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
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

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

Eric
Rowell, creator of Concrete.js,
an HTML5 Canvas Framework

Quentin
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