Dynamic Programming Basics

The problem

You climb a staircase of n steps. Each move goes up 1 or 2 steps. How many different ways reach the top?

Think about the last move. It came from step n - 1 or from step n - 2. So:

$ways(n) = ways(n-1) + ways(n-2)$

That is a recursive answer. It is correct, and it is very slow.