70. Climbing Stairs

1. Description

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?

2. Example

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

3. Constraints

• 1 <= n <= 45

4. Solutions

Dynamic Programming

Time complexity: O(n)
Space complexity: O(1)

class Solution {
public:
    int climbStairs(int n) {
        int previous = 0, current = 1;
        for (int i = 1; i <= n; ++i) {
            int next = previous + current;
            previous = current;
            current = next;
        }

        return current;
    }
};