70. Climbing Stairs.md

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?

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:

• 1 <= n <= 45

2. Solutions

Solution 1: Language: Java Dynamic Programming

• Wednesday, 10 November, 2021
• Time Complexity: $O(n)$
• Space Complexity: $O(n)$
• Runtime: 0 ms, faster than 100.00% of Java online submissions for Climbing Stairs.
• Memory Usage: 35.4 MB, less than 98.39% of Java online submissions for Climbing Stairs.

class Solution {
    public int climbStairs(int n) {
        if (n == 1) return 1;

        int dp[] = new int[n + 1];
        dp[1] = 1;
        dp[2] = 2;

        for (int i = 3; i < n + 1; i++) {
            dp[i] = dp[i - 1] + dp[i - 2];
        }
        return dp[n];
    }
}