Pass the Pillow

class Solution {
public:
    int findPillowHolder(int numPeople, int totalSeconds) {
        // Calculate complete rounds
        int rounds = totalSeconds / (numPeople - 1);
        
        // Calculate leftover seconds
        int leftover = totalSeconds % (numPeople - 1);
        
        // Determine holder position
        if (rounds % 2 == 0) {
            return leftover + 1;
        } else {
            return numPeople - leftover;
        }
    }
};

This solution in C++ solves the "Pass the Pillow" game simulation, which calculates the position of the pillow holder at a given number of elapsed seconds. The method takes two parameters: the number of people in the game (numPeople) and the total elapsed seconds (totalSeconds).

• Calculate the number of complete rounds the pillow can travel within the people circle with totalSeconds / (numPeople - 1).
• Compute any remaining seconds that don't make a full circuit with totalSeconds % (numPeople - 1).
• Determine the position of the pillow holder at the end of the elapsed time. If the rounds are even, the pillow holder’s position is directly determined by adding one to the leftovers (leftover + 1). If the rounds are odd, the pillow is moving in a reverse direction, making the position numPeople - leftover.

This function effectively simulates the changing position of the pillow in "Pass the Pillow" for any given number of people and elapsed time, ensuring that it handles both forward and reverse directions of passing based on odd or even rounds.

class Solution {

    public int pillowGame(int players, int moments) {
        // Finding how many full cycles are completed
        int completeCycles = moments / (players - 1);

        // Remaining time after all full cycles
        int remainingTime = moments % (players - 1);

        // Analyzing the current holder's position
        // continuing in sequence or reversing based on the cycle count
        if (completeCycles % 2 == 0) {
            return remainingTime + 1; // Moving forward scenario
        } else {
            return players - remainingTime; // Reversing scenario
        }
    }
}

The given Java code defines a solution for determining which player holds the pillow after a given number of moments. It handles scenarios where players may pass the pillow in sequence around a circle, potentially reversing direction at certain intervals based on the number of complete passes.

Here's a breakdown of what the code accomplishes:

• Complete Cycles Calculation: The method calculates how many complete cycles occur where all players have handled the pillow once. A cycle is (players - 1) moments long because the starting player gets the pillow again only after it has been passed to all other players.

• Remaining Time: After accounting for full cycles, the code calculates the remaining number of moments for which the pillow still needs to be passed.

• Current Holder Position: Using the complete cycle count to determine the pillow passing direction:

  • If the cycle count is even, the passing continues in the same direction and the current holder will be at position (remainingTime + 1).
  • If odd, it implies a direction change. The pillow travels backwards, and the current holder is (players - remainingTime) positions from the start.

This approach efficiently handles pillow passing for any number of players and moments using modulo and division operations to cycle through player positions.

class Game:
    def determinePosition(self, participants, duration):
        # Total full cycles of passing the pillow
        complete_cycles = duration // (participants - 1)

        # Remaining time after full cycles
        remaining_time = duration % (participants - 1)

        # Identify final holder based on the parity of complete cycles
        # Even cycles result in a forward movement.
        # Odd cycles result in a backward movement.
        if complete_cycles % 2 == 0:
            return remaining_time + 1  # Increment position forward
        else:
            return participants - remaining_time  # Calculate position backward

In the problem titled "Pass the Pillow," the goal is to find out which participant ends up with the pillow after it has been passed around for a given duration. The solution is implemented in Python and involves creating a class named Game with a method determinePosition. This method calculates which participant holds the pillow at the end of the game.

• The solution considers the number of participants and the duration of the pillow passing:
  • It first calculates how many complete cycles the group can make (where each cycle allows the pillow to be passed to each participant once).
  • It determines the remaining time after accounting for these complete cycles.
• Depending on the number of complete cycles (whether even or odd), the pillow's final position changes:
  • If the number of full cycles is even, the method calculates the position by simply adding the remaining time to the starting position.
  • If the number of full cycles is odd, the position is calculated by subtracting the remaining time from the total number of participants to account for the backward direction in the final cycle.

The final output of the method determines the position of the participant who ultimately holds the pillow by considering these two distinct scenarios (even and odd cycles). This solution efficiently handles the distribution and movement of the pillow among participants based on the provided duration and handles edge cases involving even and odd cycles intelligently.