Leetcode: 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?

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];
    }
};