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?

爬楼梯的问题，思路和 Unique Paths问题类似。我们假设到了第i个台阶，因为每次只能走一步和两步，因此到第i个台阶的方式等于到第i-1个台阶的方式和到第i-2个台阶的方式的和，这时i > 1; 递推式为dp[i] = dp[i - 1] + dp[i - 2];实现代码如下：

public class Solution {
    public int climbStairs(int n) {
        if(n <= 0) return 0;
        if(n == 1) return 1;
        if(n == 2) return 2;
        int[] dp = new int[n];
        dp[0] = 1;
        dp[1] = 2;
        for(int i = 2; i < n; i++) {
            dp[i] = dp[i - 1] + dp[i - 2];
        }
        return dp[n - 1];
    }
}