LeetCode 1866: Number of Ways to Rearrange Sticks With K Sticks Visible Solution

Master LeetCode problem 1866 (Number of Ways to Rearrange Sticks With K Sticks Visible), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

1866. Number of Ways to Rearrange Sticks With K Sticks Visible

Hard

Math Dynamic Programming Combinatorics

Problem Explanation

Explanation:

To solve this problem, we can use dynamic programming. Let's define a 2D array dp[n+1][k+1] where dp[i][j] represents the number of ways to rearrange i sticks such that j sticks are visible from the left.

The recurrence relation can be defined as follows:

If we place the longest stick first, there will be dp[i-1][j-1] ways to arrange the remaining sticks with one less stick visible.
If we place any stick other than the longest one first, there will be dp[i-1][j] ways to arrange the remaining sticks with the same number of sticks visible.

Therefore, dp[i][j] = dp[i-1][j-1] + (i-1) * dp[i-1][j].

The base cases are:

dp[i][0] = 0 for all i (no visible sticks)
dp[0][j] = 0 for all j (no sticks to arrange)
dp[1][1] = 1 (only one stick, one visible stick)

The final answer will be dp[n][k], modulo 10^9 + 7.

Time complexity: O(nk) Space complexity: O(nk)

Solution Code

class Solution {
    public int rearrangeSticks(int n, int k) {
        int MOD = 1000000007;
        long[][] dp = new long[n + 1][k + 1];
        
        dp[0][0] = 1;
        
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= Math.min(i, k); j++) {
                dp[i][j] = (dp[i-1][j-1] + (i-1) * dp[i-1][j]) % MOD;
            }
        }
        
        return (int) dp[n][k];
    }
}

Try It Yourself

Loading code editor...

Frequently Asked Questions

How to solve LeetCode 1866 (Number of Ways to Rearrange Sticks With K Sticks Visible)?

This page provides optimized solutions for LeetCode problem 1866 (Number of Ways to Rearrange Sticks With K Sticks Visible) in Java, C++, and Python, along with a detailed explanation and an interactive code editor to test your code.

What is the time complexity of LeetCode 1866 (Number of Ways to Rearrange Sticks With K Sticks Visible)?

The time complexity for LeetCode 1866 (Number of Ways to Rearrange Sticks With K Sticks Visible) varies by solution. Check the detailed explanation section for specific complexities in Java, C++, and Python implementations.

Can I run code for LeetCode 1866 on DevExCode?

Yes, DevExCode provides an interactive code editor where you can write, test, and run your code for LeetCode 1866 in Java, C++, or Python.

Back to LeetCode Solutions