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Hello 算法
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1.2. 算法是什么
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0. 写在前面
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0. 写在前面
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0.1. 关于本书
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0.2. 如何使用本书
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0.3. 小结
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1. 引言
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1. 引言
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1.1. 算法无处不在
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< label class = "md-nav__link md-nav__link--active" for = "__toc" >
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1.2. 算法是什么
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< a href = "./" class = "md-nav__link md-nav__link--active" >
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1.2. 算法是什么
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目录
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< li class = "md-nav__item" >
< a href = "#121" class = "md-nav__link" >
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1.2.1. 算法定义
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1.2.2. 数据结构定义
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1.2.3. 数据结构与算法的关系
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< a href = "../summary/" class = "md-nav__link" >
1.3. 小结
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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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2. 复杂度分析
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< li class = "md-nav__item" >
< 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 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 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 href = "../../chapter_computational_complexity/summary/" class = "md-nav__link" >
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2.4. 小结
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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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3. 数据结构简介
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< li class = "md-nav__item" >
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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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< a href = "../../chapter_data_structure/number_encoding/" class = "md-nav__link" >
3.3. 数字编码 *
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< a href = "../../chapter_data_structure/character_encoding/" class = "md-nav__link" >
3.4. 字符编码 *
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< li class = "md-nav__item" >
< a href = "../../chapter_data_structure/summary/" class = "md-nav__link" >
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3.5. 小结
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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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< label class = "md-nav__title" for = "__nav_5" >
< span class = "md-nav__icon md-icon" > < / span >
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4. 数组与链表
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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/array/" class = "md-nav__link" >
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4.1. 数组
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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/linked_list/" class = "md-nav__link" >
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4.2. 链表
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< li class = "md-nav__item" >
< a href = "../../chapter_array_and_linkedlist/list/" class = "md-nav__link" >
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4.3. 列表
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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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< label class = "md-nav__link" for = "__nav_6" id = "__nav_6_label" tabindex = "0" >
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5. 栈与队列
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< label class = "md-nav__title" for = "__nav_6" >
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5. 栈与队列
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< li class = "md-nav__item" >
< a href = "../../chapter_stack_and_queue/stack/" class = "md-nav__link" >
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5.1. 栈
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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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< li class = "md-nav__item" >
< 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 href = "../../chapter_stack_and_queue/summary/" class = "md-nav__link" >
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5.4. 小结
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< label class = "md-nav__link" for = "__nav_7" id = "__nav_7_label" tabindex = "0" >
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6. 散列表
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< 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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< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
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6.1. 哈希表
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< a href = "../../chapter_hashing/hash_collision/" class = "md-nav__link" >
6.2. 哈希冲突处理
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< / a >
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< li class = "md-nav__item" >
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< a href = "../../chapter_hashing/summary/" class = "md-nav__link" >
6.3. 小结
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< / a >
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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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< label class = "md-nav__title" for = "__nav_8" >
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7. 树
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< ul class = "md-nav__list" data-md-scrollfix >
< 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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< li class = "md-nav__item" >
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< 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 class = "md-nav__item" >
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< a href = "../../chapter_tree/array_representation_of_tree/" class = "md-nav__link" >
7.3. 二叉树数组表示
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7.4. 二叉搜索树
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< a href = "../../chapter_tree/avl_tree/" class = "md-nav__link" >
7.5. AVL 树 *
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< li class = "md-nav__item" >
< a href = "../../chapter_tree/summary/" class = "md-nav__link" >
7.6. 小结
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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" >
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8. 堆
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< label class = "md-nav__title" for = "__nav_9" >
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8. 堆
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< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
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< a href = "../../chapter_heap/heap/" class = "md-nav__link" >
8.1. 堆
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< li class = "md-nav__item" >
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< a href = "../../chapter_heap/build_heap/" class = "md-nav__link" >
8.2. 建堆操作 *
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< li class = "md-nav__item" >
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< a href = "../../chapter_heap/summary/" class = "md-nav__link" >
8.3. 小结
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_10" >
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< label class = "md-nav__link" for = "__nav_10" id = "__nav_10_label" tabindex = "0" >
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9. 图
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< label class = "md-nav__title" for = "__nav_10" >
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9. 图
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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 class = "md-nav__item" >
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< a href = "../../chapter_graph/graph_operations/" class = "md-nav__link" >
9.2. 图基础操作
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< li class = "md-nav__item" >
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9.3. 图的遍历
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< a href = "../../chapter_graph/summary/" class = "md-nav__link" >
9.4. 小结
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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" >
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10. 搜索算法
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< label class = "md-nav__title" for = "__nav_11" >
< span class = "md-nav__icon md-icon" > < / span >
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10. 搜索算法
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< / label >
< ul class = "md-nav__list" data-md-scrollfix >
< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search/" class = "md-nav__link" >
10.1. 二分查找（ ）
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< / a >
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/binary_search_edge/" class = "md-nav__link" >
10.2. 二分查找边界（ ）
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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" >
10.3. 哈希优化策略
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< li class = "md-nav__item" >
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< a href = "../../chapter_searching/searching_algorithm_revisited/" class = "md-nav__link" >
10.4. 重识搜索算法
< / a >
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< li class = "md-nav__item" >
< a href = "../../chapter_searching/summary/" class = "md-nav__link" >
10.5. 小结
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< input class = "md-nav__toggle md-toggle " type = "checkbox" id = "__nav_12" >
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< label class = "md-nav__link" for = "__nav_12" id = "__nav_12_label" tabindex = "0" >
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11. 排序算法
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< span class = "md-nav__icon md-icon" > < / span >
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< label class = "md-nav__title" for = "__nav_12" >
< span class = "md-nav__icon md-icon" > < / span >
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11. 排序算法
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11.2. 选择排序（ ）
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11.3. 冒泡排序
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11.4. 插入排序
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11.5. 快速排序
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11.6. 归并排序
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< / a >
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11.8. 桶排序
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11.9. 计数排序
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11.10. 基数排序
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11.11. 小结
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1.2.1. 算法定义
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1.2.2. 数据结构定义
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1.2.3. 数据结构与算法的关系
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< h1 id = "12" > 1.2. 算法是什么< a class = "headerlink" href = "#12" title = "Permanent link" > ¶ < / a > < / h1 >
< 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 >
< ul >
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< li > 问题是明确的，具有清晰的输入和输出定义。< / li >
< li > 解具有确定性，即给定相同的输入时，输出始终相同。< / li >
< li > 具有可行性，在有限步骤、时间和内存空间下可完成。< / 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， ： < / 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 >
< li > 数据操作尽可能快速，涵盖数据访问、添加、删除、更新等。< / li >
< li > 提供简洁的数据表示和逻辑信息，以利于算法高效运行。< / 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 >
< 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 >
< 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 > 类比「LEGO 乐高」和「数据结构与算法」，则对应关系如下表所示。< / p >
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< div class = "center-table" >
< table >
< thead >
< tr >
< th > 数据结构与算法< / th >
< th > LEGO 乐高< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td > 输入数据< / td >
< td > 未拼装的积木< / td >
< / tr >
< tr >
< td > 数据结构< / td >
< td > 积木组织形式，包括形状、大小、连接方式等< / td >
< / tr >
< tr >
< td > 算法< / td >
< td > 把积木拼成目标形态的一系列操作步骤< / td >
< / tr >
< tr >
< td > 输出数据< / td >
< td > 积木模型< / td >
< / tr >
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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 >
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< div class = "admonition tip" >
< 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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