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?

分析：动态规划，我们可以采取两种方式到达n，一种是从n-1climb 1 step，另一种是从n-2 climb 2 step。时间复杂度O(n), 空间复杂度O(n)。代码如下：

class Solution {public:    int climbStairs(int n) {        vector<int> record(n+1,0);        record[0] = 1;        record[1] = 1;        for(int i = 2; i <= n; i++){            record[i] = record[i-1] + record[i-2];        }        return record[n];    }};

Leetcode: Climbing Stairs