what is polynomial and exponential time?

Question

I am trying to understand what polynomial and exponential time is in relation to the big O notation.

I understand the basics of O notation such as linear is O(n) and O(n^2) is quadratic etc.

The only theory I have which I am not completely sure about is that

I have read this but it doesn't seem to be of much use.

I found on Wikipedia that polynomial is O(n^c) Am i right that the n is the varying number of input and c is the constant.

same with exponential? O(c^n)

If anyone could give a simple definition so I could understand it I would be greatly appreciated, thanks.

Answer 1

Polynomial bound:

Algorithm is upper bound by a polynomial on the input size n. --> poly(n)

Exponential bound:

Algorithm is upper bound by constant^poly(n) , where poly is some polynomial on input size n.