Big O Algorithm Complexity Sheet

Complexities!
Good Fair Poor

Searching
Algorithm

Data Structure

Time Complexity

Depth First Search
(DFS)

Graph of |V| vertices and |E| edges Graph of |V| vertices and |E| edges Sorted array of n elements Array

-

O(|E| + |V|)

O(|V|)

-

O(|E| + |V|)

O(|V|)

O(log(n))

O(log(n))

O(1)

O(n)

O(n)

O(1)

Graph with |V| vertices and |E| edges O((|V| + |E|) log |V|)

O((|V| + |E|) log |V|)

O(|V|)

Graph with |V| vertices and |E| edges O(|V|^2)

O(|V|^2)

O(|V|)

Graph with |V| vertices and |E| edges O(|V||E|)

O(|V||E|)

O(|V|)

Average

Breadth First
Search (BFS)
Binary search
Linear (Brute
Force)
Shortest path by
Dijkstra,
using a Min-heap as priority queue
Shortest path by
Dijkstra,
using an unsorted array as priority queue Shortest path by
Bellman-Ford

Worst

Space
Complexity
Worst

Sorting
Algorithm

Data
Structure

Time Complexity
Best

Quicksort

Array

Mergesort

Array

Heapsort

Array

Bubble Sort
Insertion
Sort
Select Sort
Bucket Sort
Radix Sort

Array
Array

O(n log(n)) O(n log(n)) O(n log(n)) O(n)
O(n)

Array
Array
Array

O(n^2)
O(n+k)
O(nk)

Average

Worst

Worst Case Auxiliary
Space Complexity
Worst

O(n log(n)) O(n log(n)) O(n log(n)) O(n^2)
O(n^2)

O(n^2)

O(n)

O(n log(n)) O(n log(n)) O(n^2)
O(n^2)

O(n)

O(n^2)
O(n+k)
O(nk)

O(n^2)
O(n^2)
O(nk)

O(1)
O(nk)
O(n+k)

O(1)
O(1)
O(1)

Data Structures
Data Structure

Time Complexity

Indexing

Average
Search
Insertion

Deletion

Basic Array
Dynamic Array
Singly-Linked
List
Doubly-Linked
List
Skip List

O(1)
O(1)
O(n)

O(n)
O(n)
O(n)

-

-

O(n)
O(1)

O(n)

O(n)

O(log(n))

Hash Table
Binary Search
Tree
Cartresian Tree
B-Tree
Red-Black Tree
Splay Tree
AVL Tree

Indexing

Space
Complex
ity
Worst

Worst
Search
Insertion

Deletion

O(n)
O(n)
O(n)

-

-

O(n)
O(1)

O(1)
O(1)
O(n)

O(n)
O(1)

O(n)
O(1)

O(n)
O(n)
O(n)

O(1)

O(1)

O(n)

O(n)

O(1)

O(1)

O(n)

O(log(n))

O(log(n))

O(log(n))

O(n)

O(n)

O(n)

O(n)

O(log(n))

O(1)
O(log(n))

O(1)
O(log(n))

O(1)
O(log(n))

O(n)

O(n)
O(n)

O(n)