每个程序员都应该收藏的算法复杂度速查表
译自：http://bigocheatsheet.com/
作者： Eric
原创：LCTT https://linux.cn/article-7480-1.html
译者： Xingyu.Wang
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 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
| 绝佳 | 不错 | 一般 | 不佳 | 糟糕 |
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
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- Cracking the Coding Interview: 150 Programming Questions and Solutions
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- Data Structures and Algorithms in Java (2nd Edition)
- High Performance JavaScript (Build Faster Web Application Interfaces)
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