每个程序员都应该收藏的算法复杂度速查表

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 OBig-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 ArrayO(1)O(n)O(n)O(n)O(1)O(n)O(n)O(n)O(n)StackO(n)O(n)O(1)O(1)O(n)O(n)O(1)O(1)O(n)Singly-Linked ListO(n)O(n)O(1)O(1)O(n)O(n)O(1)O(1)O(n)Doubly-Linked ListO(n)O(n)O(1)O(1)O(n)O(n)O(1)O(1)O(n)Skip ListO(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 TreeO(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-TreeO(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 TreeO(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 TreeO(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QuicksortO(n log(n))O(n log(n))O(n^2)O(log(n))MergesortO(n log(n))O(n log(n))O(n log(n))O(n)TimsortO(n)O(n log(n))O(n log(n))O(n)HeapsortO(n log(n))O(n log(n))O(n log(n))O(1)Bubble SortO(n)O(n^2)O(n^2)O(1)Insertion SortO(n)O(n^2)O(n^2)O(1)Selection SortO(n^2)O(n^2)O(n^2)O(1)Shell SortO(n)O((nlog(n))^2)O((nlog(n))^2)O(1)Bucket SortO(n+k)O(n+k)O(n^2)O(n)Radix SortO(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 listO(|V|+|E|)O(1)O(1)O(|V| + |E|)O(|E|)O(|V|)Incidence listO(|V|+|E|)O(1)O(1)O(|E|)O(|E|)O(|E|)Adjacency matrixO(|V|^2)O(|V|^2)O(1)O(|V|^2)O(1)O(1)Incidence matrixO(|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 HeapO(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

Big O Complexity Graph

 

推荐阅读

• Cracking the Coding Interview: 150 Programming Questions and Solutions
• Introduction to Algorithms, 3rd Edition
• Data Structures and Algorithms in Java (2nd Edition)
• High Performance JavaScript (Build Faster Web Application Interfaces)

 

贡献者

1. Eric Rowell, creator of Concrete.js, an HTML5 Canvas Framework
2. Quentin Pleple
3. Michael Abed
4. Nick Dizazzo
5. Adam Forsyth
6. David Dorfman
7. Jay Engineer
8. Jennifer Hamon
9. Josh Davis
10. Nodir Turakulov
11. Bart Massey
12. Vinnie Magro
13. Miguel Amigot
14. Drew Bailey
15. Aneel Nazareth
16. Rahul Chowdhury
17. Robert Burke
18. steven41292
19. Brandon Amos
20. Mike Davis
21. Casper Van Gheluwe
22. Joel Friedly
23. Oleg
24. Renfred Harper
25. Piper Chester
26. Eric Lefevre-Ardant
27. Jonathan McElroy
28. Si Pham
29. mcverry
30. Max Hoffmann
31. Alejandro Ramirez
32. Damon Davison
33. Alvin Wan
34. Alan Briolat
35. Drew Hannay
36. Andrew Rasmussen
37. Dennis Tsang
38. Bahador Saket