爬楼梯

Climbing Stairs

问题：爬楼梯

考察：动态规划

来源：Citadel

链接：https://www.jointaro.com/interviews/questions/climbing-stairs/

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

Example 2:

Input: n = 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

Constraints:

解析

思路：到第 i 阶只可能来自第 i-1 阶或第 i-2 阶，因此是斐波那契递推。滚动保存前两项即可。

复杂度：时间 O(n)，空间 O(1)。