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!

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 TableO(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 TreeO(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 TreeO(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 HeapO(1)O(log(n))O(log(n))O(1)O(log(n))O(log(n))
Fibonacci HeapO(1)O(log(n))O(1)O(1)O(log(n))O(1)

 

大 O 复杂度图表

Big O Complexity Graph

Big O Complexity Graph


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