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 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

$$\begin{aligned} |f(x)|\le Cg(x) \end{aligned}$$

for all x.