- C++ Big O Notation Cheat Sheet
- Big O Notation Practice Problems
- N In Big O Notation Cheat Sheet
- Big O Notation Cheat Sheet Pdf
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 Cheat Sheet. It provides a table that gives Big-Θ and Big-O complexities for a set of common operations on range of data structures, as well Big-Ω, Big-Θ, and Big-O for various array sorting algorithms. I'm thinking about buying the poster.
- Big O Notation Cheat-Sheet. Alternative Big O notations: O(1) = O(yeah). Big O Notation describes an execution limitation of a function, given an argument tends.
.NET Big-O Algorithm Complexity Cheat Sheet. Shows Big-O time and space complexities of common algorithms used in.NET and Computer Science. You can see which collection type or sorting algorithm to use at a glance to write the most efficient code. Big o cheatsheet with complexities chart Big o complete Graph!Bigo graph1 Legend!legend3!Big o cheatsheet2!DS chart4!Searching chart5 Sorting Algorithms chart!sorting chart6!Heaps chart7!graphs chart8. HackerEarth is a global.
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.
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.
C++ Big O Notation Cheat Sheet
| Sorting Algorithms | Space Complexity | Time Complexity | ||
| Worst case | Best case | Average case | Worst case | |
Bubble Sort | O(1) | O(n) | O(n2) | O(n2) |
| Heapsort | O(1) | O(n log n) | O(n log n) | O(n log n) |
| Insertion Sort | O(1) | O(n) | O(n2) | O(n2) |
| Mergesort | O(n) | O(n log n) | O(n log n) | O(n log n) |
| Quicksort | O(log n) | O(n log n) | O(n log n) | O(n log n) |
| Selection Sort | O(1) | O(n2) | O(n2) | O(n2) |
| ShellSort | O(1) | O(n) | O(n log n2) | O(n log n2) |
| Smooth Sort | O(1) | O(n) | O(n log n) | O(n log n) |
| Tree Sort | O(n) | O(n log n) | O(n log n) | O(n2) |
| Counting Sort | O(k) | O(n + k) | O(n + k) | O(n + k) |
| Cubesort | O(n) | O(n) | O(n log n) | O(n log n) |
Big O Notation Practice Problems
Data Structure Operations
In this chart, we consult some popular data structures such as Array, Binary Tree, Linked-List with 3 operations Search, Insert and Delete.
| Data Structures | Average Case | Worst Case | ||||
| Search | Insert | Delete | Search | Insert | Delete | |
| Array | O(n) | N/A | N/A | O(n) | N/A | N/A |
| AVL Tree | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) |
| B-Tree | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) |
| Binary SearchTree | O(log n) | O(log n) | O(log n) | O(n) | O(n) | O(n) |
| Doubly Linked List | O(n) | O(1) | O(1) | O(n) | O(1) | O(1) |
| Hash table | O(1) | O(1) | O(1) | O(n) | O(n) | O(n) |
| Linked List | O(n) | O(1) | O(1) | O(n) | O(1) | O(1) |
| Red-Black tree | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) | O(log n) |
| Sorted Array | O(log n) | O(n) | O(n) | O(log n) | O(n) | O(n) |
| Stack | O(n) | O(1) | O(1) | O(n) | O(1) | O(1) |
N In Big O Notation Cheat Sheet
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
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.
| n f(n) | log n | n | n log n | n2 | 2n | n! |
|---|---|---|---|---|---|---|
| 10 | 0.003ns | 0.01ns | 0.033ns | 0.1ns | 1ns | 3.65ms |
| 20 | 0.004ns | 0.02ns | 0.086ns | 0.4ns | 1ms | 77years |
| 30 | 0.005ns | 0.03ns | 0.147ns | 0.9ns | 1sec | 8.4×1015yrs |
| 40 | 0.005ns | 0.04ns | 0.213ns | 1.6ns | 18.3min | — |
| 50 | 0.006ns | 0.05ns | 0.282ns | 2.5ns | 13days | — |
| 100 | 0.07 | 0.1ns | 0.644ns | 0.10ns | 4×1013yrs | — |
| 1,000 | 0.010ns | 1.00ns | 9.966ns | 1ms | — | — |
| 10,000 | 0.013ns | 10ns | 130ns | 100ms | — | — |
| 100,000 | 0.017ns | 0.10ms | 1.67ms | 10sec | — | — |
| 1’000,000 | 0.020ns | 1ms | 19.93ms | 16.7min | — | — |
| 10’000,000 | 0.023ns | 0.01sec | 0.23ms | 1.16days | — | — |
| 100’000,000 | 0.027ns | 0.10sec | 2.66sec | 115.7days | — | — |
| 1,000’000,000 | 0.030ns | 1sec | 29.90sec | 31.7 years | — | — |