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?

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
Example 2:

Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

动态规划解法：

class Solution{
public:
    int climbStairs(int n){
        if(n == 1) return 1;
        if(n == 2) return 2;
        vector<int> memo(n+1,-1);
        memo[1] = 1;
        memo[2] = 2;
        for(int i = 3; i <= n; i++){
            memo[i] = memo[i-1] + memo[i-2];
        }
        return memo[n];
    }
};