70. Climbing Stairs -Easy

Question

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.

你正在爬楼梯，它需要n步才能到达顶端。每次你既可以走一步也可以走两步。现在问有多少种方法爬到顶端。（n是正整数）

Example

None

Solution

• 动态规划解。定义dp[i]：爬到第i层的方法数。递推式dp[i] = dp[i - 1] + dp[i - 2]，即爬一步的方法数加上爬两步的次数就是dp[i]的次数

  class Solution(object):    def climbStairs(self, n):        """        :type n: int        :rtype: int        """        ways_climb = [0] * n        for index in range(n):            if index == 0:                ways_climb[index] += 1            elif index == 1:                ways_climb[index] = ways_climb[index - 1] + 1            else:                ways_climb[index] = ways_climb[index - 1] + ways_climb[index - 2]        return ways_climb[-1]