【Leetcode】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?

到达 n 有两种途径：从 n - 1 走一步 or 从 n - 2 走两步. 

所以 f(n) = f(n - 1) + f (n - 2), 即斐波那契数列。可以迭代求解或者直接用通项公式。

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

class Solution {
public:
    int climbStairs(int n) {
        const double s = sqrt(5);
        return floor((pow((1+s)/2, n+1) + pow((1-s)/2, n+1))/s + 0.5);
    }
};