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(const int n) {
        if (n <= 3) {
            return n;
        }

        int n1 = 1, n2 = 2;
        for (int i = 3; i <= n; ++i) {
            int n3 = n1 + n2;
            n1 = n2;
            n2 = n3;
        }

        return n2;
    }
};