算法复杂度这件事
这篇文章覆盖了计算机科学里面常见算法的时间和空间的大 O（Big-O）复杂度。我之前在参加面试前，经常需要花费很多时间从互联网上查找各种搜索和排序算法的优劣，以便我在面试时不会被问住。最近这几年，我面试了几家硅谷的初创企业和一些更大一些的公司，如 Yahoo、eBay、LinkedIn 和 Google，每次我都需要准备这个，我就在问自己，“为什么没有人创建一个漂亮的大 O 速查表呢？”所以，为了节省大家的时间，我就创建了这个，希望你喜欢！
— Eric
图例
数据结构操作
| 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 |
|
|---|
| Array |
O(1) |
O(n) |
O(n) |
O(n) |
O(1) |
O(n) |
O(n) |
O(n) |
O(n) |
| Stack |
O(n) |
O(n) |
O(1) |
O(1) |
O(n) |
O(n) |
O(1) |
O(1) |
O(n) |
| Singly-Linked List |
O(n) |
O(n) |
O(1) |
O(1) |
O(n) |
O(n) |
O(1) |
O(1) |
O(n) |
| Doubly-Linked List |
O(n) |
O(n) |
O(1) |
O(1) |
O(n) |
O(n) |
O(1) |
O(1) |
O(n) |
| Skip List |
O(log(n)) |
O(log(n)) |
O(log(n)) |
O(log(n)) |
O(n) |
O(n) |
O(n) |
O(n) |
O(n log(n)) |
| Hash Table |
- |
O(1) |
O(1) |
O(1) |
- |
O(n) |
O(n) |
O(n) |
O(n) |
| Binary Search Tree |
O(log(n)) |
O(log(n)) |
O(log(n)) |
O(log(n)) |
O(n) |
O(n) |
O(n) |
O(n) |
O(n) |
| Cartesian Tree |
- |
O(log(n)) |
O(log(n)) |
O(log(n)) |
- |
O(n) |
O(n) |
O(n) |
O(n) |
| B-Tree |
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) |
| Red-Black Tree |
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) |
| Splay Tree |
- |
O(log(n)) |
O(log(n)) |
O(log(n)) |
- |
O(log(n)) |
O(log(n)) |
O(log(n)) |
O(n) |
| AVL Tree |
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) |
数组排序算法
| 算法 |
时间复杂度 |
空间复杂度 |
|---|
| |
最佳 |
平均 |
最差 |
最差 |
|---|
| Quicksort |
O(n log(n)) |
O(n log(n)) |
O(n^2) |
O(log(n)) |
| Mergesort |
O(n log(n)) |
O(n log(n)) |
O(n log(n)) |
O(n) |
| Timsort |
O(n) |
O(n log(n)) |
O(n log(n)) |
O(n) |
| Heapsort |
O(n log(n)) |
O(n log(n)) |
O(n log(n)) |
O(1) |
| Bubble Sort |
O(n) |
O(n^2) |
O(n^2) |
O(1) |
| Insertion Sort |
O(n) |
O(n^2) |
O(n^2) |
O(1) |
| Selection Sort |
O(n^2) |
O(n^2) |
O(n^2) |
O(1) |
| Shell Sort |
O(n) |
O((nlog(n))^2) |
O((nlog(n))^2) |
O(1) |
| Bucket Sort |
O(n+k) |
O(n+k) |
O(n^2) |
O(n) |
| Radix Sort |
O(nk) |
O(nk) |
O(nk) |
O(n+k) |
图操作
| 节点 / 边界管理 |
存储 |
增加顶点 |
增加边界 |
移除顶点 |
移除边界 |
查询 |
|---|
| Adjacency list |
O(|V|+|E|) |
O(1) |
O(1) |
O(|V| + |E|) |
O(|E|) |
O(|V|) |
| Incidence list |
O(|V|+|E|) |
O(1) |
O(1) |
O(|E|) |
O(|E|) |
O(|E|) |
| Adjacency matrix |
O(|V|^2) |
O(|V|^2) |
O(1) |
O(|V|^2) |
O(1) |
O(1) |
| Incidence matrix |
O(|V| ⋅ |E|) |
O(|V| ⋅ |E|) |
O(|V| ⋅ |E|) |
O(|V| ⋅ |E|) |
O(|V| ⋅ |E|) |
O(|E|) |
堆操作
| 类型 |
时间复杂度 |
|---|
| |
Heapify |
查找最大值 |
分离最大值 |
提升键 |
插入 |
删除 |
合并 |
|---|
| Linked List (sorted) |
- |
O(1) |
O(1) |
O(n) |
O(n) |
O(1) |
O(m+n) |
| Linked List (unsorted) |
- |
O(n) |
O(n) |
O(1) |
O(1) |
O(1) |
O(1) |
| Binary Heap |
O(n) |
O(1) |
O(log(n)) |
O(log(n)) |
O(log(n)) |
O(log(n)) |
O(m+n) |
| Binomial Heap |
- |
O(1) |
O(log(n)) |
O(log(n)) |
O(1) |
O(log(n)) |
O(log(n)) |
| Fibonacci Heap |
- |
O(1) |
O(log(n)) |
O(1) |
O(1) |
O(log(n)) |
O(1) |
大 O 复杂度图表
来源：oschina
链接：https://my.oschina.net/u/129252/blog/699712
