原题

You are climbing a stair case. It takes n steps to reach to the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

Note: Given n will be a positive integer.

Example 1:

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

Example 2:

Input: 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

Reference Answer

思路分析

直接使用地方法得到结果，时间复杂度比较低，递归公式为：F[n] = F[n-1] + F[n-2]

class Solution:
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n < 0:
            return 0
        temp_res = [1,2,3]
        if n <= 3:
            return temp_res[n-1]
        for index in range(3, n):
            temp_res.append(temp_res[index-1] + temp_res[index-2])
        return temp_res[n-1]