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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
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<label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
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5. 栈与队列
|
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<span class="md-nav__icon md-icon"></span>
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</label>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_6">
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<span class="md-nav__icon md-icon"></span>
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5. 栈与队列
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</label>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
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5.1. 栈（Stack）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
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5.2. 队列（Queue）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
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5.3. 双向队列（Deque）
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</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
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5.4. 小结
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</a>
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
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<label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
|
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6. 散列表
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<span class="md-nav__icon md-icon"></span>
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</label>
|
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|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_7">
|
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|
<span class="md-nav__icon md-icon"></span>
|
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6. 散列表
|
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</label>
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|
<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item">
|
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<a href="../../chapter_hashing/hash_map/" class="md-nav__link">
|
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6.1. 哈希表（Hash Map）
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</a>
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
|
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6.2. 哈希冲突处理
|
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</a>
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_hashing/summary/" class="md-nav__link">
|
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6.3. 小结
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</a>
|
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</li>
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
|
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<label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
|
|
|
7. 二叉树
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_8">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
7. 二叉树
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
|
|
<a href="../../chapter_tree/binary_tree/" class="md-nav__link">
|
|
|
7.1. 二叉树（Binary Tree）
|
|
|
</a>
|
|
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</li>
|
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<li class="md-nav__item">
|
|
|
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
|
|
|
7.2. 二叉树遍历
|
|
|
</a>
|
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</li>
|
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<li class="md-nav__item">
|
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<a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
|
|
|
7.3. 二叉搜索树
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_tree/avl_tree/" class="md-nav__link">
|
|
|
7.4. AVL 树 *
|
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|
</a>
|
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_tree/summary/" class="md-nav__link">
|
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7.5. 小结
|
|
|
</a>
|
|
|
</li>
|
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
|
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<label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
|
|
|
8. 堆
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
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|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_9">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
8. 堆
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_heap/heap/" class="md-nav__link">
|
|
|
8.1. 堆（Heap）
|
|
|
</a>
|
|
|
</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_heap/build_heap/" class="md-nav__link">
|
|
|
8.2. 建堆操作 *
|
|
|
</a>
|
|
|
</li>
|
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</ul>
|
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
|
|
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<label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
|
|
|
9. 图
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_10">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
9. 图
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_graph/graph/" class="md-nav__link">
|
|
|
9.1. 图（Graph）
|
|
|
</a>
|
|
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</li>
|
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<li class="md-nav__item">
|
|
|
<a href="../../chapter_graph/graph_operations/" class="md-nav__link">
|
|
|
9.2. 图基础操作
|
|
|
</a>
|
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</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
|
|
|
9.3. 图的遍历
|
|
|
</a>
|
|
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</li>
|
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</ul>
|
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
|
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<label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
|
|
|
10. 查找算法
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_11">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
10. 查找算法
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_searching/linear_search/" class="md-nav__link">
|
|
|
10.1. 线性查找
|
|
|
</a>
|
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|
</li>
|
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|
|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_searching/binary_search/" class="md-nav__link">
|
|
|
10.2. 二分查找
|
|
|
</a>
|
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</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_searching/hashing_search/" class="md-nav__link">
|
|
|
10.3. 哈希查找
|
|
|
</a>
|
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</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_searching/summary/" class="md-nav__link">
|
|
|
10.4. 小结
|
|
|
</a>
|
|
|
</li>
|
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</ul>
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</nav>
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</li>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
|
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|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
|
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<label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="0">
|
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11. 排序算法
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11. 排序算法
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11.1. 排序简介
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11.2. 冒泡排序
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11.3. 插入排序
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11.4. 快速排序
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11.5. 归并排序
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11.6. 小结
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参考文献
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目录
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0.1.1. 读者对象
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0.1.2. 内容结构
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复杂度分析
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</a>
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数据结构
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算法
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0.1.3. 本书定位
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<a href="#014" class="md-nav__link">
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0.1.4. 本书特点
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0.1.5. 致谢
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<a href="https://github.com/krahets/hello-algo/tree/main/docs/chapter_preface/about_the_book.md" title="编辑此页" class="md-content__button md-icon">
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<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M10 20H6V4h7v5h5v3.1l2-2V8l-6-6H6c-1.1 0-2 .9-2 2v16c0 1.1.9 2 2 2h4v-2m10.2-7c.1 0 .3.1.4.2l1.3 1.3c.2.2.2.6 0 .8l-1 1-2.1-2.1 1-1c.1-.1.2-.2.4-.2m0 3.9L14.1 23H12v-2.1l6.1-6.1 2.1 2.1Z"/></svg>
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</a>
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<h1 id="01">0.1. 关于本书<a class="headerlink" href="#01" title="Permanent link">¶</a></h1>
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<div class="admonition tip">
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<p class="admonition-title">Tip</p>
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<p>对于本章内容，建议通读<a href="https://www.hello-algo.com/chapter_preface/suggestions/">如何使用本书</a>，其余章节可根据需求选读。</p>
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</div>
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<p>五年前发生的一件事，成为了我职业生涯的重要转折点。当时的我在交大读研，对互联网求职一无所知，但仍然硬着头皮申请了 Microsoft 软件工程师实习。面试官让我在白板上写出“快速排序”代码，我畏畏缩缩地写了一个“冒泡排序”，并且还写错了<code>(ToT)</code> 。从面试官的表情上，我看到了一个大大的 "GG" 。</p>
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<p>此次失利倒逼我开始刷算法题。我采用“扫雷游戏”式的学习方法，两眼一抹黑刷题，扫到不会的“雷”就通过查资料把它“排掉”，配合周期性总结，逐渐形成了数据结构与算法的知识图景。幸运地，我在秋招斩获了多家大厂的 Offer 。</p>
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<p>回想自己当初在“扫雷式”刷题中被炸的满头包的痛苦，思考良久，<strong>我意识到一本“前期刷题必看”的读物可以使算法小白少走许多弯路</strong>。写作意愿滚滚袭来，那就动笔吧：</p>
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<h4 align="center"> Hello，算法！ </h4>
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<h2 id="011">0.1.1. 读者对象<a class="headerlink" href="#011" title="Permanent link">¶</a></h2>
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<p>如果您是「算法初学者」，完全没有接触过算法，或者已经有少量刷题，对数据结构与算法有朦胧的理解，在会与不会之间反复横跳，那么这本书就是为您而写！本书能够带来：</p>
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<ul>
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<li>带领你完整学习数据结构与算法，初步搭建知识框架，使刷题事半功倍；</li>
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<li>提供写法标准整洁、可一键运行的配套代码，帮助你养成良好的编程习惯；</li>
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</ul>
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<p>如果您是「算法老手」，已经积累一定刷题量，接触过大多数题型，那么本书内容对你来说可能稍显基础，但仍能够带来以下价值：</p>
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<ul>
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<li>本书篇幅不长，并且包含较多对比性和总结性的内容，可以帮助你回顾与梳理算法知识体系；</li>
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<li>源代码实现了各种经典数据结构和算法，可以作为“刷题工具库”或“算法实现字典”来使用；</li>
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</ul>
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<p>如果您是「算法大佬」，请受我膜拜！希望您可以抽时间提出意见建议，或者<a href="https://www.hello-algo.com/chapter_preface/contribution/">一起参与创作</a>，帮助各位同学获取更好的学习内容，感谢！</p>
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<div class="admonition success">
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<p class="admonition-title">前置条件</p>
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<p>您需要至少具备任一语言的编程基础，能够阅读和编写简单代码。</p>
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</div>
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<h2 id="012">0.1.2. 内容结构<a class="headerlink" href="#012" title="Permanent link">¶</a></h2>
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<p>本书主要内容分为复杂度分析、数据结构、算法三个部分。</p>
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<p><img alt="Hello 算法内容结构" src="../about_the_book.assets/hello_algo_mindmap.png" /></p>
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<p align="center"> Fig. Hello 算法内容结构 </p>
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<h3 id="_1">复杂度分析<a class="headerlink" href="#_1" title="Permanent link">¶</a></h3>
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<p>首先介绍数据结构与算法的评价维度、算法效率的评估方法，引出了计算复杂度概念。</p>
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<p>接下来，从 <strong>函数渐近上界</strong> 入手，分别介绍了 <strong>时间复杂度</strong> 和 <strong>空间复杂度</strong>，包括推算方法、常见类型、示例等。同时，剖析了 <strong>最差、最佳、平均</strong> 时间复杂度的联系与区别。</p>
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<h3 id="_2">数据结构<a class="headerlink" href="#_2" title="Permanent link">¶</a></h3>
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<p>首先介绍了常用的 <strong>基本数据类型</strong> 、以及它们是如何在内存中存储的。</p>
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<p>接下来，介绍了两种 <strong>数据结构分类方法</strong>，包括逻辑结构与物理结构。</p>
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<p>后续展开介绍了 <strong>数组、链表、栈、队列、散列表、树、堆、图</strong> 等数据结构，关心以下内容：</p>
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<ul>
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<li>基本定义：数据结构的设计来源、存在意义；</li>
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<li>主要特点：在各项数据操作中的优势、劣势；</li>
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<li>常用操作：例如访问、更新、插入、删除、遍历、搜索等；</li>
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<li>常见类型：在算法题或工程实际中，经常碰到的数据结构类型；</li>
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<li>典型应用：此数据结构经常搭配哪些算法使用；</li>
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<li>实现方法：对于重要的数据结构，将给出完整的实现示例；</li>
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</ul>
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<h3 id="_3">算法<a class="headerlink" href="#_3" title="Permanent link">¶</a></h3>
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<p>包括 <strong>查找算法、排序算法、搜索与回溯、动态规划、分治算法</strong>，内容包括：</p>
|
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<ul>
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<li>基本定义：算法的设计思想；</li>
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<li>主要特点：使用前置条件、优势和劣势；</li>
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<li>算法效率：最差和平均时间复杂度、空间复杂度；</li>
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<li>实现方法：完整的算法实现，以及优化措施；</li>
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<li>示例题目：结合例题加深理解；</li>
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</ul>
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<h2 id="013">0.1.3. 本书定位<a class="headerlink" href="#013" title="Permanent link">¶</a></h2>
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<p>总体上看，我认为可将学习数据结构与算法的过程分为三个阶段。</p>
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<ul>
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<li><strong>第一阶段，算法入门</strong>。熟悉各种数据结构的特点、用法，学习各种算法的原理、流程、用途、效率等。</li>
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<li><strong>第二阶段，刷算法题</strong>。可以先从热门题单开刷，推荐<a href="https://leetcode.cn/problem-list/xb9nqhhg/">剑指 Offer</a>、<a href="https://leetcode.cn/problem-list/2cktkvj/">LeetCode Hot 100</a>，先积累至少 100 道题量，熟悉大多数的算法问题。刚开始刷题时，“遗忘”是最大的困扰点，但这是很正常的，请不要担心。学习中有一种概念叫“周期性回顾”，同一道题隔段时间做一次，在重复 3 轮以上后，往往就能牢记于心了。</li>
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<li><strong>第三阶段，搭建知识体系</strong>。在学习方面，可以阅读算法专栏文章、解题框架、算法教材，不断地丰富知识体系。在刷题方面，可以开始采用进阶刷题方案，例如按专题分类、一题多解、一解多题等，相应刷题计划与心得可以在社区中找到，在此不做赘述。</li>
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</ul>
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<p>根据观察，很多同学都是从“第二阶段”开始学习算法的。而作为入门教程，<strong>本书内容主要对应“第一阶段”</strong>，致力于帮助读者更高效地开展第二、三阶段的学习。</p>
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<p><img alt="算法学习路线" src="../suggestions.assets/learning_route.png" /></p>
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<p align="center"> Fig. 算法学习路线 </p>
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<h2 id="014">0.1.4. 本书特点<a class="headerlink" href="#014" title="Permanent link">¶</a></h2>
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<p><strong>以实践为主</strong>。我们知道，学习英语期间光啃书本是远远不够的，需要多听、多说、多写，在实践中培养语感、积累经验。编程语言也是一门语言，因此学习方法也应是类似的，需要多看优秀代码、多敲键盘、多思考代码逻辑。</p>
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<p>本书的理论部分占少量篇幅，主要分为两类：一是基础且必要的概念知识，以培养读者对于算法的感性认识；二是重要的分类、对比或总结，这是为了帮助你站在更高视角俯瞰各个知识点，形成连点成面的效果。</p>
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<p>实践部分主要由示例和代码组成。代码配有简要注释，复杂示例会尽可能地使用视觉化的形式呈现。我强烈建议读者对照着代码自己敲一遍，如果时间有限，也至少逐行读、复制并运行一遍，配合着讲解将代码吃透。</p>
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<p><strong>视觉化学习</strong>。信息时代以来，视觉化的脚步从未停止。媒体形式经历了文字短信、图文 Email 、动图、短（长）视频、交互式 Web 、3D 游戏等演变过程，信息的视觉化程度越来越高、愈加符合人类感官、信息传播效率大大提升。科技界也在向视觉化迈进，iPhone 就是一个典型例子，其相对于传统手机是高度视觉化的，包含精心设计的字体、主题配色、交互动画等。</p>
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<p>近两年，短视频成为最受欢迎的信息媒介，可以在短时间内将高密度的信息“灌”给我们，有着极其舒适的观看体验。阅读则不然，读者与书本之间天然存在一种“疏离感”，我们看书会累、会走神、会停下来想其他事、会划下喜欢的句子、会思考某一片段的含义，这种疏离感给了读者与书本之间对话的可能，拓宽了想象空间。</p>
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<p>本书作为一本入门教材，希望可以保有书本的“慢节奏”，但也会避免与读者产生过多“疏离感”，而是努力将知识完整清晰地推送到你聪明的小脑袋瓜中。我将采用视觉化的方式（例如配图、动画），尽我可能清晰易懂地讲解复杂概念和抽象示例。</p>
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<p><strong>内容精简化</strong>。大多数的经典教科书，会把每个主题都讲的很透彻。虽然透彻性正是其获得读者青睐的原因，但对于想要快速入门的初学者来说，这些教材的实用性不足。本书会避免引入非必要的概念、名词、定义等，也避免展开不必要的理论分析，毕竟这不是一本真正意义上的教材，主要任务是尽快地带领读者入门。</p>
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<p>引入一些生活案例或趣味内容，非常适合作为知识点的引子或者解释的补充，但当融入过多额外元素时，内容会稍显冗长，也许反而使读者容易迷失、抓不住重点，这也是本书需要避免的。</p>
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<p>敲代码如同写字，“美”是统一的追求。本书力求美观的代码，保证规范的变量命名、统一的空格与换行、对齐的缩进、整齐的注释等。</p>
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<h2 id="015">0.1.5. 致谢<a class="headerlink" href="#015" title="Permanent link">¶</a></h2>
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<p>本书的成书过程中，我获得了许多人的帮助，包括但不限于：</p>
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<ul>
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<li>感谢我的女朋友泡泡担任本书的首位读者，从算法小白的视角为本书的写作提出了许多建议，使这本书更加适合算法初学者来阅读。</li>
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<li>感谢腾宝、琦宝、飞宝为本书起了个响当当的名字，好听又有梗，直接唤起我最初敲下第一行代码 "Hello, World!" 的回忆。</li>
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<li>感谢我的导师李博，在小酌畅谈时您告诉我“觉得应该做就去做”，坚定了我写这本书的决心。</li>
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<li>感谢苏潼为本书设计了封面和 LOGO ，我有些强迫症，前后多次修改，谢谢你的耐心。</li>
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<li>感谢 @squidfunk 给出的写作排版建议，以及优秀开源项目 <a href="https://github.com/squidfunk/mkdocs-material/tree/master">Material-for-MkDocs</a> 。</li>
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</ul>
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<p>本书鼓励“手脑并用”的学习方式，在这点上受到了《动手学深度学习》很大影响，也在此向各位同学强烈推荐这本著作，包括<a href="https://github.com/d2l-ai/d2l-zh">中文版</a>、<a href="https://github.com/d2l-ai/d2l-en">英文版</a>、<a href="https://space.bilibili.com/1567748478">李沐老师 bilibili 主页</a>。</p>
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<p>在写作过程中，我阅读了许多数据结构与算法的教材与文章，这些著作为本书作出了很好的榜样，保证了本书内容的正确性与质量，感谢前辈们的精彩创作！</p>
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<p>感谢父母，你们一贯的支持与鼓励给了我自由度来做这些有趣的事。</p>
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