Big O notation cheat sheet provides the extended Big O notations for top interview questions. What is Big O notations? Big O notations describe the time or space required for the execution in software program. The execution can be an operation in data structures, such as add, delete or traverse. It can also be an algorithm, such as sort or search. They indicate the worst-case scenario. You can choose the best implementation based on time and space complexity.

In this post, I list the Big O notation cheat sheet for major data structures and well-know algorithms. It also covers some complicated algorithms, such as recursion, DFS and BFS in graph, and memoization in Dynamic programming. The extended Big O notations are the by-product of Java Coding Interview Pocket Book. In this book, every answer for the question includes the Big O notation.

At the end of this post, there is a list of top interview questions aggregated from varied web sites.

### Table of Content

- Big O-Notations of Data Structures
- Big O-Notations of Java Collections
- Big O-Notations for major Algorithms by categories
- Big O-Notations of Sorting Algorithms
- Big O-Notations of problems using Recursions
- Big O-Notations of problems using DFS and BFS
- Big O-Notations Cheat Sheet Poster
- Top interview questions

Big O-Notations of Data Structures

Data structure |
Access |
Insert |
Delete |
Search |
Traverse |

Linear |
|||||

Array |
O(1) |
O(1) |
O(n) |
O(n) |
O(n) |

Ordered array |
O(1) |
O(n) |
O(n) |
O(logn) |
O(n) |

Linked list |
O(n) |
O(1) |
O(n) |
O(n) |
O(n) |

Matrix |
O(1) |
O(1) |
O(1) |
O(m*n) |
O(m*n) |

Stack |
O(1) |
O(1) |
O(1) |
O(n) |
O(n) |

Queue |
O(1) |
O(1) |
O(1) |
O(n) |
O(n) |

Non-linear |
|||||

Tree |
O(n) |
O(1) |
O(n) |
O(n) |
O(n) |

Balanced tree |
O(logn) |
O(logn) |
O(logn) |
O(logn) |
O(n) |

Graph |
O(V) |
O(1) |
O(V+E) |
O(V+E) |
O(V+E) |

Trie |
O(s) |
O(s) |
O(s) |
O(s) |
O(n*s) |

Suffix trie |
O(s) |
O(s) |
O(s) |
O(s) |
O(s^2) |

Big O-Notations of Java Collections

Java
Collections APIs |
Access |
Insert |
Delete |
Search |
Traverse |

List |
|||||

ArrayList |
O(1) |
O(1) |
O(n) |
O(n) |
O(n) |

LinkedList |
O(n) |
O(1) |
O(n) |
O(n) |
O(n) |

Stack |
O(1) |
O(1) |
O(1) |
O(n) |
O(n) |

Queue |
|||||

ArrayDeque |
O(1) |
O(1) |
O(1) |
O(n) |
O(n) |

PriorityQueue |
O(logn) |
O(logn) |
O(logn) |
O(logn) |
O(n) |

Map |
|||||

HashMap |
O(1) |
O(1) |
O(1) |
O(1) |
O(n) |

LinkedHashMap |
O(1) |
O(1) |
O(1) |
O(1) |
O(n) |

TreeMap |
O(logn) |
O(logn) |
O(logn) |
O(logn) |
O(n) |

Dictionary |
|||||

Hashtable |
O(1) |
O(1) |
O(1) |
O(1) |
O(n) |

Set |
|||||

HashSet |
O(1) |
O(1) |
O(1) |
O(1) |
O(n) |

LinkedHashSet |
O(1) |
O(1) |
O(1) |
O(1) |
O(n) |

TreeSet |
O(logn) |
O(logn) |
O(logn) |
O(logn) |
O(n) |

Big O-Notations for major Algorithms by categories

Algorithms |
Time |
Space |
Used area |

Sorting |
|||

Bubble, Selection, Insertion |
O(n^2) |
O(1) |
Simple sort |

Merge sort |
O(n*logn) |
O(n) |
Stable sort |

Quick sort |
O(n*logn) |
O(logn) |
Quick sort |

Searching |
|||

Linear search |
O(n) |
O(1) |
Search in non-sorted array |

Binary search |
O(logn) |
O(1) |
Search in sorted array |

Recursion |
|||

Factorial |
O(n) |
O(n) |
Math |

Valid parentheses |
O(Cn) |
O(Cn) |
String |

Permutation |
O(n!) |
O(n!) |
Array, String |

All subsets |
O(2^n) |
O(2^n) |
Array, String |

Dynamic Programming |
|||

Fibonacci |
O(n) |
O(1) |
Math |

Knapsack |
O(n*w) |
O(n*w) |
Array |

Edit distance |
O(s*t) |
O(t) |
String |

Num of unique paths in matrix |
O(m*n) |
O(n) |
Matrix |

Big O-Notations of Sorting Algorithms

Sort |
Best |
Avg |
Worst |
Space |
Stable |

Bubble sort |
O(n) |
O(n^2) |
O(n^2) |
O(1) |
Yes |

Selection sort |
O(n^2) |
O(n^2) |
O(n^2) |
O(1) |
No |

Insertion sort |
O(n) |
O(n^2) |
O(n^2) |
O(1) |
Yes |

Merge sort |
O(n*logn) |
O(n*logn) |
O(n*logn) |
O(n) |
Yes |

Quick sort |
O(n*logn) |
O(n*logn) |
O(n^2) |
O(logn) |
No |

Big O-Notations of problems using Recursions

Combinatorics |
Sample questions |
Formulas |
Time |

Permutations |
Permutation of array |
P(n, k) = n!/(n-k)! |
O(P(n,k)), O(n!) when k=n |

Combinations |
Combination of range 1..n size k |
C(n, k) = n!/(n-k)!k! |
O(C(n,k)) |

Combinations of subset |
Combination of subset strings |
C(m, n) = m^n |
O(m^n) |

All subsets |
All subset of array |
C(2, n)= 2^n |
O(2^n) |

Catalan numbers |
Generate valid parentheses |
Cn = (2n)!/(n+1)!n! |
O(Cn) |

Big O-Notations of problems using DFS and BFS

DFS and BFS use cases |
Sample questions |
Time |

DFS in tree |
Tree in-order traversal |
O(n) |

DFS in string without memo |
Word break with recursion |
O(2 |

DFS in string with memo |
Word break with rec and memo |
O(s |

DFS in graph with memo |
Graph DFS traversal |
O(V+E) |

DFS in matrix with memo |
Number of island |
O(m*n) |

BFS in tree |
Tree level order traversal |
O(n) |

BFS/Bi-directional BFS in string with memo |
Word ladder with memo |
O(s*n) |

BFS in graph with memo |
Graph BFS traversal |
O(V+E) |

Find path with BFS in graph |
Find path from src to dest |
O(b |

Find path with Bi-directional BFS in graph |
Find path with bi-directional BFS |
O(b |

Shortest path with BFS in unweighted and undirected graph |
Shortest path from src to dest |
O(V+E) |

Shortest path with BFS in adjacent matrix |
Shortest path between cells |
O(m*n) |

Big O Notation Cheat Sheet poster

Download Big O Notation Cheat Sheet Poster web version.

Purchase Big O Notation Cheat Sheet Poster .

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