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@@ -3484,7 +3484,32 @@
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<article class="md-content__inner md-typeset">
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<!--
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to
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deal in the Software without restriction, including without limitation the
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rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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sell copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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IN THE SOFTWARE.
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-->
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<!-- Tags -->
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<!-- Actions -->
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_stack_and_queue/deque.md" title="编辑此页" class="md-content__button md-icon">
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Hack: check whether the content contains a h1 headline. If it doesn't, the
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page title (or respectively site name) is used as the main headline.
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<h1 id="53">5.3 双向队列<a class="headerlink" href="#53" title="Permanent link">¶</a></h1>
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<p>在队列中，我们仅能在头部删除或在尾部添加元素。如图 5-7 所示，「双向队列 deque」提供了更高的灵活性，允许在头部和尾部执行元素的添加或删除操作。</p>
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<p><img alt="双向队列的操作" src="../deque.assets/deque_operations.png" /></p>
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<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>
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<p>我们知道，软件的“撤销”功能通常使用栈来实现：系统将每次更改操作 <code>push</code> 到栈中，然后通过 <code>pop</code> 实现撤销。然而，考虑到系统资源的限制，软件通常会限制撤销的步数（例如仅允许保存 <span class="arithmatex">\(50\)</span> 步）。当栈的长度超过 <span class="arithmatex">\(50\)</span> 时，软件需要在栈底（即队首）执行删除操作。<strong>但栈无法实现该功能，此时就需要使用双向队列来替代栈</strong>。请注意，“撤销”的核心逻辑仍然遵循栈的先入后出原则，只是双向队列能够更加灵活地实现一些额外逻辑。</p>
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<!-- Was this page helpful? -->
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<h2 id="__comments">评论</h2>
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class="md-footer__inner md-grid"
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aria-label="页脚"
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<a
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href="../queue/"
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class="md-footer__link md-footer__link--prev"
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aria-label="上一页: 5.2 &nbsp; 队列"
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rel="prev"
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
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5.2 队列
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z"/></svg>
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</a>
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</nav>
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<h5 align="center" id="__comments">欢迎你提出疑问或建议</h5>
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<script
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src="https://giscus.app/client.js"
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</main>
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<footer class="md-footer">
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<nav class="md-footer__inner md-grid" aria-label="页脚" >
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<a href="../queue/" class="md-footer__link md-footer__link--prev" aria-label="上一页: 5.2 &nbsp; 队列" rel="prev">
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<div class="md-footer__button md-icon">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
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5.2 队列
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</a>
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<a href="../summary/" class="md-footer__link md-footer__link--next" aria-label="下一页: 5.4 &nbsp; 小结" rel="next">
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5.4 小结
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M4 11v2h12l-5.5 5.5 1.42 1.42L19.84 12l-7.92-7.92L10.5 5.5 16 11H4Z"/></svg>
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</div>
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</a>
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</nav>
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<!--
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Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to
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deal in the Software without restriction, including without limitation the
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rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
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sell copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in
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all copies or substantial portions of the Software.
|
||||
|
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
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IN THE SOFTWARE.
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-->
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