70. Climbing Stairs

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

 

class Solution:
    def climbStairs(self, n: int) -> int:
        climbs = {}
        climbs[1] = 1
        climbs[2] = 2
        def climb(n):
            if n in climbs:
                return climbs[n]
            else:
                climbs[n] = climb(n-1) + climb(n-2)
                return climbs[n]
        return climb(n)
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