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</a>
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</div>
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<ul class="md-nav__list" data-md-scrollfix>
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<li class="md-nav__item md-nav__item--section md-nav__item--nested">
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<label class="md-nav__link" for="__nav_1" id="__nav_1_label" tabindex="0">
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0. 写在前面
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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_1_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_1">
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<span class="md-nav__icon md-icon"></span>
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0. 写在前面
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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_preface/about_the_book/" class="md-nav__link">
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0.1. 关于本书
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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_preface/suggestions/" class="md-nav__link">
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0.2. 如何使用本书
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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_preface/summary/" class="md-nav__link">
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0.3. 小结
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</a>
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</nav>
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<label class="md-nav__link" for="__nav_2" id="__nav_2_label" tabindex="0">
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1. 引言
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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_2_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_2">
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<span class="md-nav__icon md-icon"></span>
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1. 引言
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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_introduction/algorithms_are_everywhere/" class="md-nav__link">
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1.1. 算法无处不在
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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_introduction/what_is_dsa/" class="md-nav__link">
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1.2. 算法是什么
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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_introduction/summary/" class="md-nav__link">
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1.3. 小结
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</a>
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</li>
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</nav>
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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_3" >
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<label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
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2. 复杂度分析
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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_3_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_3">
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<span class="md-nav__icon md-icon"></span>
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2. 复杂度分析
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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_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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<li class="md-nav__item">
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<a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
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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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<a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
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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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</li>
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<li class="md-nav__item">
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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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</li>
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</ul>
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</nav>
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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_4" >
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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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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
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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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<ul class="md-nav__list" data-md-scrollfix>
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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>
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<li class="md-nav__item">
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<a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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3.2. 数据结构分类
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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_data_structure/summary/" class="md-nav__link">
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3.3. 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_5" >
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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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</label>
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<nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_5">
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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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</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_array_and_linkedlist/array/" class="md-nav__link">
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4.1. 数组
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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/linked_list/" class="md-nav__link">
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4.2. 链表
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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/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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<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
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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--section md-nav__item--nested">
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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
|
|
|
<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">
|
|
|
<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
|
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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. 树
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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_8_label" aria-expanded="false">
|
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<label class="md-nav__title" for="__nav_8">
|
|
|
<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">
|
|
|
<a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
|
|
|
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
|
|
|
</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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|
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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
|
|
|
</a>
|
|
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</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--active md-nav__item--section md-nav__item--nested">
|
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|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" checked>
|
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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="true">
|
|
|
<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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|
|
|
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|
|
<li class="md-nav__item">
|
|
|
<a href="../graph/" class="md-nav__link">
|
|
|
9.1. 图
|
|
|
</a>
|
|
|
</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../graph_operations/" class="md-nav__link">
|
|
|
9.2. 图基础操作
|
|
|
</a>
|
|
|
</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../graph_traversal/" class="md-nav__link">
|
|
|
9.3. 图的遍历
|
|
|
</a>
|
|
|
</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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|
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|
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|
|
<a href="./" class="md-nav__link md-nav__link--active">
|
|
|
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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|
|
|
|
|
|
|
|
|
|
|
|
<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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|
|
|
|
|
|
|
|
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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>
|
|
|
</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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|
|
|
|
|
|
|
|
|
|
|
|
<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
|
|
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|
|
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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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|
|
|
|
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|
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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>
|
|
|
</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
|
|
|
11.2. 冒泡排序
|
|
|
</a>
|
|
|
</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
|
|
|
11.3. 插入排序
|
|
|
</a>
|
|
|
</li>
|
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|
<li class="md-nav__item">
|
|
|
<a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
|
|
|
11.4. 快速排序
|
|
|
</a>
|
|
|
</li>
|
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11.5. 归并排序
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</a>
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11.6. 小结
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<h1 id="94">9.4. 小结<a class="headerlink" href="#94" title="Permanent link">¶</a></h1>
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<ul>
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<li>图由顶点和边组成，可以表示为一组顶点和一组边构成的集合。</li>
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<li>相比线性关系（链表）和分治关系（树），网络关系（图）的自由度更高，也从而更为复杂。</li>
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<li>有向图的边存在方向，连通图中的任意顶点都可达，有权图的每条边都包含权重变量。</li>
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<li>邻接矩阵使用方阵来表示图，每一行（列）代表一个顶点，矩阵元素代表边，使用 <span class="arithmatex">\(1\)</span> 或 <span class="arithmatex">\(0\)</span> 来表示两个顶点之间有边或无边。邻接矩阵的增删查操作效率很高，但占用空间大。</li>
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<li>邻接表使用多个链表来表示图，第 <span class="arithmatex">\(i\)</span> 条链表对应顶点 <span class="arithmatex">\(i\)</span> ，其中存储了该顶点的所有邻接顶点。邻接表相对邻接矩阵更加节省空间，但由于需要通过遍历链表来查找边，因此时间效率较低。</li>
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<li>当邻接表中的链表过长时，可以将其转化为红黑树或哈希表，从而提升查询效率。</li>
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<li>从算法思想角度分析，邻接矩阵体现“以空间换时间”，邻接表体现“以时间换空间”</li>
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<li>图可以用于建模各类现实系统，例如社交网络、地铁线路等。</li>
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<li>树是图的一种特例，树的遍历也是图的遍历的一种特例。</li>
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<li>图的广度优先遍历是一种由近及远、层层扩张的搜索方式，常借助队列实现。</li>
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<li>图的深度优先遍历是一种优先走到底、无路可走再回头的搜索方式，常基于递归来实现。</li>
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</ul>
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