Leetcode 70 Climbing Stairs 爬楼梯的方法（动态规划）

题目描述：

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

从楼梯最下面开始，每次可以爬1级或者2级，求爬到最上面的方法数

思路：

    1.典型的动态规划问题。辅助数组保存到这一级的方法数，显然ans[0]=ans[1]=1，之后每一级都有从下一级爬上来和下两极爬上来两种做法，即dp[i]=dp[i-1]+dp[i-2]

代码：

class Solution {
public:
    int climbStairs(int n) 
    {
        int ans[100];
        ans[0]=ans[1]=1;
        for(int i=2;i<=n;i++)
            ans[i]=ans[i-1]+ans[i-2];
        return ans[n];
    }
};