動機

複習基本DP

Problem

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 = 2Output: 2Explanation: There are two ways to climb to the top.1. 1 step + 1 step2. 2 steps

Example 2:

Input: n = 3Output: 3Explanation: There are three ways to climb to the top.1. 1 step + 1 step + 1 step2. 1 step + 2 steps3. 2 steps + 1 step

 

Constraints:

  • 1 <= n <= 45

Sol

只能走1或2步，而現在的步數從之前的步數延伸而來

class Solution:
    @functools.lru_cache(None)
    def climbStairs(self, n: int) -> int:
        if n == 1:
            return 1
        elif n == 2:
            return 2
        else:
            return self.climbStairs(n-1)+self.climbStairs(n-2)