[LeetCode]Climbing Stairs

题目链接:(链接)

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?

解题思路：

斐波那契数列，

1. 迭代：f(n) = f(n - 1) + f(n - 2)

class Solution {
public:
    // 斐波那契数列, f(n) = f(n - 1) + f(n - 2)
    int climbStairs(int n) {
        if (n <= 1) {
            return 1;
        }
        
        int  a = 1, b = 1;
        for (int i = 2; i <= n; ++i) {
            int tmp = b;
            b = a + b;
            a = tmp;
        }
        
        return b;
    }
};

2. 斐波那契额公式

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);
    }
};