from random import randint import numpy as np from time import time # Edit this section to change runtime parameters for solvers below MAX_TILING_K_VALUE = 12 NUM_RAND_TILING_GAMES = 10 TILING_K_VALUES = [i for i in range(1, MAX_TILING_K_VALUE)] MAX_RAND_COIN_VALUE = 21 NUM_RAND_COIN_GAMES = 10 COINS_K_VALUES = [i for i in range(1, MAX_RAND_COIN_VALUE)] # End adjustment section class TilingSolver(object): EMPTY_CELL = " " REMOVED_CELL = " X " USE_POSITION = 1 EXISTING_POSITION = 0 CELL_OPTIONS = { "tl": [[USE_POSITION, USE_POSITION], [USE_POSITION, EXISTING_POSITION]], "tr": [[USE_POSITION, USE_POSITION], [EXISTING_POSITION, USE_POSITION]], "bl": [[USE_POSITION, EXISTING_POSITION], [USE_POSITION, USE_POSITION]], "br": [[EXISTING_POSITION, USE_POSITION], [USE_POSITION, USE_POSITION]] } def __init__(self, k_value, special_print=False, removed_cell=None): self.k_value = k_value self.removed_cell = removed_cell self.two_to_k = 2 ** self.k_value self.tile_table = [] self.current_tile_number = "001" self.generate_starting_table() self.start_time = time() self.tile(self.two_to_k, self.tile_table, self.removed_cell) self.total_time = time() - self.start_time self.print_tile_table(special_print) def generate_starting_table(self): # noinspection PyTypeChecker self.tile_table = np.full((self.two_to_k, self.two_to_k), self.EMPTY_CELL) if not self.removed_cell: self.removed_cell = randint(0, self.two_to_k - 1), randint(0, self.two_to_k - 1) x, y = self.removed_cell # noinspection PyUnresolvedReferences self.tile_table[y][x] = self.REMOVED_CELL def print_tile_table(self, special_print): if not special_print: print("Solved k=%s in %0.5f seconds." % (self.k_value, self.total_time)) for row in self.tile_table: print("|", end="") for column in row: print(column, end="|") print() print() else: print("%s\t%s\t%f" % (self.k_value, self.two_to_k, self.total_time)) def tile(self, size, table, missing_cell_location): table_min = 0 table_half = size // 2 table_max = size top_left = table[table_min: table_half, table_min: table_half] top_right = table[table_min: table_half, table_half: table_max] bottom_left = table[table_half: table_max, table_min: table_half] bottom_right = table[table_half: table_max, table_half: table_max] missing_x, missing_y = missing_cell_location x_option = "r" if missing_x < table_half else "l" y_option = "b" if missing_y < table_half else "t" tile_placement_option = y_option + x_option option = self.CELL_OPTIONS[tile_placement_option] if option[0][0] == self.USE_POSITION: table[table_half - 1][table_half - 1] = self.current_tile_number if option[0][1] == self.USE_POSITION: table[table_half - 1][table_half] = self.current_tile_number if option[1][0] == self.USE_POSITION: table[table_half][table_half - 1] = self.current_tile_number if option[1][1] == self.USE_POSITION: table[table_half][table_half] = self.current_tile_number self.increment_tile_number() if size == 2: return self.tile(table_half, top_left, self.get_missing_tile_location(table_half, top_left)) self.tile(table_half, top_right, self.get_missing_tile_location(table_half, top_right)) self.tile(table_half, bottom_left, self.get_missing_tile_location(table_half, bottom_left)) self.tile(table_half, bottom_right, self.get_missing_tile_location(table_half, bottom_right)) def increment_tile_number(self): self.current_tile_number = "%03d" % (int(self.current_tile_number) + 1) def get_missing_tile_location(self, size, table): for row_index in range(size): for column_index in range(size): if table[row_index][column_index] != self.EMPTY_CELL: return column_index, row_index class ODDSolver(object): GOOD_COIN_WEIGHT = randint(1, 100) BAD_COIN_WEIGHT_MIN = GOOD_COIN_WEIGHT + 1 BAD_COIN_WEIGHT_MAX = 5 * BAD_COIN_WEIGHT_MIN HEAVIER = "heavier" LIGHTER = "lighter" EQUAL = "equal" def __init__(self, k_value, special_print=False): self.k_value = k_value self.three_to_k = 3 ** self.k_value self.coins = [] self.setup_coins() start_left_range = 0, self.three_to_k // 3 start_mid_range = self.three_to_k // 3, (self.three_to_k * 2) // 3 start_right_range = (self.three_to_k * 2) // 3, self.three_to_k self.start_time = time() self.bad_coin_at_position = self.run_solver(start_left_range, start_mid_range, start_right_range) self.total_time = time() - self.start_time self.print_result(special_print) def setup_coins(self): self.coins = np.full(self.three_to_k, self.GOOD_COIN_WEIGHT) self.coins[randint(0, self.three_to_k - 1)] = randint(self.BAD_COIN_WEIGHT_MIN, self.BAD_COIN_WEIGHT_MAX) def run_solver(self, left_range, mid_range, right_range): left_mid = self.weigh(left_range, mid_range) mid_right = self.weigh(mid_range, right_range) left_right = self.weigh(left_range, right_range) heaviest = None if left_mid != self.EQUAL: heaviest = left_range if left_mid == self.HEAVIER else mid_range if mid_right != self.EQUAL: heaviest = mid_range if mid_right == self.HEAVIER else right_range if left_right != self.EQUAL: heaviest = left_range if left_right == self.HEAVIER else right_range if left_range[-1] - left_range[0] == 1 or \ mid_range[-1] - mid_range[0] == 1 or \ right_range[-1] - right_range[0] == 1: return heaviest[0] range_min = heaviest[0] range_max = heaviest[-1] range_diff = range_max - range_min start_left_range = range_min, (range_diff // 3) + range_min start_mid_range = (range_diff // 3) + range_min, ((2 * range_diff) // 3) + range_min start_right_range = ((2 * range_diff) // 3) + range_min, range_max return self.run_solver(start_left_range, start_mid_range, start_right_range) def weigh(self, left_range, right_range): left_sum = self.coins[left_range[0]: left_range[1]].sum() right_sum = self.coins[right_range[0]: right_range[1]].sum() if left_sum > right_sum: return self.HEAVIER elif left_sum < right_sum: return self.LIGHTER else: return self.EQUAL def print_result(self, special_print): if not special_print: print("Solved odd coin problem with k=%s in %0.5f seconds. Bad coin at position %s." % (self.k_value, self.total_time, self.bad_coin_at_position)) else: print("%s\t%s\t%f" % (self.k_value, self.three_to_k, self.total_time)) if __name__ == '__main__': for current_k in TILING_K_VALUES: for _ in range(NUM_RAND_TILING_GAMES): TilingSolver(current_k, True) print() for current_k in COINS_K_VALUES: for _ in range(NUM_RAND_COIN_GAMES): ODDSolver(current_k, True)