0070: Climbing Stairs

Problem Statement

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

Code Solution

from functools import lru_cache

class Solution:
    def climbStairs(self, n):
		
		@cache
        def rec(k):
            if k >= n:
                return 0
            takeit = rec(k + 1)
            skipit = rec(k + 2)
            return 1 + takeit + skipit
        
        return rec(n)