---
title: Big-O
draft: true
sr-due: 2022-06-01
sr-interval: 62
sr-ease: 271
---
tags: #review

---
# Big-O
>Big O means $f(n) = O(g(n))$ if there is some constant $A > 0$ such that for all sufficiently large n, $f(n) ≤ A × g(n).$

- Big O provides *upper bounds* only. (usually on worst case runtimes)
	- sometimes cost will be much less
		- does not take special cases into account
		- upper bound
- $O$ says that $g(n)$ provides an upper bound for $f(n)$ 
	- "Insertion sort is $O(n^2)$" -> the maximum number of basic operations in never more than some constanct times $n^2$
- if $f(n) =O(g(n))$ then the opposite is also true
- usually $f(n)$ is complex but $g(n)$ is very simple