Climbing Stairs

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

LeetCode: Climbing Stairs

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

Example:

Input: n = 2
Output: 2
Explanation: 
1. 1 step + 1 step
2. 2 steps

Input: n = 3
Output: 3
Explanation:
1. 1 step + 1 step + 1 step
2. 1 step + 2 steps
3. 2 steps + 1 step

Hints

Hint 1

Think about the pattern: how many ways to reach step n if you can come from step n-1 or step n-2?

Hint 2

This is actually the Fibonacci sequence! ways(n) = ways(n-1) + ways(n-2)

Hint 3

You only need to keep track of the last two values, not the entire array. Can you optimize space to O(1)?