I'm working on a simulation problem for a game called Dodgeball. Here are the rules: Each player stands on a field at a specific integer coordinate. The game starts with one player receiving the ball from a given direction among: N, NE, E, SE, S, SW, W, NW (clockwise order). When a player receives the ball, they rotate clockwise (in 45° increments) until they find another player exactly in that direction. They then throw the ball and leave the game. If multiple players are in the same direction, the ball always goes to the closest one. The game ends when a player cannot pass the ball to anyone else. I need to compute: The number of throws before the game ends. The last player to receive the ball. I've written a Python program using angle and distance calculations to determine the next player, but the results are incorrect.Here's my code import json import math # Directions in clockwise order directions = ['N', 'NE', 'E', 'SE', 'S', 'SW', 'W', 'NW'] def get_direction_index(d): return directions.index(d) def get_next_player(current_player, players, direction_index): x, y = players[current_player] min_dist = float('inf') next_player = -1 for i in range(len(players)): if i == current_player: continue nx, ny = players # Calculate the direction vector dir_x = nx - x dir_y = ny - y # Calculate the angle angle = math.atan2(dir_y, dir_x) # Convert to degrees and normalize angle_deg = math.degrees(angle) if angle_deg < 0: angle_deg += 360 # Find the closest direction target_angle = direction_index * 45 print(f"Player {i}: angle_deg = {angle_deg}, target_angle = {target_angle}, dist = {dir_x**2 + dir_y**2}") if abs((angle_deg - target_angle + 360) % 360 - 180) < 22.5: # Allow for a margin of error dist = dir_x**2 + dir_y**2 if dist < min_dist: min_dist = dist next_player = i return next_player def simulate_game(players, start_dir, start_player): throws = 0 current_player = start_player - 1 direction_index = get_direction_index(start_dir) while True: next_player = get_next_player(current_player, players, direction_index) if next_player == -1: break throws += 1 current_player = next_player direction_index = (direction_index + 1) % 8 print(f"Throw {throws}: current_player = {current_player + 1}, direction_index = {direction_index}") return throws, current_player + 1 def main(): with open("input.json", "r") as f: data = json.load(f) for case in data: players = case["players"] start_dir = case["startingDirection"] start_player = case["startingPlayer"] throws, last_player = simulate_game(players, start_dir, start_player) print(throws, last_player) if __name__ == "__main__": main() When I test my program with the following input: [ { "players": [ [-10, -10], [-10, 10], [0, -10], [0, 10], [10, -10], [10, 10], [-9, -10], [-9, 0] ], "startingDirection": "NW", "startingPlayer": 5 }, { "players": [ [-1000000, -1000000], [-1000000, 1000000], [0, -1000000], [0, 1000000], [1000000, -1000000], [1000000, 1000000], [-999999, -1000000], [-999999, 0] ], "startingDirection": "SE", "startingPlayer": 4 } ] I expect the output to be 4 8 5 6 But instead i get : 1 8 1 5 It seems my code is not correctly finding the next player at each step. Possible Causes: Incorrect angle calculation or approximation issues I'm using math.atan2() to compute angles and math.degrees() to convert them, but maybe my angle comparison logic is flawed. Incorrect closest-player selection I'm picking the player with the smallest Euclidean distance dir_x**2 + dir_y**2, but my method might be incorrect. Incorrect direction update I update direction_index using (direction_index + 1) % 8. Is this the correct way to rotate directions in this game? Questions: Is my angle computation logic correct? Should I normalize angles differently? Is my method for selecting the closest player correct? How can I verify it? Is there a more robust way to handle player rotation? Continue reading...
