70-Climbing-Stairs.md

70. Climbing Stairs

You are climbing a staircase. It takes n steps to reach 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: n = 2
Output: 2
Explanation: There are two ways to climb to the top.
1. 1 step + 1 step
2. 2 steps

Example 2:

Input: n = 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

Solution

from math import sqrt

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

Typical Fibonacci number.