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krahets/hello-algo
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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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1.2.3. 数据结构与算法的关系
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1.3. 小结
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<a href="../../chapter_computational_complexity/">2. 复杂度</a>
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2. 复杂度
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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
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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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<div class="md-nav__link md-nav__link--index ">
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<a href="../../chapter_array_and_linkedlist/">4. 数组与链表</a>
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<label for="__nav_5">
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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_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 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 class="md-nav__item 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 class="md-nav__item md-nav__item--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
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<div class="md-nav__link md-nav__link--index ">
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<a href="../../chapter_hashing/">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="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（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_hashing/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="../../chapter_hashing/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">
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<a href="../../chapter_hashing/summary/" class="md-nav__link">
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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--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">
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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_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">
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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--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">
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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_9_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_9">
|
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<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--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 ">
|
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<a href="../../chapter_graph/">9. 图</a>
|
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<label for="__nav_10">
|
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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_10_label" aria-expanded="false">
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<label class="md-nav__title" for="__nav_10">
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<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">
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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--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--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">
|
|
|
<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">
|
|
|
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
|
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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/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">
|
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11.5. 快速排序
|
|
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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/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">
|
|
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11.7. 堆排序
|
|
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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/bucket_sort/" class="md-nav__link">
|
|
|
11.8. 桶排序
|
|
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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/counting_sort/" class="md-nav__link">
|
|
|
11.9. 计数排序
|
|
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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/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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|
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11.11. 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--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_divide_and_conquer/">12. 分治</a>
|
|
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|
|
<label for="__nav_13">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
</label>
|
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|
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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. 分治
|
|
|
</label>
|
|
|
<ul class="md-nav__list" data-md-scrollfix>
|
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<li class="md-nav__item">
|
|
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<a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
|
|
|
12.1. 分治算法（New）
|
|
|
</a>
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</li>
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<li class="md-nav__item">
|
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<a href="../../chapter_divide_and_conquer/build_binary_tree/" class="md-nav__link">
|
|
|
12.2. 构建树问题（New）
|
|
|
</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--nested">
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<input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
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<div class="md-nav__link md-nav__link--index ">
|
|
|
<a href="../../chapter_backtracking/">13. 回溯</a>
|
|
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|
|
<label for="__nav_14">
|
|
|
<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_14_label" aria-expanded="false">
|
|
|
<label class="md-nav__title" for="__nav_14">
|
|
|
<span class="md-nav__icon md-icon"></span>
|
|
|
13. 回溯
|
|
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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">
|
|
|
<a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
|
|
|
13.1. 回溯算法
|
|
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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_backtracking/permutations_problem/" class="md-nav__link">
|
|
|
13.2. 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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|
|
13.3. 子集和问题
|
|
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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/n_queens_problem/" class="md-nav__link">
|
|
|
13.4. 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">
|
|
|
13.5. 小结
|
|
|
</a>
|
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</li>
|
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1.2.1. 算法定义
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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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<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，包含清晰的输入和输出定义。</li>
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<li>具有可行性，能够在有限步骤、时间和内存空间下完成。</li>
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<li>各步骤都有确定的含义，相同的输入和运行条件下，输出始终相同。</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」是计算机中组织和存储数据的方式。为了提高数据存储和操作性能，数据结构的设计目标包括：</p>
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<ul>
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<li>空间占用尽量减少，节省计算机内存。</li>
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<li>数据操作尽可能快速，涵盖数据访问、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，以便使得算法高效运行。</li>
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</ul>
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<p>数据结构设计是一个充满权衡的过程，这意味着要在某方面取得优势，往往需要在另一方面作出妥协。例如，链表相较于数组，在数据添加和删除操作上更加便捷，但牺牲了数据访问速度；图相较于链表，提供了更丰富的逻辑信息，但需要占用更大的内存空间。</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」高度相关且紧密结合，具体表现在：</p>
|
|
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<ul>
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<li>数据结构是算法的基石。数据结构为算法提供了结构化存储的数据，以及用于操作数据的方法。</li>
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<li>算法是数据结构发挥的舞台。数据结构本身仅存储数据信息，通过结合算法才能解决特定问题。</li>
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<li>特定算法通常有对应最优的数据结构。算法通常可以基于不同的数据结构进行实现，但最终执行效率可能相差很大。</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>
|
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<p align="center"> Fig. 数据结构与算法的关系 </p>
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<p>我们可以把数据结构与算法类比为拼装积木。一套积木，除了包含许多零件之外，还附有详细的组装说明书。我们按照说明书一步步操作，就能组装出精美的积木模型。</p>
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<p><img alt="拼装积木" src="../what_is_dsa.assets/assembling_blocks.jpg" /></p>
|
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<p align="center"> Fig. 拼装积木 </p>
|
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<p>两者的详细对应关系如下表所示。</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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</tr>
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</tbody>
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</table>
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</div>
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<p>值得注意的是，数据结构与算法独立于编程语言。正因如此，本书得以提供多种编程语言的实现。</p>
|
|
|
<div class="admonition tip">
|
|
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<p class="admonition-title">约定俗成的简称</p>
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|
|
<p>在实际讨论时，我们通常会将「数据结构与算法」简称为「算法」。例如，众所周知的 LeetCode 算法题目，实际上同时考察了数据结构和算法两方面的知识。</p>
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</div>
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<h2 id="__comments">评论</h2>
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