Climbing Stairs

1. Question

n级台阶，每次可以走一级或两级，问有多少种走法。

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?

2. Solution（O(n)）

该问题可用分治法解决。第一步可以走一级或两级，那么相应的问题转化为剩余n-1和n-2级台阶的走法，即

• T(n) = T(n-1) + T(n-2)

这正好也同斐波那契数的计算相同，问题转化为求第n个斐波那契数。

public class Solution {
    public int climbStairs(int n) {
        if(n<=2) return n;
        int p=1;
        int q=2;
        for( int i=2; i<n-1; i++ ){
            int res;
            res = p+q;
            p = q;
            q = res;
        }
        return p+q;
    }
}