Complexities Table

Know Thy Complexities!

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 Google, Facebook, Yahoo, LinkedIn, and eBay, and each time that I prepared for an interview, I thought to myself "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! - Eric

If you're trying to catch them all, you might also check out the Pokemon Go Evolution Chart.

Big-O Complexity Chart

HorribleBadFairGoodExcellent

O(log n), O(1)O(n)O(n log n)O(n^2)O(2^n)O(n!)OperationsElements

Common Data Structure Operations

Data StructureTime ComplexitySpace Complexity AverageWorstWorst AccessSearchInsertionDeletionAccessSearchInsertionDeletion ArrayΘ(1)Θ(n)Θ(n)Θ(n)O(1)O(n)O(n)O(n)O(n)StackΘ(n)Θ(n)Θ(1)Θ(1)O(n)O(n)O(1)O(1)O(n)QueueΘ(n)Θ(n)Θ(1)Θ(1)O(n)O(n)O(1)O(1)O(n)Singly-Linked ListΘ(n)Θ(n)Θ(1)Θ(1)O(n)O(n)O(1)O(1)O(n)Doubly-Linked ListΘ(n)Θ(n)Θ(1)Θ(1)O(n)O(n)O(1)O(1)O(n)Skip ListΘ(log(n))Θ(log(n))Θ(log(n))Θ(log(n))O(n)O(n)O(n)O(n)O(n log(n))Hash TableN/AΘ(1)Θ(1)Θ(1)N/AO(n)O(n)O(n)O(n)Binary Search TreeΘ(log(n))Θ(log(n))Θ(log(n))Θ(log(n))O(n)O(n)O(n)O(n)O(n)Cartesian TreeN/AΘ(log(n))Θ(log(n))Θ(log(n))N/AO(n)O(n)O(n)O(n)B-TreeΘ(log(n))Θ(log(n))Θ(log(n))Θ(log(n))O(log(n))O(log(n))O(log(n))O(log(n))O(n)Red-Black TreeΘ(log(n))Θ(log(n))Θ(log(n))Θ(log(n))O(log(n))O(log(n))O(log(n))O(log(n))O(n)Splay TreeN/AΘ(log(n))Θ(log(n))Θ(log(n))N/AO(log(n))O(log(n))O(log(n))O(n)AVL TreeΘ(log(n))Θ(log(n))Θ(log(n))Θ(log(n))O(log(n))O(log(n))O(log(n))O(log(n))O(n)KD TreeΘ(log(n))Θ(log(n))Θ(log(n))Θ(log(n))O(n)O(n)O(n)O(n)O(n)

Array Sorting Algorithms

AlgorithmTime ComplexitySpace Complexity BestAverageWorstWorstQuicksortΩ(n log(n))Θ(n log(n))O(n^2)O(log(n))MergesortΩ(n log(n))Θ(n log(n))O(n log(n))O(n)TimsortΩ(n)Θ(n log(n))O(n log(n))O(n)HeapsortΩ(n log(n))Θ(n log(n))O(n log(n))O(1)Bubble SortΩ(n)Θ(n^2)O(n^2)O(1)Insertion SortΩ(n)Θ(n^2)O(n^2)O(1)Selection SortΩ(n^2)Θ(n^2)O(n^2)O(1)Tree SortΩ(n log(n))Θ(n log(n))O(n^2)O(n)Shell SortΩ(n log(n))Θ(n(log(n))^2)O(n(log(n))^2)O(1)Bucket SortΩ(n+k)Θ(n+k)O(n^2)O(n)Radix SortΩ(nk)Θ(nk)O(nk)O(n+k)Counting SortΩ(n+k)Θ(n+k)O(n+k)O(k)CubesortΩ(n)Θ(n log(n))O(n log(n))O(n)

Learn More

• 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)

Get the Official Big-O Cheat Sheet Poster

Contributors

1. Eric Rowell 
2. Quentin Pleple 
3. Michael Abed 
4. Nick Dizazzo 
5. Adam Forsyth 
6. Felix Zhu 
7. Jay Engineer 
8. Josh Davis 
9. Nodir Turakulov 
10. Jennifer Hamon
11. David Dorfman 
12. Bart Massey 
13. Ray Pereda 
14. Si Pham 
15. Mike Davis 
16. mcverry 
17. Max Hoffmann 
18. Bahador Saket 
19. Damon Davison 
20. Alvin Wan 
21. Alan Briolat
22. Drew Hannay 
23. Andrew Rasmussen 
24. Dennis Tsang 
25. Vinnie Magro 
26. Adam Arold 
27. Alejandro Ramirez 
28. Aneel Nazareth 
29. Rahul Chowdhury
30. Jonathan McElroy 
31. steven41292 
32. Brandon Amos 
33. Joel Friedly 
34. Casper Van Gheluwe 
35. Eric Lefevre-Ardant 
36. Oleg 
37. Renfred Harper 
38. Piper Chester
39. Miguel Amigot 
40. Apurva K 
41. Matthew Daronco 
42. Yun-Cheng Lin 
43. Clay Tyler 
44. Orhan Can Ozalp 
45. Ayman Singh 
46. David Morton 
47. Aurelien Ooms
48. Sebastian Paaske Torholm 
49. Koushik Krishnan 
50. Drew Bailey 
51. Robert Burke

Make this Page Better

Edit these tables!