Find the Winner of the Circular Game

There are n friends that are playing a game. The friends are sitting in a circle and are numbered from 1 to n in clockwise order. More formally, moving clockwise from the i<sup>th</sup> friend brings you to the (i+1)<sup>th</sup> friend for 1 <= i < n, and moving clockwise from the n<sup>th</sup> friend brings you to the 1<sup>st</sup> friend.

The rules of the game are as follows:

1. Start at the 1<sup>st</sup> friend.

2. Count the next k friends in the clockwise direction including the friend you started at. The counting wraps around the circle and may count some friends more than once.

3. The last friend you counted leaves the circle and loses the game.

4. If there is still more than one friend in the circle, go back to step 2 starting from the friend immediately clockwise of the friend who just lost and repeat.

5. Else, the last friend in the circle wins the game.

Given the number of friends, n, and an integer k, return the winner of the game.

LeetCode Problem - 1823

import java.util.Queue;
import java.util.LinkedList;

class Solution {

    // Method to find the winner of the game
    public int findTheWinner(int n, int k) {
        Queue<Integer> queue = new LinkedList<>();

        // Add all participants to the queue
        for (int i = 1; i <= n; i++) {
            queue.add(i);
        }

        // Process the queue until only one participant remains
        while (queue.size() > 1) {
            // Move the first k-1 participants to the back of the queue
            for (int i = 0; i < k - 1; i++) {
                queue.add(queue.poll());
            }
            // Remove the k-th participant from the queue
            queue.poll();
        }

        // The remaining participant is the winner
        return queue.peek();
    }
}