Day-31_Climbing_Staris.py

'''
	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?

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
 

Constraints:

1 <= n <= 45
   Hide Hint #1  
To reach nth step, what could have been your previous steps? (Think about the step sizes)

'''

class Solution:
    def climbStairs(self, n: int) -> int:
        return round((0.5+sqrt(5)/2)**(n+1)/sqrt(5))