Polynomial time and exponential time

Question

Could someone explain the difference between polynomial-time, non-polynomial-time, and exponential-time algorithms?

For example, if an algorithm takes O(n^2) time, t

Answer 1

O(n^2) is polynomial time. The polynomial is f(n) = n^2. On the other hand, O(2^n) is exponential time, where the exponential function implied is f(n) = 2^n. The difference is whether the function of n places n in the base of an exponentiation, or in the exponent itself.

Any exponential growth function will grow significantly faster (long term) than any polynomial function, so the distinction is relevant to the efficiency of an algorithm, especially for large values of n.