70 - 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?

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思路分析：

利用DP的方法，一个台阶的方法次数为1次，两个台阶的方法次数为2个。n个台阶的方法可以理解成上n-2个台阶，然后2步直接上最后一步；或者上n-1个台阶，再单独上一步。
公式是S[n] = S[n-1] + S[n-2] S[1] = 1 S[2] = 2

class Solution {
public:
    int climbStairs(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        long long f[100];
        f[0] = 1;
        f[1] = 1;
        
        for(int i = 2; i < 100; i++)
            f[i] = f[i-1] + f[i-2];
            
        return f[n]; 
    }
};