LeetCode70 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?

Input:2
Output:2

题意是给一个n层的阶梯，每次可以爬一层或者两层，求到n层有多少种解法。可以非常明显的看出推导公式为dp[i]=dp[i-1]+dp[i-2]; 因为到第i层只能从i-1层或i-2层上来。具体代码如下：

class Solution {
public:
    int climbStairs(int n) {
        vector<int> dp(n+1,0);
        dp[1]=1;
        dp[2]=2;
        for(int i=3;i<=n;i++)
        {
            dp[i]=dp[i-1]+dp[i-2];
        }
        return dp[n];
    }
};