70. Climbing Stairs

题目：

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?

Note: Given n will be a positive integer.

思路：这道题目本质上是个动态规划的问题，虽然也可以用递归的方法做，但是时间复杂度太高，那么用动态规划就需要建立状态转移方程：X(i) = X(i-1) + X(i-2);   每次有两种选择，两种选择之后又是各有两种选择，如下图所示：

代码：

//简单的动态规划问题class Solution {public:    int climbStairs(int n) {        vector<int> res(n+1);        res[0] = 1;        res[1] = 1;        for(int i =2;i<=n;i++)        {            res[i] = res[i-1] + res[i-2];         }        return res[n];                    }};