# Big O notation – leetcode cheat sheet

Big O notation cheat sheet provides the Big O notations for all data structures and algorithm including sorting, search, recursion, DFS and BFS, and memoization, Dynamic programming etc. The links are provided to download the jpg file of the cheat sheets. At the end, you can also download the Big O notation cheat sheet compilation in one poster.

### Big O-Notation 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-Notation of 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-Notation 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-Notation leetcode cheat sheet in 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-Notation leetcode cheat sheet in 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(2s) DFS in string with memo Word break with rec and memo O(s2) 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(bd) Find path with Bi-directional BFS in graph Find path with bi-directional BFS O(bd/2) 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 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)