本篇基本上是原做的翻译。转载请保留本段文字。git
复杂度一般会使用大-O 记号来表示，好比快速排序的平均时间复杂度是 O(nlog(n))O(nlog(n))。虽然我是「理解派」，可是虽然每一个算法/数据结构都理解了，不时仍有可能忘记具体某个算法/数据结构的复杂度（特别是在最好、最坏和平均情形下的复杂度）。所以制做一个速查表是蛮有必要的。算法
动手前先看看是否已经有轮子是一个好习惯，果不其然，我找到了原做。数组
图例
抽象数据结构的操做复杂度
| 数据结构 |
时间复杂度 |
空间复杂度 |
| |
平均 |
最差 |
最差 |
| |
访问 |
搜索 |
插入 |
删除 |
访问 |
搜索 |
插入 |
删除 |
|
| 顺序表 |
O(1)O(1) |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
O(1)O(1) |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
| 栈 |
O(n)O(n) |
O(n)O(n) |
O(1)O(1) |
O(1)O(1) |
O(n)O(n) |
O(n)O(n) |
O(1)O(1) |
O(1)O(1) |
O(n)O(n) |
| 单链表 |
O(n)O(n) |
O(n)O(n) |
O(1)O(1) |
O(1)O(1) |
O(n)O(n) |
O(n)O(n) |
O(1)O(1) |
O(1)O(1) |
O(n)O(n) |
| 双链表 |
O(n)O(n) |
O(n)O(n) |
O(1)O(1) |
O(1)O(1) |
O(n)O(n) |
O(n)O(n) |
O(1)O(1) |
O(1)O(1) |
O(n)O(n) |
| 跳表 |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
O(nlog(n))O(nlog(n)) |
| 散列表 |
- |
O(1)O(1) |
O(1)O(1) |
O(1)O(1) |
- |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
| 二叉搜索树 |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
| 笛卡尔树 |
- |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
- |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
O(n)O(n) |
| B-树 |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(n)O(n) |
| 红黑树 |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(n)O(n) |
| 伸展树 |
- |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
- |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(n)O(n) |
| AVL 树 |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(n)O(n) |
数组排序
| 算法 |
时间复杂度 |
空间复杂度 |
| |
最佳 |
平均 |
最差 |
最差 |
| 快速排序 |
O(nlog(n))O(nlog(n)) |
O(nlog(n))O(nlog(n)) |
O(n2)O(n2) |
O(log(n))O(log(n)) |
| 归并排序 |
O(nlog(n))O(nlog(n)) |
O(nlog(n))O(nlog(n)) |
O(nlog(n))O(nlog(n)) |
O(n)O(n) |
| Timsort |
O(n)O(n) |
O(nlog(n))O(nlog(n)) |
O(nlog(n))O(nlog(n)) |
O(n)O(n) |
| 堆排序 |
O(nlog(n))O(nlog(n)) |
O(nlog(n))O(nlog(n)) |
O(nlog(n))O(nlog(n)) |
O(1)O(1) |
| 冒泡排序 |
O(n)O(n) |
O(n2)O(n2) |
O(n2)O(n2) |
O(1)O(1) |
| 插入排序 |
O(n)O(n) |
O(n2)O(n2) |
O(n2)O(n2) |
O(1)O(1) |
| 选择排序 |
O(n2)O(n2) |
O(n2)O(n2) |
O(n2)O(n2) |
O(1)O(1) |
| 希尔排序 |
O(n)O(n) |
O((nlog(n))2)O((nlog(n))2) |
O((nlog(n))2)O((nlog(n))2) |
O(1)O(1) |
| 桶排序 |
O(n+k)O(n+k) |
O(n+k)O(n+k) |
O(n2)O(n2) |
O(n)O(n) |
| 基数排序 |
O(nk)O(nk) |
O(nk)O(nk) |
O(nk)O(nk) |
O(n+k)O(n+k) |
图操做
| 节点 / 边界管理 |
存储 |
增长顶点 |
增长边界 |
移除顶点 |
移除边界 |
查询 |
| 邻接表 |
O(|V|+|E|)O(|V|+|E|) |
O(1)O(1) |
O(1)O(1) |
O(|V|+|E|)O(|V|+|E|) |
O(|E|)O(|E|) |
O(|V|)O(|V|) |
| 邻接矩阵 |
O(|V|2)O(|V|2) |
O(|V|2)O(|V|2) |
O(1)O(1) |
O(|V|2)O(|V|2) |
O(1)O(1) |
O(1)O(1) |
堆操做
| 类型 |
时间复杂度 |
| |
建堆 |
查找最大值 |
分离最大值 |
提高键 |
插入 |
删除 |
合并 |
| （排好序的）链表 |
- |
O(1)O(1) |
O(1)O(1) |
O(n)O(n) |
O(n)O(n) |
O(1)O(1) |
O(m+n)O(m+n) |
| （未排序的）链表 |
- |
O(n)O(n) |
O(n)O(n) |
O(1)O(1) |
O(1)O(1) |
O(1)O(1) |
O(1)O(1) |
| 二叉堆 |
O(n)O(n) |
O(1)O(1) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(m+n)O(m+n) |
| 二项堆 |
- |
O(1)O(1) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
O(1)O(1) |
O(log(n))O(log(n)) |
O(log(n))O(log(n)) |
| 斐波那契堆 |
- |
O(1)O(1) |
O(log(n))O(log(n)) |
O(1)O(1) |
O(1)O(1) |
O(log(n))O(log(n)) |
O(1)O(1) |
大-O 复杂度曲线
