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This webpage covers the space and time Big-O complexities of common algorithms used in Computer Science. When preparing for technical interviews in the past, I found myself spending hours crawling the internet putting together the best, average, and worst case complexities for search and sorting algorithms so that I wouldn’t be stumped when asked about them.
VisuAlgo.net. visualising data structures and algorithms through animation
| Data Structure | Time Complexity | Space Complexity | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Average | Worst | Worst | |||||||
| Access | Search | Insertion | Deletion | Access | Search | Insertion | Deletion | ||
| 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) |
| Queue | 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 | N/A | O(1) | O(1) | O(1) | N/A | 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 | N/A | O(log(n)) | O(log(n)) | O(log(n)) | N/A | 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 | N/A | O(log(n)) | O(log(n)) | O(log(n)) | N/A | 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) |
| KD Tree | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(n) | O(n) | O(n) | O(n) | O(n) |
| Algorithm | Time Complexity | Space Complexity | ||
|---|---|---|---|---|
| Best | Average | Worst | Worst | |
| Quicksort | O(n log(n)) | O(n log(n)) | O(n^2) | O(log(n)) |
| Mergesort | O(nlog(n)) | O(nlog(n)) | O(nlog(n)) | O(n) |
| Timsort | O(n) | O(nlog(n)) | O(nlog(n)) | O(n) |
| Heapsort | O(nlog(n)) | O(nlog(n)) | O(nlog(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) |
| Tree Sort | O(n log(n)) | O(n log(n)) | O(n^2) | O(n) |
| Shell Sort | O(n log(n)) | O(n(log(n))^2) | O(n(log(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) |
| Counting Sort | O(n+k) | O(n+k) | O(n+k) | O(k) |
| Cubesort | O(n) | O(n log(n)) | O(n log(n)) | O(n) |
| Data Structure | Time Complexity | ||||||
|---|---|---|---|---|---|---|---|
| Storage | Add Vertex | Add Edge | Remove Vertex | Remove Edge | Query | ||
| 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|) | |
| Data Structure | Time Complexity | ||||||
|---|---|---|---|---|---|---|---|
| Find Max | Extract Max | Increase Key | Insert | Delete | Merge | ||
| Binary Heap | O(1) | O(log(n)) | O(log(n)) | O(log(n)) | O(log(n)) | O(m+n) | |
| Pairing Heap | O(1) | O(log(n)) |
O(log(n)) |
O(1) | O(log(n)) |
O(1) | |
| 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) | |
| Algorithm | Time Complexity | Space Complexity | |
|---|---|---|---|
| Average | Worst | Worst | |
| Dijkstra’s algorithm | O(|E| log |V|) | O(|V|^2) | O(|V| + |E|) |
| A* search algorithm | O(|E|) | O(b^d) | O(b^d) |
| Prim’s algorithm | O(|E| log |V|) | O(|V|^2) | O(|V| + |E|) |
| Bellman–Ford algorithm | O(|E| ? |V|) | O(|E| ? |V|) | O(|V|) |
| Floyd-Warshall algorithm | O(|V|^3) | O(|V|^3) | O(|V|^2) |
| Topological sort | O(|V| + |E|) | O(|V| + |E|) | O(|V| + |E| |
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原文地址：http://blog.csdn.net/songzitea/article/details/52154174
