2682-find-the-losers-of-the-circular-game.js

/**
 * 2682. Find the Losers of the Circular Game
 * https://leetcode.com/problems/find-the-losers-of-the-circular-game/
 * Difficulty: Easy
 *
 * 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 ith friend brings you to
 * the (i+1)th friend for 1 <= i < n, and moving clockwise from the nth friend brings you to the 1st
 * friend.
 *
 * The rules of the game are as follows:
 *
 * 1st friend receives the ball.
 * - After that, 1st friend passes it to the friend who is k steps away from them in the clockwise
 *   direction.
 * - After that, the friend who receives the ball should pass it to the friend who is 2 * k steps
 *   away from them in the clockwise direction.
 * - After that, the friend who receives the ball should pass it to the friend who is 3 * k steps
 *   away from them in the clockwise direction, and so on and so forth.
 *
 * In other words, on the ith turn, the friend holding the ball should pass it to the friend who
 * is i * k steps away from them in the clockwise direction.
 *
 * The game is finished when some friend receives the ball for the second time.
 *
 * The losers of the game are friends who did not receive the ball in the entire game.
 *
 * Given the number of friends, n, and an integer k, return the array answer, which contains the
 * losers of the game in the ascending order.
 */

/**
 * @param {number} n
 * @param {number} k
 * @return {number[]}
 */
var circularGameLosers = function(n, k) {
  const visited = new Set();
  let current = 0;
  let step = 1;

  while (!visited.has(current)) {
    visited.add(current);
    current = (current + step * k) % n;
    step++;
  }

  const result = [];
  for (let i = 0; i < n; i++) {
    if (!visited.has(i)) {
      result.push(i + 1);
    }
  }

  return result;
};