Dequeue elements */</span>
<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="c1">// Note that shift() has a time complexity of O(n) as it&#39;s an array</span>
<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popFront</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">shift</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// Front element dequeued</span>
<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popBack</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// Rear element dequeued</span>
<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popFront</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">shift</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element dequeued</span>
<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popBack</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// The last element dequeued</span>
<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a>
<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="cm">/* Get the length of the deque */</span>
<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
@ -1909,19 +1909,19 @@
<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">();</span>
<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/* Enqueue elements */</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">addLast</span><span class="p">(</span><span class="m">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the rear</span>
<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">addLast</span><span class="p">(</span><span class="m">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the tail</span>
<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">addLast</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">addLast</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">addFirst</span><span class="p">(</span><span class="m">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the front</span>
<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">addFirst</span><span class="p">(</span><span class="m">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the head</span>
<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">deque</span><span class="p">.</span><span class="n">addFirst</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* Access elements */</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">first</span><span class="p">;</span><span class="w"> </span><span class="c1">// Front element</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">last</span><span class="p">;</span><span class="w"> </span><span class="c1">// Rear element</span>
<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">first</span><span class="p">;</span><span class="w"> </span><span class="c1">// The first element</span>
<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">last</span><span class="p">;</span><span class="w"> </span><span class="c1">// The last element</span>
<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a>
<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="cm">/* Dequeue elements */</span>
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// Front element dequeued</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span><span class="w"> </span><span class="c1">// Rear element dequeued</span>
<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// The first element dequeued</span>
<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span><span class="w"> </span><span class="c1">// The last element dequeued</span>
<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a>
<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="cm">/* Get the length of the deque */</span>
<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
@ -1935,22 +1935,22 @@
<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">deque</span>: <span class="nc">VecDeque</span><span class="o">&lt;</span><span class="kt">u32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">VecDeque</span>::<span class="n">new</span><span class="p">();</span>
<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* Enqueue elements */</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the rear</span>
<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the tail</span>
<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_front</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the front</span>
<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_front</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// Add to the head</span>
<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_front</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a>
<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="cm">/* Access elements */</span>
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">front</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Front element</span>
<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">front</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// The first element</span>
<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="p">}</span>
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">rear</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">back</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Rear element</span>
<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">rear</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">back</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// The last element</span>
<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="p">}</span>
<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a>
<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="cm">/* Dequeue elements */</span>
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">pop_front</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">pop_front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Front element dequeued</span>
<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">pop_front</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">pop_front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// The first element dequeued</span>
<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="p">}</span>
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">pop_rear</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">pop_back</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// Rear element dequeued</span>
<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">pop_rear</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">pop_back</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// The last element dequeued</span>
<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="p">}</span>
<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a>
<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="cm">/* Get the length of the deque */</span>
@ -1971,15 +1971,14 @@
</div>
</div>
<details class="pythontutor">
<summary>Code Visualization</summary>
<p><div style="height: 549px; width: 100%;"><iframe class="pythontutor-iframe" src="https://pythontutor.com/iframe-embed.html#code=from%20collections%20import%20deque%0A%0A%22%22%22Driver%20Code%22%22%22%0Aif%20__name__%20%3D%3D%20%22__main__%22%3A%0A%20%20%20%20%23%20%E5%88%9D%E5%A7%8B%E5%8C%96%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%0A%20%20%20%20deq%20%3D%20deque%28%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%85%A5%E9%98%9F%0A%20%20%20%20deq.append%282%29%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%87%B3%E9%98%9F%E5%B0%BE%0A%20%20%20%20deq.append%285%29%0A%20%20%20%20deq.append%284%29%0A%20%20%20%20deq.appendleft%283%29%20%20%23%20%E6%B7%BB%E5%8A%A0%E8%87%B3%E9%98%9F%E9%A6%96%0A%20%20%20%20deq.appendleft%281%29%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%20deque%20%3D%22,%20deq%29%0A%0A%20%20%20%20%23%20%E8%AE%BF%E9%97%AE%E5%85%83%E7%B4%A0%0A%20%20%20%20front%20%3D%20deq%5B0%5D%20%20%23%20%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%20front%20%3D%22,%20front%29%0A%20%20%20%20rear%20%3D%20deq%5B-1%5D%20%20%23%20%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%20rear%20%3D%22,%20rear%29%0A%0A%20%20%20%20%23%20%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20pop_front%20%3D%20deq.popleft%28%29%20%20%23%20%E9%98%9F%E9%A6%96%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20%20pop_front%20%3D%22,%20pop_front%29%0A%20%20%20%20print%28%22%E9%98%9F%E9%A6%96%E5%87%BA%E9%98%9F%E5%90%8E%20deque%20%3D%22,%20deq%29%0A%20%20%20%20pop_rear%20%3D%20deq.pop%28%29%20%20%23%20%E9%98%9F%E5%B0%BE%E5%85%83%E7%B4%A0%E5%87%BA%E9%98%9F%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%87%BA%E9%98%9F%E5%85%83%E7%B4%A0%20%20pop_rear%20%3D%22,%20pop_rear%29%0A%20%20%20%20print%28%22%E9%98%9F%E5%B0%BE%E5%87%BA%E9%98%9F%E5%90%8E%20deque%20%3D%22,%20deq%29%0A%0A%20%20%20%20%23%20%E8%8E%B7%E5%8F%96%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E7%9A%84%E9%95%BF%E5%BA%A6%0A%20%20%20%20size%20%3D%20len%28deq%29%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E9%95%BF%E5%BA%A6%20size%20%3D%22,%20size%29%0A%0A%20%20%20%20%23%20%E5%88%A4%E6%96%AD%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%0A%20%20%20%20is_empty%20%3D%20len%28deq%29%20%3D%3D%200%0A%20%20%20%20print%28%22%E5%8F%8C%E5%90%91%E9%98%9F%E5%88%97%E6%98%AF%E5%90%A6%E4%B8%BA%E7%A9%BA%20%3D%22,%20is_empty%29&codeDivHeight=472&codeDivWidth=350&cumulative=false&curInstr=3&heapPrimitives=nevernest&origin=opt-frontend.js&py=311&rawInputLstJSON=%5B%5D&textReferences=false"> </iframe></div>
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</details>
<h2 id="532-implementing-a-double-ended-queue">5.3.2 &nbsp; Implementing a Double-Ended Queue *<a class="headerlink" href="#532-implementing-a-double-ended-queue" title="Permanent link">&para;</a></h2>
<p>The implementation of a double-ended queue is similar to that of a regular queue, with the choice of either linked lists or arrays as the underlying data structure.</p>
<p>The implementation of a double-ended queue is similar to that of a regular queue, it can be based on either a linked list or an array as the underlying data structure.</p>
<h3 id="1-implementation-based-on-doubly-linked-list">1. &nbsp; Implementation Based on Doubly Linked List<a class="headerlink" href="#1-implementation-based-on-doubly-linked-list" title="Permanent link">&para;</a></h3>
<p>Recall from the previous section that we used a regular singly linked list to implement a queue, as it conveniently allows for deleting the head node (corresponding to dequeue operation) and adding new nodes after the tail node (corresponding to enqueue operation).</p>
<p>For a double-ended queue, both the head and the tail can perform enqueue and dequeue operations. In other words, a double-ended queue needs to implement another symmetric direction of operations. For this, we use a "doubly linked list" as the underlying data structure of the double-ended queue.</p>
<p>Recall from the previous section that we used a regular singly linked list to implement a queue, as it conveniently allows for deleting from the head (corresponding to the dequeue operation) and adding new elements after the tail (corresponding to the enqueue operation).</p>
<p>For a double-ended queue, both the head and the tail can perform enqueue and dequeue operations. In other words, a double-ended queue needs to implement operations in the opposite direction as well. For this, we use a "doubly linked list" as the underlying data structure of the double-ended queue.</p>
<p>As shown in the Figure 5-8 , we treat the head and tail nodes of the doubly linked list as the front and rear of the double-ended queue, respectively, and implement the functionality to add and remove nodes at both ends.</p>
<div class="tabbed-set tabbed-alternate" data-tabs="2:5"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListDeque</label><label for="__tabbed_2_2">pushLast()</label><label for="__tabbed_2_3">pushFirst()</label><label for="__tabbed_2_4">popLast()</label><label for="__tabbed_2_5">popFirst()</label></div>
<div class="tabbed-content">
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<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a>[file]{array_deque}-[func]{}
</code></pre></div>
<h2 id="533-applications-of-double-ended-queue">5.3.3 &nbsp; Applications of Double-Ended Queue<a class="headerlink" href="#533-applications-of-double-ended-queue" title="Permanent link">&para;</a></h2>
<p>The double-ended queue combines the logic of both stacks and queues, <strong>thus it can implement all the application scenarios of these two, while offering greater flexibility</strong>.</p>
<p>We know that the "undo" feature in software is typically implemented using a stack: the system <code>pushes</code> each change operation onto the stack, and then <code>pops</code> to implement undoing. However, considering the limitations of system resources, software often restricts the number of undo steps (for example, only allowing the last 50 steps). When the length of the stack exceeds 50, the software needs to perform a deletion operation at the bottom of the stack (the front of the queue). <strong>But a regular stack cannot perform this function, which is where a double-ended queue becomes necessary</strong>. Note that the core logic of "undo" still follows the Last-In-First-Out principle of a stack, but a double-ended queue can more flexibly implement some additional logic.</p>
<p>The double-ended queue combines the logic of both stacks and queues, <strong>thus, it can implement all their respective use cases while offering greater flexibility</strong>.</p>
<p>We know that software's "undo" feature is typically implemented using a stack: the system <code>pushes</code> each change operation onto the stack and then <code>pops</code> to implement undoing. However, considering the limitations of system resources, software often restricts the number of undo steps (for example, only allowing the last 50 steps). When the stack length exceeds 50, the software needs to perform a deletion operation at the bottom of the stack (the front of the queue). <strong>But a regular stack cannot perform this function, where a double-ended queue becomes necessary</strong>. Note that the core logic of "undo" still follows the Last-In-First-Out principle of a stack, but a double-ended queue can more flexibly implement some additional logic.</p>
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