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70. Climbing Stairs

Difficulty Topics

Description

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

climbing-stairs.py
class Solution:
    def climbStairs(self, n: int) -> int:

        @cache
        def fib(k):
            if k == 1: return 1
            if k == 2: return 2

            return fib(k - 2) + fib(k - 1)

        return fib(n)