每个程序员都应该收藏的算法复杂度速查表
2016-06-20 12:36
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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
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
推荐阅读
Cracking the Coding Interview: 150 Programming Questions and SolutionsIntroduction to Algorithms, 3rd Edition
Data Structures and Algorithms in Java (2nd Edition)
High Performance JavaScript (Build Faster Web Application Interfaces)
贡献者
Eric Rowell, creator of Concrete.js, an HTML5 Canvas FrameworkQuentin Pleple
Michael Abed
Nick Dizazzo
Adam Forsyth
David Dorfman
Jay Engineer
Jennifer Hamon
Josh Davis
Nodir Turakulov
Bart Massey
Vinnie Magro
Miguel Amigot
Drew Bailey
Aneel Nazareth
Rahul Chowdhury
Robert Burke
steven41292
Brandon Amos
Mike Davis
Casper Van Gheluwe
Joel Friedly
Oleg
Renfred Harper
Piper Chester
Eric Lefevre-Ardant
Jonathan McElroy
Si Pham
mcverry
Max Hoffmann
Alejandro Ramirez
Damon Davison
Alvin Wan
Alan Briolat
Drew Hannay
Andrew Rasmussen
Dennis Tsang
Bahador Saket
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