Hi there! 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. Over the last few years, I've interviewed at several Silicon Valley startups, and also some bigger companies, like Yahoo, eBay, LinkedIn, and Google, and each time that I prepared for an interview, I thought to msyelf "Why oh why hasn't someone created a nice Big-O cheat sheet?". So, to save all of you fine folks a ton of time, I went ahead and created one. Enjoy!
Searching
| Algorithm | Data Structure | Time Complexity | Space Complexity | ||||
|---|---|---|---|---|---|---|---|
| Best | Average | Worst | Worst | ||||
| Depth First Search (DFS) | Tree | O(1) | - | O(b^d) | O(|V|) | ||
| Breadth First Search (BFS) | Tree | O(1) | - | O(b^d) | O(b^d) | ||
| Binary | Tree | O(1) | O(log(n)) | O(log(n)) | O(1) | ||
| Linear (Brute Force) | Array | O(1) | O(n) | O(n) | O(1) | ||
Sorting
| Algorithm | Data Structure | Time Complexity | Space Complexity | ||||
|---|---|---|---|---|---|---|---|
| Best | Average | Worst | Worst | ||||
| Quicksort | Array | O(n log(n)) | O(n log(n)) | O(n^2) | O(log(n)) | ||
| Mergesort | Array | O(n log(n)) | O(n log(n)) | O(n log(n)) | O(n) | ||
| Bubble Sort | Array | O(n) | O(n^2) | O(n^2) | O(1) | ||
| Insertion Sort | Array | O(n) | O(n^2) | O(n^2) | O(1) | ||
Data Structures
| Data Structure | Time Complexity | Space Complexity | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Average | Worst | Worst | |||||||
| Indexing | Search | Insertion | Deletion | Indexing | Search | Insertion | Deletion | ||
| Basic Array | O(1) | O(n) | - | - | O(1) | O(n) | - | - | O(n) |
| Dynamic Array | O(1) | O(n) | O(n) | - | O(1) | O(n) | O(n) | - | 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) |
| 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(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(n) |
| Red-Black 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(n) |
Graphs
| Node / Edge Management | Storage | Add Vertex | Add Edge | Remove Vertex | Remove Edge | Query |
|---|---|---|---|---|---|---|
| Adjacency list | O(|V|+|E|) | O(1) | O(1) | O(|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|) |
|V| denotes the number of vertices; |E| denotes the number of edges.
Big-O Complexity Graph
