70. Climbing Stairs

Problem

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?

Solution

题目思路了很简单了：

dp[i] = dp[i-1] + dp[i-2];

要走到第i台阶，可以从i－1台阶迈一台阶上来，也可以从i－2台阶迈两台阶上来。所有，迈到i层台阶的方式总共有dp[i-1]+dp[i-2]

class Solution {public:    int climbStairs(int n) {        vector<int> dp(n, 0);        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];    }};