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?

Note: Given n will be a positive integer.

Example 1:

Input: 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps
Example 2:

Input: 3
Output: 3
Explanation: There are three ways to climb to the top.
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

https://leetcode.com/problems/climbing-stairs/description/
http://blog.zhengyi.one/fibonacci-in-logn.html
矩阵快速求法
'''
#fibonacci

class Solution:
    #steps = dict()
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        return int((((1+5**0.5)/2)**(n+1) - ((1-5**0.5)/2)**(n+1) )/5**0.5)
        
        """
        if n in self.steps.keys():
            return self.steps[n]
        if n == 0 or 1:
            return 1
        else:
            res = self.climbStairs(n-2) + self.climbStairs(n-1)
        self.steps[n] = res
        return res
        """