Leetcode 70 Climbing Stairs

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Leetcode 70 Climbing Stairs

题目描述

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

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/climbing-stairs
著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

思路解析

到达第 $n$ 阶台阶的路径数 $=$ 到达第 $n - 1$ 阶台阶的路径数 $+$ 到达第 $n - 2$ 阶台阶的路径数，整个过程可以用Fibonacci数列来描述，代码如下：

class Solution:
    def climbStairs(self, n: int) -> int:
        if n <= 0:
            return 0
        if n == 1:
            return 1
        dp = [0 for i in range(n+1)]
        dp[1] = 1
        dp[2] = 2
        for i in range(3, n + 1):
            dp[i] = dp[i - 1] + dp[i - 2]
        return dp[n]