Climbing Stairs

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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

You can solve this problem using dynamic programming. Here's a JavaScript implementation:

function climbStairs(n) {
    if (n === 1) return 1;

    const dp = new Array(n + 1);
    dp[1] = 1;
    dp[2] = 2;

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

    return dp[n];
}

// Test cases
console.log(climbStairs(2)); // Output: 2
console.log(climbStairs(3)); // Output: 3

This implementation uses dynamic programming to store the number of distinct ways to climb each step up to n. It iterates through each step from 3 to n, calculating the number of ways to reach the current step by summing the number of ways to reach the previous two steps. Finally, it returns the number of ways to reach the top.