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2. 复杂度分析
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2.1. 算法效率评估
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2.2. 时间复杂度
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2.3. 空间复杂度
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2.4. 小结
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3. 数据结构简介
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3.1. 数据结构分类
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3.2. 基本数据类型
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3.3. 数字编码 *
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3.4. 字符编码 *
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3.5. 小结
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4. 数组与链表
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4.1. 数组
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4.2. 链表
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<li class="md-nav__item">
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<a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
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4.3. 列表
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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_array_and_linkedlist/summary/" class="md-nav__link">
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4.4. 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_6" >
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<div class="md-nav__link md-nav__link--index ">
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<a href="../../chapter_stack_and_queue/">5. 栈与队列</a>
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<label for="__nav_6">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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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
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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
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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
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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--active md-nav__item--section md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" checked>
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<div class="md-nav__link md-nav__link--index ">
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<a href="../">6. 散列表</a>
|
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<label for="__nav_7">
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<span class="md-nav__icon md-icon"></span>
|
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="true">
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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="../hash_map/" class="md-nav__link">
|
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6.1. 哈希表（New）
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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="../hash_collision/" class="md-nav__link">
|
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6.2. 哈希冲突（New）
|
|
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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="../hash_algorithm/" class="md-nav__link">
|
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6.3. 哈希算法（New）
|
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</a>
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</li>
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<li class="md-nav__item md-nav__item--active">
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<input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
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<a href="./" class="md-nav__link md-nav__link--active">
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6.4. 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_8" >
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<div class="md-nav__link md-nav__link--index ">
|
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|
<a href="../../chapter_tree/">7. 树</a>
|
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|
<label for="__nav_8">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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</div>
|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_8">
|
|
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<span class="md-nav__icon md-icon"></span>
|
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7. 树
|
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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_tree/binary_tree/" class="md-nav__link">
|
|
|
7.1. 二叉树
|
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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/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/array_representation_of_tree/" class="md-nav__link">
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7.3. 二叉树数组表示
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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">
|
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7.4. 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">
|
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7.5. 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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7.6. 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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<div class="md-nav__link md-nav__link--index ">
|
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|
<a href="../../chapter_heap/">8. 堆</a>
|
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|
|
<label for="__nav_9">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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</div>
|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_9">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
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8. 堆
|
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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_heap/heap/" class="md-nav__link">
|
|
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8.1. 堆
|
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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_heap/build_heap/" class="md-nav__link">
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8.2. 建堆操作
|
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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_heap/top_k/" class="md-nav__link">
|
|
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8.3. Top-K 问题（New）
|
|
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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_heap/summary/" class="md-nav__link">
|
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8.4. 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_10" >
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<div class="md-nav__link md-nav__link--index ">
|
|
|
<a href="../../chapter_graph/">9. 图</a>
|
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|
|
<label for="__nav_10">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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</div>
|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
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|
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<label class="md-nav__title" for="__nav_10">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
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9. 图
|
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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_graph/graph/" class="md-nav__link">
|
|
|
9.1. 图
|
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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_graph/graph_operations/" class="md-nav__link">
|
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9.2. 图基础操作
|
|
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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_graph/graph_traversal/" class="md-nav__link">
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9.3. 图的遍历
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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_graph/summary/" class="md-nav__link">
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9.4. 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_11" >
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<div class="md-nav__link md-nav__link--index ">
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<a href="../../chapter_searching/">10. 搜索</a>
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<label for="__nav_11">
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<span class="md-nav__icon md-icon"></span>
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</label>
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</div>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_11">
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<span class="md-nav__icon md-icon"></span>
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10. 搜索
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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_searching/binary_search/" class="md-nav__link">
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10.1. 二分查找
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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_searching/binary_search_edge/" class="md-nav__link">
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10.2. 二分查找边界
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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_searching/replace_linear_by_hashing/" class="md-nav__link">
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10.3. 哈希优化策略
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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_searching/searching_algorithm_revisited/" class="md-nav__link">
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10.4. 重识搜索算法
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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_searching/summary/" class="md-nav__link">
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10.5. 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_12" >
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<div class="md-nav__link md-nav__link--index ">
|
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<a href="../../chapter_sorting/">11. 排序</a>
|
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<label for="__nav_12">
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|
|
<span class="md-nav__icon md-icon"></span>
|
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</label>
|
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</div>
|
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
|
|
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<label class="md-nav__title" for="__nav_12">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
11. 排序
|
|
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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_sorting/sorting_algorithm/" class="md-nav__link">
|
|
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11.1. 排序算法
|
|
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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_sorting/selection_sort/" class="md-nav__link">
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11.2. 选择排序
|
|
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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_sorting/bubble_sort/" class="md-nav__link">
|
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11.3. 冒泡排序
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
|
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11.4. 插入排序
|
|
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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_sorting/quick_sort/" class="md-nav__link">
|
|
|
11.5. 快速排序
|
|
|
</a>
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
|
|
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11.6. 归并排序
|
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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_sorting/heap_sort/" class="md-nav__link">
|
|
|
11.7. 堆排序
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
|
|
<a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
|
|
|
11.8. 桶排序
|
|
|
</a>
|
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</li>
|
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<li class="md-nav__item">
|
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|
<a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
|
|
|
11.9. 计数排序
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
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|
<a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
|
|
|
11.10. 基数排序
|
|
|
</a>
|
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</li>
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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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11.11. 小结
|
|
|
</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_13" >
|
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<div class="md-nav__link md-nav__link--index ">
|
|
|
<a href="../../chapter_backtracking/">12. 回溯</a>
|
|
|
|
|
|
<label for="__nav_13">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
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|
|
</div>
|
|
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|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_13">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
12. 回溯
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
|
|
<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
|
|
|
12.1. 回溯算法
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
|
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<a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
|
|
|
12.2. 全排列问题
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
|
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<a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
|
|
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12.3. 子集和问题（New）
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
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<a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
|
|
|
12.4. N 皇后问题
|
|
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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_backtracking/summary/" class="md-nav__link">
|
|
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12.5. 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_14" >
|
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<label class="md-nav__link" for="__nav_14" id="__nav_14_label" tabindex="0">
|
|
|
13. 附录
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
|
|
|
|
|
<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_14">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
13. 附录
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
|
|
<a href="../../chapter_appendix/installation/" class="md-nav__link">
|
|
|
13.1. 编程环境安装
|
|
|
</a>
|
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</li>
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<li class="md-nav__item">
|
|
|
<a href="../../chapter_appendix/contribution/" class="md-nav__link">
|
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13.2. 一起参与创作
|
|
|
</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_15" >
|
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<div class="md-nav__link md-nav__link--index ">
|
|
|
<a href="../../chapter_reference/">参考文献</a>
|
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</div>
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<h1 id="64">6.4. 小结<a class="headerlink" href="#64" title="Permanent link">¶</a></h1>
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<ul>
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<li>输入 <code>key</code> ，哈希表能够在 <span class="arithmatex">\(O(1)\)</span> 时间内查询到 <code>value</code> ，效率非常高。</li>
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<li>常见的哈希表操作包括查询、添加键值对、删除键值对和遍历哈希表等。</li>
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<li>哈希函数将 <code>key</code> 映射为数组索引，从而访问对应桶并获取 <code>value</code> 。</li>
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<li>两个不同的 <code>key</code> 可能在经过哈希函数后得到相同的数组索引，导致查询结果出错，这种现象被称为哈希冲突。</li>
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<li>哈希表容量越大，哈希冲突的概率就越低。因此可以通过扩容哈希表来缓解哈希冲突。与数组扩容类似，哈希表扩容操作的开销很大。</li>
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<li>负载因子定义为哈希表中元素数量除以桶数量，反映了哈希冲突的严重程度，常用作触发哈希表扩容的条件。</li>
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<li>链式地址通过将单个元素转化为链表，将所有冲突元素存储在同一个链表中。然而，链表过长会降低查询效率，可以进一步将链表转换为红黑树来提高效率。</li>
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<li>开放寻址通过多次探测来处理哈希冲突。线性探测使用固定步长，缺点是不能删除元素，且容易产生聚集。多次哈希使用多个哈希函数进行探测，相较线性探测更不易产生聚集，但多个哈希函数增加了计算量。</li>
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<li>不同编程语言采取了不同的哈希表实现。例如，Java 的 <code>HashMap</code> 使用链式地址，而 Python 的 <code>Dict</code> 采用开放寻址。</li>
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<li>在哈希表中，我们希望哈希算法具有确定性、高效率和均匀分布的特点。在密码学中，哈希算法还应该具备抗碰撞性和雪崩效应。</li>
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<li>哈希算法通常采用大质数作为模数，以最大化地保证哈希值的均匀分布，减少哈希冲突。</li>
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<li>常见的哈希算法包括 MD5, SHA-1, SHA-2, SHA3 等。MD5 常用语校验文件完整性，SHA-2 常用于安全应用与协议。</li>
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<li>编程语言通常会为数据类型提供内置哈希算法，用于计算哈希表中的桶索引。通常情况下，只有不可变对象是可哈希的。</li>
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