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Big-O Cheat Sheet
Generated December 10, 2013. Brandon Amos http://bamos.github.io
1 Searching
Algorithm Data Structure Time Complexity Space Complexity Average Worst Depth First Search (DFS) Graph of |V | vertices and |E| edges
- O (|E| + |V |) O (|V |)
Breadth First Search (BFS) Graph of^ |V^ |^ vertices and |E| edges
- O (|E| + |V |) O (|V |)
Binary search Sorted array of n elements O (log(n)) O (log(n)) O (1) Linear (Brute Force) Array O (n) O (n) O (1) Shortest path by Dijkstra, using a Min-heap as prior- ity queue
Graph with |V | vertices and |E| edges
O ((|V | + |E|) log |V |) O ((|V | + |E|) log |V |) O (|V |)
Shortest path by Dijkstra, using an unsorted array as priority queue
Graph with |V | vertices and |E| edges
O
( |V |^2
) O
( |V |^2
) O (|V |)
Shortest path by Bellman- Ford
Graph with |V | vertices and |E| edges
O (|V ||E|) O (|V ||E|) O (|V |)
2 Sorting
Algorithm Data Structure Time Complexity Worst Case Auxiliary Space Complexity Best Average Worst Quicksort Array O (n log(n)) O (n log(n)) O
( n^2
) O (n) Mergesort Array O (n log(n)) O (n log(n)) O (n log(n)) O (n) Heapsort Array O (n log(n)) O (n log(n)) O (n log(n)) O (1) 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) Select Sort Array^ O^
( n^2
) O
( n^2
) O
( n^2
) O (1) Bucket Sort Array^ O^ (n^ +^ k)^ O^ (n^ +^ k)^ O^
( n^2
) O (nk) Radix Sort Array^ O^ (nk)^ O^ (nk)^ O^ (nk)^ O^ (n^ +^ k)
3 Data Structures
Data Structure Time Complexity^ Space Complex- ity Average 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 (n) O (1) O (n) 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) 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 -^ 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 (log(n)) O (n) O (n) O (n) O (n) O (n) Cartresian 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^ (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 - 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^ (log(n))^ O^ (log(n))^ O^ (n)
