Question

I can understand the run time complexity in the algorithm.
But just a bit confuse that when we knew the Algorithm run time complexity is O(n).

we can tell that f(n)< g(n)..

what is g(n) exactly..?

sorry with the rookie question..

thanks.

Answer 1

Let f(x) and g(x) be two functions defined on some subset of the real numbers. One writes

f(x) = O(g(x)) as x -> infinity

if and only if there exists a positive real number M and a real number x0 such that

|f(x)| <= M |g(x)| for all x > x0

In general, f(x) is the real cost (e.g. number of execution steps) of an algorithm on input scale of x, while g(x) is much simpler than f(x) which can be used to characterize the complexity behavior of f(x).