算法复杂度速查表

http://easygeek.com.cn/article/IjaQVf.html

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 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