Big O notation - Falmouth-Games-Academy/comp350-research-journal GitHub Wiki

Generally, the efficiency of an algorithm can be gauged by how long it takes to run as a function of the size of the input 1(http://www.scs.ryerson.ca/~mth110/Handouts/PD/bigO.pdf). This can be used as a measure when optimising. Big O Notation (The capital O also known as Landau's Symbol) sometimes called asymptotic analysis is used to describe the Time Complexity for a program. Both Time Complexity and Space Complexity are functions of the size of the problem to be solved 2(https://books.google.co.uk/books?hl=en&lr=&id=vdZ4Bm-LnHMC&oi=fnd&pg=PR5&dq=Optimal+reliability+modeling:+principles+and+applications&ots=dnumi_syk0&sig=R5z90TwE7ueO37jLOpkP9wCrtvA#v=onepage&q=Optimal%20reliability%20modeling%3A%20principles%20and%20applications&f=false). W. Kuo and M. J. Zuo 2(https://books.google.co.uk/books?hl=en&lr=&id=vdZ4Bm-LnHMC&oi=fnd&pg=PR5&dq=Optimal+reliability+modeling:+principles+and+applications&ots=dnumi_syk0&sig=R5z90TwE7ueO37jLOpkP9wCrtvA#v=onepage&q=Optimal%20reliability%20modeling%3A%20principles%20and%20applications&f=false) believe that while Space Complexity is of concern, it is often not as important as the Time Complexity. Big O notation ranks the efficiency of an algorithm, it does this with regard to "O" and "n" examples below. O refers to the order of the function and its growth rate and n is the length of the array to be sorted 3(https://medium.freecodecamp.org/all-you-need-to-know-about-big-o-notation-to-crack-your-next-coding-interview-9d575e7eec4).

Notation Name Example
O(1) Constant Find if binary number is odd or even
O(log(n)) Logarithmic Find item in sorted array using binary search
O(log(log(n)) Double logarithmic (iterative logarithmic)
o(n) Sublinear
O(n) Linear Find item in unsorted array
O(n log(n)) Loglinear, Linearithmic, Quasilinear, or Supralinear Merge sort / heap sort
O(n^2) Quadratic Bubble sort / insertion sort
O(n^3) Cubic
O(n^c) Polynomial (different class for each c > 1)
O(c^n) Exponential (different class for each c > 1) Travelling salesman problem using dynamic programming
O(n!) Factorial Travelling salesman problem via brute force

Big O cheat sheet [4]

References

[1] Danziger, P. "Big O Notation." Journal, Retrieve: April (2010).

[2] W. Kuo and M. J. Zuo, Optimal reliability modeling: principles and applications. John Wiley & Sons, 2003 , p. 62.

[3] https://medium.freecodecamp.org/all-you-need-to-know-about-big-o-notation-to-crack-your-next-coding-interview-9d575e7eec4

[4] http://bigocheatsheet.com/

[5] Brilliant - Choosing a Sorting Algorithm, accessed on 9th Febuary 2019.