Climbing Stairs

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

This is just Fibonacci numbers. The number of distinct ways for n steps are the sum of distinct ways for n-1 (because we can move 1 step first, then move the rest n - 1 steps) and distinct ways for n - 2 (because we can move 2 steps first, there are two ways to do it: move 1 steps twice and move 2 steps once, the former is a duplicate for the n - 1 case so we should eliminate).

//f(n) = f(n-1) + f(n-2); n>2
    public int climbStairs(int n) {
        if (n<=2) {
            if (n<=0) {
                return 0;
            } else if (n==1) {
                return 1;
            } else {
                return 2;
            }
        } else {
            int[] value = {1,2};            
            int sum = 0;
            while (n>2) {
                sum = value[0] + value[1];
                value[0] = value[1];
                value[1] = sum;
                n--;
            }
            return sum;
        }        
    }