Big O Notation and Algorithm Efficiency

Abstract

When we do a computation, we would like to do it as fast as possible, or at least pretty fast. In order to talk about (roughly) what that means, we need to introduce big O notationBig O notation. Let f(x) and g(x) be two functions, we say that {\$}{\$}f(x)=O(g(x)){\$}{\$}if there is some constant {\$}{\$}C>0{\$}{\$}, which does not depend on x, so that {\$}{\$}{\backslash}begin{\{}aligned{\}} |f(x)|{\backslash}le Cg(x) {\backslash}end{\{}aligned{\}}{\$}{\$}for all x.