Big O Notation Cheat Sheet



Know Thy Complexities! 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. Big-O Algorithm Complexity Cheat Sheet (Know Thy Complexities!) @ericdrowell. Big O Notation Bubble Sort Data Modeling Data Structures Cheat Sheets Sorting.

  1. Big O Notation Cheat Sheet Pdf
  2. Big 0 Notation Cheat Sheet
  3. Big Oh Cheat Sheet

When measuring the efficiency of an algorithm, we usually take into account the time and space complexity. In this article, we will glimpse those factors on some sorting algorithms and data structures, also we take a look at the growth rate of those operations.

Big-O Complexity Chart

First, we consider the growth rate of some familiar operations, based on this chart, we can visualize the difference of an algorithm with O(1) when compared with O(n2). As the input larger and larger, the growth rate of some operations stays steady, but some grow further as a straight line, some operations in the rest part grow as exponential, quadratic, factorial.

Big o notation computer science cheat sheetCheat

Sorting Algorithms

In order to have a good comparison between different algorithms we can compare based on the resources it uses: how much time it needs to complete, how much memory it uses to solve a problem or how many operations it must do in order to solve the problem:

  • Time efficiency: a measure of the amount of time an algorithm takes to solve a problem.
  • Space efficiency: a measure of the amount of memory an algorithm needs to solve a problem.
  • Complexity theory: a study of algorithm performance based on cost functions of statement counts.
Sorting AlgorithmsSpace ComplexityTime Complexity
Worst case Best case Average case Worst case

Bubble Sort
O(1)O(n)O(n2)O(n2)
HeapsortO(1)O(n log n)O(n log n)O(n log n)
Insertion SortO(1)O(n)O(n2)O(n2)
MergesortO(n)O(n log n)O(n log n)O(n log n)
QuicksortO(log n)O(n log n)O(n log n)O(n log n)
Selection SortO(1)O(n2)O(n2)O(n2)
ShellSortO(1)O(n)O(n log n2)O(n log n2)
Smooth SortO(1)O(n)O(n log n)O(n log n)
Tree SortO(n)O(n log n)O(n log n)O(n2)
Counting SortO(k)O(n + k)O(n + k)O(n + k)
CubesortO(n)O(n)O(n log n)O(n log n)

Data Structure Operations

Big O Notation Cheat Sheet

In this chart, we consult some popular data structures such as Array, Binary Tree, Linked-List with 3 operations Search, Insert and Delete.

Big oh notation log
Data StructuresAverage CaseWorst Case
SearchInsertDeleteSearchInsertDelete
ArrayO(n)N/AN/AO(n)N/AN/A
AVL TreeO(log n)O(log n)O(log n)O(log n)O(log n)O(log n)
B-TreeO(log n)O(log n)O(log n)O(log n)O(log n)O(log n)
Binary SearchTreeO(log n)O(log n)O(log n)O(n)O(n)O(n)
Doubly Linked ListO(n)O(1)O(1)O(n)O(1)O(1)
Hash tableO(1)O(1)O(1)O(n)O(n)O(n)
Linked ListO(n)O(1)O(1)O(n)O(1)O(1)
Red-Black treeO(log n)O(log n)O(log n)O(log n)O(log n)O(log n)
Sorted ArrayO(log n)O(n)O(n)O(log n)O(n)O(n)
StackO(n)O(1)O(1)O(n)O(1)O(1)

Growth of Functions

The order of growth of the running time of an algorithm gives a simple characterization of the algorithm’s efficiency and also allows us to compare the relative performance of alternative algorithms.

Big O Notation Cheat Sheet Pdf

Big

Big 0 Notation Cheat Sheet

Below we have the function n f(n) with n as an input, and beside it we have some operations which take input n and return the total time to calculate some specific inputs.

Big Oh Cheat Sheet

n f(n)log nnn log nn22nn!
100.003ns0.01ns0.033ns0.1ns1ns3.65ms
200.004ns0.02ns0.086ns0.4ns1ms77years
300.005ns0.03ns0.147ns0.9ns1sec8.4×1015yrs
400.005ns0.04ns0.213ns1.6ns18.3min
500.006ns0.05ns0.282ns2.5ns13days
1000.070.1ns0.644ns0.10ns4×1013yrs
1,0000.010ns1.00ns9.966ns1ms
10,0000.013ns10ns130ns100ms
100,0000.017ns0.10ms1.67ms10sec
1’000,0000.020ns1ms19.93ms16.7min
10’000,0000.023ns0.01sec0.23ms1.16days
100’000,0000.027ns0.10sec2.66sec115.7days
1,000’000,0000.030ns1sec29.90sec31.7 years