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.

Example 1:

Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

分析：

因為每次只能爬1階或者2階，所以到達第n階是從第n-1或者n-2階爬上來的，所以爬到第n階的方法總數為到第n-1階的方法數加上到第n-2階的方法數。依次遞推到n為1和2的的情況，遞推公式為：num[n] = num[n-1] + num[n-2]。

class Solution {
public:
    int climbStairs(int n)
 {
//下標從0開始，所以第n階的方法數為num[n-1]
       if(n == 1)
           return 1;
        vector<int> num(n);
        num[0]=1;
        num[1]=2;
        for(int i=2; i<n; i++)
        {
            num[i] = num[i-1]+num[i-2];
        }
        return num[n-1];
    }
};