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0. 写在前面
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0. 写在前面
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1.1. 算法无处不在
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1.2. 算法是什么
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1.2. 算法是什么
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1.2.1. 算法定义
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1.2.2. 数据结构定义
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<li class="md-nav__item">
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<a href="#123" class="md-nav__link">
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1.2.3. 数据结构与算法的关系
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1.3. 小结
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2. 复杂度分析
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<li class="md-nav__item">
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<a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
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2.1. 算法效率评估
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</a>
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</li>
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2.2. 时间复杂度
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</a>
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</li>
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<li class="md-nav__item">
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2.3. 空间复杂度
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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_computational_complexity/space_time_tradeoff/" class="md-nav__link">
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2.4. 权衡时间与空间
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</a>
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<a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
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2.5. 小结
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</a>
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</nav>
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<label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
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3. 数据结构简介
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<span class="md-nav__icon md-icon"></span>
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</label>
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<label class="md-nav__title" for="__nav_4">
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<span class="md-nav__icon md-icon"></span>
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3. 数据结构简介
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</label>
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/data_and_memory/" class="md-nav__link">
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3.1. 数据与内存
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</a>
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<li class="md-nav__item">
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3.2. 数据结构分类
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</a>
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3.3. 小结
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</a>
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</nav>
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<label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
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4. 数组与链表
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<span class="md-nav__icon md-icon"></span>
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4. 数组与链表
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4.1. 数组（Array）
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</a>
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<li class="md-nav__item">
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4.2. 链表（Linked List）
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</a>
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<li class="md-nav__item">
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4.3. 列表（List）
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</a>
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4.4. 小结
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</a>
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</nav>
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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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</label>
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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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<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">
|
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<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">
|
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7. 二叉树
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
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|
|
|
<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>
|
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|
<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">
|
|
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7.2. 二叉树遍历
|
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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/binary_search_tree/" class="md-nav__link">
|
|
|
7.3. 二叉搜索树
|
|
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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/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
|
|
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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_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>
|
|
|
|
|
|
<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>
|
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</li>
|
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<li class="md-nav__item">
|
|
|
<a href="../../chapter_heap/summary/" class="md-nav__link">
|
|
|
8.3. 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_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>
|
|
|
</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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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_graph/summary/" class="md-nav__link">
|
|
|
9.4. 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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|
|
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|
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|
|
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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>
|
|
|
</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>
|
|
|
</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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|
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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">
|
|
|
11. 排序算法
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_12">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
11. 排序算法
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_sorting/intro_to_sort/" class="md-nav__link">
|
|
|
11.1. 排序简介
|
|
|
</a>
|
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|
</li>
|
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<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
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11.2. 冒泡排序
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</a>
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</li>
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<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
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11.3. 插入排序
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</a>
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<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
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11.4. 快速排序
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</a>
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<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
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11.5. 归并排序
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</a>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/summary/" class="md-nav__link">
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11.6. 小结
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</a>
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12.2. 一起参与创作
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1.2.1. 算法定义
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<h1 id="12">1.2. 算法是什么<a class="headerlink" href="#12" title="Permanent link">¶</a></h1>
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<h2 id="121">1.2.1. 算法定义<a class="headerlink" href="#121" title="Permanent link">¶</a></h2>
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<p>「算法 Algorithm」是在有限时间内解决特定问题的一组指令或操作步骤。算法具有以下特性：</p>
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<ul>
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<li>问题是明确的，需要拥有明确的输入和输出定义。</li>
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<li>解具有确定性，即给定相同输入时，输出一定相同。</li>
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<li>具有可行性，可在有限步骤、有限时间、有限内存空间下完成。</li>
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<li>独立于编程语言，即可用多种语言实现。</li>
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</ul>
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<h2 id="122">1.2.2. 数据结构定义<a class="headerlink" href="#122" title="Permanent link">¶</a></h2>
|
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<p>「数据结构 Data Structure」是在计算机中组织与存储数据的方式。为了提高数据存储和操作性能，数据结构的设计原则有：</p>
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<ul>
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<li>空间占用尽可能小，节省计算机内存。</li>
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<li>数据操作尽量快，包括数据访问、添加、删除、更新等。</li>
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<li>提供简洁的数据表示和逻辑信息，以便算法高效运行。</li>
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</ul>
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<p>数据结构的设计是一个充满权衡的过程，这意味着如果获得某方面的优势，则往往需要在另一方面做出妥协。例如，链表相对于数组，数据添加删除操作更加方便，但牺牲了数据的访问速度；图相对于链表，提供了更多的逻辑信息，但需要占用更多的内存空间。</p>
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<h2 id="123">1.2.3. 数据结构与算法的关系<a class="headerlink" href="#123" title="Permanent link">¶</a></h2>
|
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|
<p>「数据结构」与「算法」是高度相关、紧密嵌合的，体现在：</p>
|
|
|
<ul>
|
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|
<li>数据结构是算法的底座。数据结构为算法提供结构化存储的数据，以及操作数据的对应方法。</li>
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<li>算法是数据结构发挥的舞台。数据结构仅存储数据信息，结合算法才可解决特定问题。</li>
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|
|
<li>算法有对应最优的数据结构。给定算法，一般可基于不同的数据结构实现，而最终执行效率往往相差很大。</li>
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</ul>
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|
|
<p><img alt="数据结构与算法的关系" src="../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" /></p>
|
|
|
<p align="center"> Fig. 数据结构与算法的关系 </p>
|
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|
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<p>如果将「LEGO 乐高」类比到「数据结构与算法」，那么可以得到下表所示的对应关系。</p>
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<div class="center-table">
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<table>
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<thead>
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<tr>
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<th>数据结构与算法</th>
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<th>LEGO 乐高</th>
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</tr>
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</thead>
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<tbody>
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<tr>
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<td>输入数据</td>
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<td>未拼装的积木</td>
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</tr>
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<tr>
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<td>数据结构</td>
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<td>积木组织形式，包括形状、大小、连接方式等</td>
|
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</tr>
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<tr>
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<td>算法</td>
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<td>把积木拼成目标形态的一系列操作步骤</td>
|
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</tr>
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<tr>
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<td>输出数据</td>
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<td>积木模型</td>
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<p class="admonition-title">约定俗成的简称</p>
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<p>在实际讨论中，我们通常会将「数据结构与算法」直接简称为「算法」。例如，我们熟称的 LeetCode 算法题目，实际上同时考察了数据结构和算法两部分知识。</p>
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