[Leetcode]@python 70. Climbing Stairs

题目链接

https://leetcode.com/problems/climbing-stairs/

题目原文

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?

题目大意

爬楼梯，一次可以爬一步或者两步。如果要爬n层，问一共有多少种爬法。比如说，如果是3层，可以有[[1,1,1],[1,2],[2,1]]共3种方法。

解题思路

可以使用DP进行求解，是斐波那契数列的变形，arr[n] = arr[n-1] + arr[n-2] (n>2)

代码

class Solution(object):
    def climbStairs(self, n):
        """
        :type n: int
        :rtype: int
        """
        if n == 1 or n == 2:
            return n
        arr = [0 for i in range(n+1)]
        arr[1] = 1
        arr[2] = 2
        for i in range(3,n+1):
            arr[i] = arr[i-1]+arr[i-2]
        return arr[n]