[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)

 1 class Solution {
 2 public:
 3     // 斐波那契数列, f(n) = f(n - 1) + f(n - 2)
 4     int climbStairs(int n) {
 5         if (n <= 1) {
 6             return 1;
 7         }
 8         
 9         int  a = 1, b = 1;
10         for (int i = 2; i <= n; ++i) {
11             int tmp = b;
12             b = a + b;
13             a = tmp;
14         }
15         
16         return b;
17     }
18 };

2. 斐波那契额公式

1 class Solution {
2 public:
3     int climbStairs(int n) {
4         const double s = sqrt(5);
5         return floor((pow((1+s)/2, n+1) + pow((1-s)/2, n+1))/s + 0.5);
6     }
7 };