├── .gitignore ├── minimax.pickle ├── README.md ├── specific_games.py ├── move_sequence_draw.py ├── find_strategy_overlap.py ├── boardstates.py ├── minimax.py ├── audiovisualize.py ├── game_extrapolation.py ├── utils.py ├── draw_game_states.py ├── draw_states_tree.py └── LICENSE.txt /.gitignore: -------------------------------------------------------------------------------- 1 | .idea 2 | __pycache__ -------------------------------------------------------------------------------- /minimax.pickle: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/MarcTheSpark/TicTacToe/HEAD/minimax.pickle -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | Tic-Tac-Toe Analysis and Music 2 | ------------------------------ 3 | 4 | The official git repo for the videos "There are exactly 14 different games of Tic-Tac-Toe" and "Actually, maybe 5 | there's only one game of Tic-Tac-Toe". -------------------------------------------------------------------------------- /specific_games.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | 4 | start_game = np.array( 5 | [[[0, 0, 0], 6 | [0, 0, 0], 7 | [0, 0, 0]]] 8 | ) 9 | 10 | start_with_center = np.array( 11 | [[[0, 0, 0], 12 | [0, 0, 0], 13 | [0, 0, 0]], 14 | [[0, 0, 0], 15 | [0, 1, 0], 16 | [0, 0, 0]]] 17 | ) 18 | 19 | start_with_edge = np.array( 20 | [[[0, 0, 0], 21 | [0, 0, 0], 22 | [0, 0, 0]], 23 | [[0, 0, 0], 24 | [1, 0, 0], 25 | [0, 0, 0]]] 26 | ) 27 | 28 | start_with_corner = np.array( 29 | [[[0, 0, 0], 30 | [0, 0, 0], 31 | [0, 0, 0]], 32 | [[1, 0, 0], 33 | [0, 0, 0], 34 | [0, 0, 0]]] 35 | ) 36 | 37 | start_with_corner_middle = np.array( 38 | [[[0, 0, 0], 39 | [0, 0, 0], 40 | [0, 0, 0]], 41 | [[1, 0, 0], 42 | [0, 0, 0], 43 | [0, 0, 0]], 44 | [[1, 0, 0], 45 | [0, -1, 0], 46 | [0, 0, 0]]] 47 | ) -------------------------------------------------------------------------------- /move_sequence_draw.py: -------------------------------------------------------------------------------- 1 | from game_extrapolation import extrapolate_all_games, remove_near_duplicates 2 | from specific_games import start_game 3 | from utils import flat_format 4 | import numpy as np 5 | 6 | 7 | games = extrapolate_all_games([start_game], prune_symmetrical=True, skill=4) 8 | games = remove_near_duplicates(games) 9 | 10 | 11 | flattened = [flat_format(x) for x in games] 12 | move_sequences = [[int(np.argwhere(array[i] != array[i-1])[0]) + 1 for i in range(1, len(array))] 13 | for array in flattened] 14 | 15 | 16 | all_moves = {} 17 | for move_sequence in move_sequences: 18 | current_move_dict = all_moves 19 | for move in move_sequence: 20 | if move not in current_move_dict: 21 | current_move_dict[move] = {} 22 | current_move_dict = current_move_dict[move] 23 | 24 | 25 | # -------------------------- Pygame script ------------------------------- 26 | 27 | import pygame 28 | 29 | SCREEN_DIM = 1920, 1080 30 | MARGINS = 100, 100 31 | 32 | x_step = (SCREEN_DIM[0] - 2 * MARGINS[0]) / 8 33 | y_step = (SCREEN_DIM[1] - 2 * MARGINS[1]) / 8 34 | 35 | 36 | def draw_move_lines(screen, move_dict, origin=None): 37 | if origin: 38 | for x in move_dict: 39 | endpoint = origin[0] + x_step, MARGINS[1] + (x - 1) * y_step 40 | pygame.draw.line(screen, (255, 255, 255), origin, endpoint, 2) 41 | draw_move_lines(screen, move_dict[x], endpoint) 42 | else: 43 | for x in move_dict: 44 | draw_move_lines(screen, move_dict[x], (MARGINS[0], MARGINS[1] + (x - 1) * y_step)) 45 | 46 | 47 | def main(): 48 | # Initialize pygame 49 | pygame.init() 50 | 51 | # Set up the display 52 | screen = pygame.display.set_mode(SCREEN_DIM) 53 | 54 | # Set running to True to keep the window open 55 | running = True 56 | while running: 57 | for event in pygame.event.get(): 58 | if event.type == pygame.QUIT: 59 | running = False 60 | 61 | # Fill the screen with a black color 62 | screen.fill((0, 0, 0)) 63 | 64 | # Draw a single white line segment 65 | draw_move_lines(screen, all_moves) 66 | 67 | # Update the display 68 | pygame.display.flip() 69 | 70 | pygame.quit() 71 | 72 | 73 | if __name__ == "__main__": 74 | main() 75 | -------------------------------------------------------------------------------- /find_strategy_overlap.py: -------------------------------------------------------------------------------- 1 | from boardstates import BoardStatesList 2 | from minimax import get_best_moves 3 | from game_extrapolation import find_winning_locations, find_win_setup_locations, find_open_locations 4 | import numpy as np 5 | from utils import square_format 6 | 7 | 8 | def get_heuristic_moves(current_board, skill=0): 9 | """ 10 | Extrapolates next possible moves. If skill is 0, then any move is considered. 11 | If skill is 1, then we will at least take a win if it's available on our turn. 12 | If skill is 2, then we will avoid, if possible, giving our opponent a winning move. 13 | If skill is 3, then we try to set up a 2 in a row, if possible 14 | If skill is 4, then we try to do a fork if possible and if not try for 2 in a row 15 | If skill is 5, then we do any move that is included in skill=3 or a minimax move 16 | If skill is 6, then we do any move that is included in skill=4 or a minimax move 17 | If skill is 7, then we do pure minimax play 18 | """ 19 | 20 | whose_turn = 1 if np.sum(current_board) % 2 == 0 else -1 21 | 22 | winning_moves = find_winning_locations(current_board) 23 | player_wins, opponent_wins = winning_moves if whose_turn == 1 else winning_moves[::-1] 24 | 25 | if skill >= 1 and len(player_wins) > 0: 26 | return player_wins 27 | elif skill >= 2 and len(opponent_wins) > 0: 28 | return opponent_wins 29 | elif skill >= 3: 30 | # using more "sophisticated" strategies 31 | if skill >= 7: 32 | # Perfect (minimax) skill (what does this mean exactly) 33 | return get_best_moves(current_board) 34 | elif skill >= 6: 35 | # Minimax 36 | minimax_next_moves = get_best_moves(current_board) 37 | # Heuristic (fork if we can) 38 | good_plays = find_win_setup_locations(current_board, whose_turn, only_the_best=True) 39 | # mix of minimax and heuristic 40 | return sorted(set(good_plays + minimax_next_moves)) 41 | elif skill >= 5: 42 | # Minimax 43 | minimax_next_moves = get_best_moves(current_board) 44 | # Heuristic (fork if we can) 45 | good_plays = find_win_setup_locations(current_board, whose_turn, only_the_best=False) 46 | # mix of minimax and heuristic 47 | return sorted(set(good_plays + minimax_next_moves)) 48 | else: 49 | good_plays = find_win_setup_locations(current_board, whose_turn, only_the_best=skill >= 4) 50 | if len(good_plays) > 0: 51 | return good_plays 52 | else: 53 | return find_open_locations(current_board) 54 | else: 55 | return find_open_locations(current_board) 56 | 57 | 58 | for state in BoardStatesList.complete().board_states[3]: 59 | heuristic_moves = set(get_heuristic_moves(square_format(state), 4)) 60 | best_moves = set(get_best_moves(state)) 61 | num_open_moves = len(find_open_locations(state)) 62 | # union should not be everything, neither should be a subset of the other 63 | if best_moves.issubset(heuristic_moves) or heuristic_moves.issubset(best_moves) or len(heuristic_moves.union(best_moves)) == num_open_moves: 64 | continue 65 | print(state) 66 | print(heuristic_moves) 67 | print(best_moves) 68 | print("---") 69 | -------------------------------------------------------------------------------- /boardstates.py: -------------------------------------------------------------------------------- 1 | from itertools import combinations 2 | import math 3 | import numpy as np 4 | from utils import square_format, tuple_format 5 | 6 | 7 | def get_all_rotations_and_reflections(board_state: tuple): 8 | board_state = square_format(board_state) 9 | return set( 10 | tuple_format(np.flip(np.rot90(board_state, rot, axes=(0, 1)), 1)) if flip 11 | else tuple_format(np.rot90(board_state, rot, axes=(0, 1))) 12 | for rot in range(4) 13 | for flip in range(2) 14 | ) 15 | 16 | 17 | def get_standard_form(board_state): 18 | return min(get_all_rotations_and_reflections(board_state)) 19 | 20 | 21 | def get_all_board_states_after_move_n(n): 22 | """ 23 | Returns a list of board states after the nth move as a 9-tuple 24 | """ 25 | board_states = [] 26 | num_x_moves = math.ceil(n / 2) 27 | num_o_moves = n - num_x_moves 28 | for x_moves in combinations(range(1, 10), num_x_moves): 29 | remaining_moves = tuple(x for x in range(1, 10) if x not in x_moves) 30 | for o_moves in combinations(remaining_moves, num_o_moves): 31 | board_states.append(tuple(1 if i in x_moves else -1 if i in o_moves else 0 for i in range(1, 10))) 32 | return board_states 33 | 34 | 35 | class BoardStatesList: 36 | 37 | def __init__(self, board_states_after_each_move): 38 | self.board_states = [[tuple_format(board) for board in sorted(x)] for x in board_states_after_each_move] 39 | while len(self.board_states) < 10: 40 | self.board_states.append([]) 41 | 42 | @classmethod 43 | def from_games(cls, games): 44 | """ 45 | Get a list of all board states used in the given games. 46 | """ 47 | used_states = [set() for _ in range(10)] 48 | for game in games: 49 | for i, state in enumerate(game): 50 | used_states[i].add(state) 51 | return cls(used_states) 52 | 53 | def standard_forms_only(self): 54 | """ 55 | Returns a copy of the same board states list pruned to only contain the standard rotation/reflection 56 | of each board state. 57 | """ 58 | return BoardStatesList([ 59 | tuple(sorted(set( 60 | get_standard_form(board_state) 61 | for board_state in board_states_after_move_n 62 | ))) 63 | for board_states_after_move_n in self.board_states 64 | ]) 65 | 66 | def get_state_index(self, board_state): 67 | """Given a board state as a 9-tuple, returns its move number and index.""" 68 | move_num = sum(abs(x) for x in board_state) 69 | this_move_states = self.board_states[move_num] 70 | try: 71 | return move_num, this_move_states.index(board_state) 72 | except ValueError: 73 | return None 74 | 75 | def index_sequence_to_board_sequence(self, state_sequence): 76 | return [self.board_states[i][state_num] for i, state_num in enumerate(state_sequence)] 77 | 78 | @classmethod 79 | def complete(cls): 80 | return cls([get_all_board_states_after_move_n(n) for n in range(10)]) 81 | 82 | def sizes_per_move(self): 83 | return tuple(len(x) for x in self.board_states) 84 | 85 | def __repr__(self): 86 | return f"BoardStatesIndex({self.board_states})" 87 | 88 | 89 | if __name__ == '__main__': 90 | complete_index = BoardStatesList.complete() 91 | print(complete_index) 92 | print(complete_index.sizes_per_move()) 93 | print(complete_index.standard_forms_only().sizes_per_move()) 94 | print(complete_index.get_state_index((0, 0, 1, 0, -1, 0, 0, 0, 0))) 95 | print(get_standard_form((0, 0, 1, 0, -1, 0, 0, 0, 0))) 96 | -------------------------------------------------------------------------------- /minimax.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | import math 3 | import boardstates 4 | import pickle 5 | from functools import cache 6 | from utils import check_win, find_open_locations, square_format, tuple_format 7 | 8 | 9 | X_WIN_SCORE = 10 10 | O_WIN_SCORE = -10 11 | DRAW_SCORE = 0 12 | 13 | 14 | def get_board_score(board): 15 | if check_win(board, 1): 16 | return X_WIN_SCORE 17 | elif check_win(board, -1): 18 | return O_WIN_SCORE 19 | elif np.sum(np.abs(board)) == 9: 20 | return DRAW_SCORE 21 | else: 22 | return None 23 | 24 | 25 | def get_move_array(i, j, value): 26 | """Returns a 2d TTT board with all zeros except for value at coordinates i, j""" 27 | out = np.zeros((3, 3), dtype=int) 28 | out[i, j] = value 29 | return out 30 | 31 | 32 | @cache 33 | def minimax(current_board: tuple, current_player: int): 34 | """ 35 | Takes a board as a 9-tuple and a player (1 or -1) and returns the score 36 | """ 37 | if get_board_score(current_board) is not None: 38 | return get_board_score(current_board) 39 | 40 | current_board_square = square_format(current_board) 41 | 42 | if current_player == 1: 43 | # x is playing; we want to maximize score 44 | return max(minimax(tuple_format(current_board_square + get_move_array(i, j, 1)), -current_player) 45 | for (i, j) in find_open_locations(current_board_square)) 46 | else: 47 | # O is playing; we want to maximize score 48 | return min(minimax(tuple_format(current_board_square + get_move_array(i, j, -1)), -current_player) 49 | for (i, j) in find_open_locations(current_board_square)) 50 | 51 | 52 | def calc_best_moves(board, player): 53 | board = square_format(board) 54 | if player == 1: 55 | best_score = -math.inf 56 | best_moves = [] 57 | for (i, j) in find_open_locations(board): 58 | next_board_tuple = tuple_format(board + get_move_array(i, j, player)) 59 | board_score = minimax(next_board_tuple, -player) 60 | if board_score == best_score: 61 | best_moves.append(next_board_tuple) 62 | elif board_score > best_score: 63 | best_moves = [next_board_tuple] 64 | best_score = board_score 65 | else: # player == -1 66 | best_score = math.inf 67 | best_moves = [] 68 | for (i, j) in find_open_locations(board): 69 | next_board_tuple = tuple_format(board + get_move_array(i, j, player)) 70 | board_score = minimax(next_board_tuple, -player) 71 | if board_score == best_score: 72 | best_moves.append(next_board_tuple) 73 | elif board_score < best_score: 74 | best_moves = [next_board_tuple] 75 | best_score = board_score 76 | 77 | return best_moves 78 | 79 | 80 | def get_all_rotations_and_reflections(square_board): 81 | return [ 82 | np.flip(np.rot90(square_board, rot, axes=(0, 1)), 1) if flip 83 | else np.rot90(square_board, rot, axes=(0, 1)) 84 | for rot in range(4) 85 | for flip in range(2) 86 | ] 87 | 88 | 89 | if __name__ == '__main__': 90 | best_moves_dict = {} 91 | for i, states_after_move_n in enumerate(boardstates.BoardStatesList.complete().board_states): 92 | for state in tuple_format(states_after_move_n): 93 | best_moves_dict[state] = calc_best_moves(state, 1 if i % 2 == 0 else -1) 94 | with open('minimax.pickle', 'wb') as handle: 95 | pickle.dump(best_moves_dict, handle, protocol=pickle.HIGHEST_PROTOCOL) 96 | 97 | else: 98 | with open('minimax.pickle', 'rb') as handle: 99 | best_moves_dict = pickle.load(handle) 100 | 101 | 102 | def get_best_moves(board): 103 | board = tuple_format(board) 104 | next_moves = [np.array(next_board) for next_board in best_moves_dict[board]] 105 | next_move_indices = [int(np.where(next_move != board)[0]) for next_move in next_moves] 106 | return [divmod(x, 3) for x in next_move_indices] 107 | 108 | 109 | if __name__ == '__main__': 110 | print(get_best_moves((0, 1, 0, -1, 0, 0, 0, 0, 0))) -------------------------------------------------------------------------------- /audiovisualize.py: -------------------------------------------------------------------------------- 1 | import pygame 2 | import numpy as np 3 | import time 4 | from specific_games import start_with_center, start_game 5 | from game_extrapolation import extrapolate_all_games, remove_near_duplicates 6 | from scamp import Session, wait, wait_for_children_to_finish 7 | 8 | 9 | the_20_games = extrapolate_all_games([start_with_center], skill=4) 10 | the_14_games = remove_near_duplicates(the_20_games) 11 | games = the_14_games 12 | 13 | # # One random game 14 | # game = np.array( 15 | # [[[0, 0, 0], 16 | # [0, 0, 0], 17 | # [0, 0, 0]], 18 | # [[0, 0, 0], 19 | # [1, 0, 0], 20 | # [0, 0, 0]], 21 | # [[0, 0, 0], 22 | # [1, -1, 0], 23 | # [0, 0, 0]], 24 | # [[0, 0, 0], 25 | # [1, -1, 0], 26 | # [0, 0, 1]], 27 | # [[0, -1, 0], 28 | # [1, -1, 0], 29 | # [0, 0, 1]], 30 | # [[0, -1, 0], 31 | # [1, -1, 0], 32 | # [0, 1, 1]], 33 | # [[0, -1, 0], 34 | # [1, -1, 0], 35 | # [-1, 1, 1]], 36 | # [[0, -1, 0], 37 | # [1, -1, 0], 38 | # [-1, 1, 1]]] 39 | # ) 40 | # game_iter = iter([game]) 41 | 42 | 43 | # # tons of games in random order 44 | # all_games = extrapolate_all_games([start_game], skill=2) 45 | # import random 46 | # random.shuffle(all_games) 47 | # game_iter = iter(all_games) 48 | 49 | 50 | # Initialize Pygame 51 | pygame.init() 52 | 53 | # Constants 54 | WIDTH, HEIGHT = 900, 900 55 | LINE_WIDTH = 10 56 | BOARD_ROWS, BOARD_COLS = 3, 3 57 | SQUARE_SIZE = WIDTH // BOARD_COLS 58 | WHITE = (255, 255, 255) 59 | BLACK = (0, 0, 0) 60 | O_COLOR = (0, 255, 0) 61 | X_COLOR = (255, 150, 50) 62 | 63 | # Set up the screen 64 | screen = pygame.display.set_mode((WIDTH, HEIGHT)) 65 | pygame.display.set_caption("Tic Tac Toe Animation") 66 | 67 | 68 | def draw_board(x0, y0, width, height): 69 | square_size = width // BOARD_COLS 70 | screen.fill(BLACK, rect=(x0, y0, width, height)) 71 | for row in range(1, BOARD_ROWS): 72 | pygame.draw.line(screen, WHITE, (x0, row * square_size), (width, row * square_size), LINE_WIDTH) 73 | for col in range(1, BOARD_COLS): 74 | pygame.draw.line(screen, WHITE, (col * square_size, y0), (col * square_size, height), LINE_WIDTH) 75 | 76 | 77 | def draw_xo(game_state, x0, y0, width, height, winning_line=None, winning_player=None): 78 | square_size = width // BOARD_COLS 79 | for row in range(BOARD_ROWS): 80 | for col in range(BOARD_COLS): 81 | center = (int(col * square_size + square_size // 2), int(row * square_size + square_size // 2)) 82 | if game_state[row][col] == -1: 83 | color = O_COLOR if (winning_player == -1 and is_winning_square(row, col, winning_line)) else WHITE 84 | pygame.draw.circle(screen, color, center, square_size * 0.4, LINE_WIDTH) 85 | elif game_state[row][col] == 1: 86 | color = X_COLOR if (winning_player == 1 and is_winning_square(row, col, winning_line)) else WHITE 87 | margin = square_size * 0.1 88 | pygame.draw.line(screen, color, (col * square_size + margin, row * square_size + margin), 89 | (col * square_size + square_size - margin, 90 | row * square_size + square_size - margin), int(LINE_WIDTH * 1.2)) 91 | pygame.draw.line(screen, color, 92 | (col * square_size + margin, row * square_size + square_size - margin), 93 | (col * square_size + square_size - margin, row * square_size + margin), 94 | int(LINE_WIDTH * 1.2)) 95 | 96 | 97 | def check_winner(game_state): 98 | """ 99 | Returns the coordinates of the start and end of the winning line, or (None, None) if no winning line 100 | Kinda a weird way of formatting this information? 101 | """ 102 | # Check rows and columns 103 | for i in range(3): 104 | if abs(game_state[i, :].sum()) == 3: # Check rows 105 | return ((i, 0), (i, 2)), game_state[i, 0] 106 | if abs(game_state[:, i].sum()) == 3: # Check columns 107 | return ((0, i), (2, i)), game_state[0, i] 108 | 109 | # Check diagonals 110 | if abs(np.diag(game_state).sum()) == 3: 111 | return ((0, 0), (2, 2)), game_state[0, 0] 112 | if abs(np.diag(np.fliplr(game_state)).sum()) == 3: 113 | return ((0, 2), (2, 0)), game_state[0, 2] 114 | 115 | return None, None # No winner 116 | 117 | 118 | def is_winning_square(row, col, winning_line): 119 | """ 120 | Checks if this square is on the given winning line. 121 | """ 122 | if not winning_line: 123 | return False 124 | ((start_row, start_col), (end_row, end_col)) = winning_line 125 | if start_row == end_row: # Winning row 126 | return row == start_row 127 | elif start_col == end_col: # Winning column 128 | return col == start_col 129 | elif start_row < end_row and start_col < end_col: # Diagonal from top-left to bottom-right 130 | return row == col 131 | else: # Diagonal from top-right to bottom-left 132 | return row + col == 2 133 | 134 | 135 | s = Session().run_as_server() 136 | s.print_available_midi_output_devices() 137 | ohs = s.new_midi_part("midi through Port-0") 138 | exes = s.new_midi_part("midi through Port-1") 139 | ohs_long = s.new_midi_part("midi through Port-2") 140 | exes_long = s.new_midi_part("midi through Port-3") 141 | 142 | 143 | def coords_to_pitch(coords): 144 | return 70 - 4.98 * coords[1] + 3.86 * coords[0] 145 | 146 | 147 | def roll_chord(inst, pitches, volume=1, spacing=0.07, length=1): 148 | length_left = length 149 | for pitch in pitches: 150 | inst.play_note(pitch, volume, length_left, blocking=False) 151 | wait(spacing) 152 | length_left -= spacing 153 | wait_for_children_to_finish() 154 | 155 | 156 | def animate_game(all_games, frame_dur): 157 | last_state = None 158 | for game_state in all_games: 159 | winning_line, winning_player = check_winner(game_state) 160 | if last_state is not None: 161 | delta = game_state - last_state 162 | coords = list(zip(*np.where(delta != 0)))[0] 163 | if winning_line: 164 | inst = ohs_long if np.sum(delta) == -1 else exes_long 165 | coords1, coords3 = winning_line 166 | coords2 = ((coords1[0] + coords3[0]) / 2, (coords1[1] + coords3[1]) / 2) 167 | chord = [coords_to_pitch(coord) for coord in (coords1, coords2, coords3)] 168 | inst.play_chord(chord, [0.2, 1.0], frame_dur/3) 169 | # s.fork(roll_chord, (inst, chord, 0.7)) 170 | else: 171 | inst = ohs if np.sum(delta) == -1 else exes 172 | inst.play_note(coords_to_pitch(coords), 0.6, frame_dur / 3) 173 | last_state = game_state 174 | draw_board(0, 0, WIDTH, HEIGHT) 175 | draw_xo(game_state, 0, 0, WIDTH, HEIGHT, winning_line, winning_player) 176 | pygame.display.update() 177 | time.sleep(frame_dur) 178 | 179 | 180 | for game in games: 181 | for event in pygame.event.get(): 182 | if event.type == pygame.QUIT: 183 | break 184 | 185 | # Start the animation (adjust frame_dur as needed) 186 | animate_game(game, frame_dur=0.2) 187 | time.sleep(0.6) 188 | 189 | pygame.quit() 190 | -------------------------------------------------------------------------------- /game_extrapolation.py: -------------------------------------------------------------------------------- 1 | """There are exactly 20 different* games of Tic-Tac-Toe""" 2 | 3 | import numpy as np 4 | from minimax import get_best_moves 5 | from utils import (find_open_locations, is_game_over, find_winning_locations, find_win_setup_locations, are_symmetrical, 6 | check_win_status, summarize_games, print_games_summary) 7 | from specific_games import start_game, start_with_center 8 | 9 | 10 | def extrapolate_one_step(game, skill=0): 11 | """ 12 | Extrapolates next possible moves. If skill is 0, then any move is considered. 13 | If skill is 1, then we will at least take a win if it's available on our turn. 14 | If skill is 2, then we will avoid, if possible, giving our opponent a winning move. 15 | If skill is 3, then we try to set up a 2 in a row, if possible 16 | If skill is 4, then we try to do a fork if possible and if not try for 2 in a row 17 | If skill is 5, then we do any move that is included in skill=3 or a minimax move 18 | If skill is 6, then we do any move that is included in skill=4 or a minimax move 19 | If skill is 7, then we do pure minimax play 20 | """ 21 | extrapolated = [] 22 | # Determine whose turn it is (1 for O's turn, -1 for X's turn) 23 | current_board = game[-1] 24 | whose_turn = 1 if np.sum(current_board) % 2 == 0 else -1 25 | 26 | winning_moves = find_winning_locations(current_board) 27 | player_wins, opponent_wins = winning_moves if whose_turn == 1 else winning_moves[::-1] 28 | 29 | if skill >= 1 and len(player_wins) > 0: 30 | next_moves = player_wins 31 | elif skill >= 2 and len(opponent_wins) > 0: 32 | next_moves = opponent_wins 33 | elif skill >= 3: 34 | # using more "sophisticated" strategies 35 | if skill >= 7: 36 | # Perfect (minimax) skill (what does this mean exactly) 37 | next_moves = get_best_moves(current_board) 38 | elif skill >= 6: 39 | # Minimax 40 | minimax_next_moves = get_best_moves(current_board) 41 | # Heuristic (fork if we can) 42 | good_plays = find_win_setup_locations(current_board, whose_turn, only_the_best=True) 43 | # mix of minimax and heuristic 44 | next_moves = sorted(set(good_plays + minimax_next_moves)) 45 | elif skill >= 5: 46 | # Minimax 47 | minimax_next_moves = get_best_moves(current_board) 48 | # Heuristic (fork if we can) 49 | good_plays = find_win_setup_locations(current_board, whose_turn, only_the_best=False) 50 | # mix of minimax and heuristic 51 | next_moves = sorted(set(good_plays + minimax_next_moves)) 52 | else: 53 | good_plays = find_win_setup_locations(current_board, whose_turn, only_the_best=skill >= 4) 54 | if len(good_plays) > 0: 55 | next_moves = good_plays 56 | else: 57 | next_moves = find_open_locations(current_board) 58 | else: 59 | next_moves = find_open_locations(current_board) 60 | 61 | 62 | for i, j in next_moves: 63 | # Create a new board with the current move 64 | new_board = np.copy(current_board) 65 | new_board[i, j] = whose_turn 66 | # Create a new game state by adding the new board to the game history 67 | new_game = np.concatenate((game, [new_board]), axis=0) 68 | extrapolated.append(new_game) 69 | return extrapolated 70 | 71 | 72 | def prune_symmetrical_games(games_list): 73 | to_remove = set() # A set to keep track of indices of games to be removed 74 | n = len(games_list) 75 | 76 | for i in range(n): 77 | if i in to_remove: 78 | continue # Skip if this game is already marked for removal 79 | 80 | for j in range(i + 1, n): 81 | if j in to_remove: 82 | continue # Skip if the other game is already marked for removal 83 | 84 | if are_symmetrical(games_list[i], games_list[j]): 85 | to_remove.add(j) # Mark the symmetrical game for removal 86 | 87 | # Removing the marked games 88 | # Since removing by index can be tricky (as the list size changes), we'll do it in a reversed order 89 | for index in sorted(to_remove, reverse=True): 90 | del games_list[index] 91 | 92 | return games_list 93 | 94 | 95 | def extrapolate_all_games(unfinished_games, skill=0, prune_symmetrical=True, show_log=True): 96 | 97 | finished_games = [] 98 | 99 | for game in reversed(unfinished_games): 100 | if is_game_over(game): 101 | unfinished_games.remove(game) 102 | finished_games.append(game) 103 | 104 | while len(unfinished_games) > 0: 105 | if show_log: 106 | print(f"PRE: {len(unfinished_games)}, {len(finished_games)}") 107 | unfinished_games = [ 108 | extrapolated_game 109 | for game in unfinished_games 110 | for extrapolated_game in 111 | (prune_symmetrical_games(extrapolate_one_step(game, skill=skill)) 112 | if prune_symmetrical else extrapolate_one_step(game, skill=skill)) 113 | ] 114 | if show_log: 115 | print(f"EXTRAPOLATE: {len(unfinished_games)}, {len(finished_games)}") 116 | for i in reversed(range(len(unfinished_games))): 117 | if is_game_over(unfinished_games[i]): 118 | finished_games.append(unfinished_games[i]) 119 | del unfinished_games[i] 120 | if show_log: 121 | print(f"PRUNE ENDED: {len(unfinished_games)}, {len(finished_games)}") 122 | return finished_games 123 | 124 | 125 | def remove_near_duplicates(games): 126 | """ 127 | Remove games that are duplicates up until the last two moves. 128 | 129 | :param games: A list of 3D NumPy arrays representing Tic-Tac-Toe games. 130 | :return: A list of games with near duplicates removed. 131 | """ 132 | indices_to_remove = set() 133 | 134 | for i in range(len(games)): 135 | if i in indices_to_remove: 136 | continue # Skip if this game is already marked for removal 137 | 138 | for j in range(i + 1, len(games)): 139 | if j in indices_to_remove: 140 | continue # Skip if the other game is already marked for removal 141 | 142 | # Compare the games up to the penultimate move 143 | game_i_slice = games[i][:-2, :, :] 144 | game_j_slice = games[j][:-2, :, :] 145 | 146 | if check_win_status(games[i]) == check_win_status(games[j]) and np.array_equal(game_i_slice, game_j_slice): 147 | indices_to_remove.add(j) # Mark the duplicate game for removal 148 | 149 | # Create a new list of unique games 150 | unique_games = [games[i] for i in range(len(games)) if i not in indices_to_remove] 151 | 152 | return unique_games 153 | 154 | 155 | if __name__ == '__main__': 156 | # 9! = 362880, but this doesn't account for games that end early 157 | print(len(extrapolate_all_games([start_game], prune_symmetrical=False)), "games in total") # 255168 158 | print(len(extrapolate_all_games([start_game])), "games in total") # 31896 159 | print(len(extrapolate_all_games([start_game], skill=1)), "games with idiotic moves removed") # 6956 160 | print(len(extrapolate_all_games([start_game], skill=2)), "games with dumb moves removed") # 2936 161 | print(len(extrapolate_all_games([start_game], skill=3)), "games with decent player") # 146 162 | print(len(extrapolate_all_games([start_game], skill=4)), "games with good player") # 102 163 | games = extrapolate_all_games([start_with_center], skill=4) 164 | games = remove_near_duplicates(games) 165 | -------------------------------------------------------------------------------- /utils.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | 4 | # ------------------ Formatting Utils ------------------------ 5 | 6 | 7 | def flat_format(game_or_board: np.ndarray): 8 | if not isinstance(game_or_board, np.ndarray): 9 | game_or_board = np.array(game_or_board) 10 | if game_or_board.shape[-1:] == (9, ): 11 | return game_or_board 12 | else: 13 | return game_or_board.reshape(game_or_board.shape[:-2] + (9,)) 14 | 15 | 16 | def square_format(game_or_board: np.ndarray): 17 | if not isinstance(game_or_board, np.ndarray): 18 | game_or_board = np.array(game_or_board) 19 | if game_or_board.shape[-2:] == (3, 3): 20 | return game_or_board 21 | else: 22 | return game_or_board.reshape(game_or_board.shape[:-1] + (3, 3)) 23 | 24 | 25 | def ndarray_to_tuple(arr): 26 | if arr.ndim == 1: 27 | return tuple(arr) 28 | return tuple(ndarray_to_tuple(arr[i]) for i in range(len(arr))) 29 | 30 | 31 | def tuple_format(game_or_board): 32 | return ndarray_to_tuple(flat_format(game_or_board)) 33 | 34 | 35 | # -------------------------- board utils ---------------------------- 36 | 37 | 38 | def check_win(board, player): 39 | board = square_format(board) 40 | # Check rows, columns, and diagonals for a win 41 | for i in range(3): 42 | if all(board[i, :] == player) or all(board[:, i] == player): 43 | return True 44 | if all(np.diag(board) == player) or all(np.diag(np.fliplr(board)) == player): 45 | return True 46 | return False 47 | 48 | 49 | def find_open_locations(board): 50 | """Find coordinates of all the zeros for a square formatted board""" 51 | board = square_format(board) 52 | return [(i, j) for i in range(3) for j in range(3) if board[i, j] == 0] 53 | 54 | 55 | def check_win(board, player): 56 | board = square_format(board) 57 | # Check rows, columns, and diagonals for a win 58 | for i in range(3): 59 | if all(board[i, :] == player) or all(board[:, i] == player): 60 | return True 61 | if all(np.diag(board) == player) or all(np.diag(np.fliplr(board)) == player): 62 | return True 63 | return False 64 | 65 | 66 | def find_winning_locations(board): 67 | """ 68 | Identify all O-win-locations and X-win-locations on a Tic-Tac-Toe board. 69 | 70 | :param board: A 3x3 NumPy array representing the Tic-Tac-Toe board. 71 | :return: Two lists containing the coordinates of winning locations for O and X. 72 | """ 73 | board = square_format(board) 74 | 75 | o_wins = [] 76 | x_wins = [] 77 | 78 | for i, j in find_open_locations(board): 79 | if board[i, j] == 0: 80 | # Check for O win 81 | temp_board = np.copy(board) 82 | temp_board[i, j] = 1 # Place an O 83 | if check_win(temp_board, 1): 84 | o_wins.append((i, j)) 85 | 86 | # Check for X win 87 | temp_board[i, j] = -1 # Place an X 88 | if check_win(temp_board, -1): 89 | x_wins.append((i, j)) 90 | 91 | return o_wins, x_wins 92 | 93 | 94 | def find_win_setup_locations(board, player, only_the_best=False): 95 | setup_to_win = [] 96 | threshold = 1 97 | for i, j in find_open_locations(board): 98 | # Check for O win 99 | temp_board = np.copy(board) 100 | temp_board[i, j] = player # Place an O 101 | 102 | index = 0 if player == 1 else 1 103 | num_win_locations = len(find_winning_locations(temp_board)[index]) 104 | if num_win_locations >= threshold: 105 | if only_the_best and num_win_locations > threshold: 106 | threshold = num_win_locations # needs to be at least as good as the next best one 107 | setup_to_win.clear() 108 | setup_to_win.append((i, j)) 109 | return setup_to_win 110 | 111 | 112 | # ---------------------------------- Game utils ------------------------------------------ 113 | 114 | 115 | def are_symmetrical(game1, game2): 116 | """ 117 | Check if two Tic-Tac-Toe games are rotationally or mirror symmetrical. 118 | 119 | :param game1: A 3D NumPy array representing the first Tic-Tac-Toe game (nx3x3). 120 | :param game2: A 3D NumPy array representing the second Tic-Tac-Toe game (nx3x3). 121 | :return: True if the games are symmetrical, False otherwise. 122 | """ 123 | game1 = square_format(game1) 124 | game2 = square_format(game2) 125 | 126 | # Check if game lengths are different 127 | if game1.shape[0] != game2.shape[0]: 128 | return False 129 | 130 | # Check for direct, rotational, and mirror symmetry 131 | for k in range(0, 4): # Rotations of 90, 180, 270 degrees 132 | rotated_game2 = np.rot90(game2, k, axes=(1, 2)) 133 | if np.array_equal(game1, rotated_game2) or \ 134 | np.array_equal(game1, np.flip(rotated_game2, 2)): 135 | return True 136 | 137 | return False 138 | 139 | 140 | def is_valid_game(game): 141 | """ 142 | Check if a Tic-Tac-Toe game is valid. (Probably not perfect.) 143 | 144 | :param game: A 3D NumPy array representing the Tic-Tac-Toe game (nx3x3). 145 | :return: True if the game is valid, False otherwise. 146 | """ 147 | game = square_format(game) 148 | 149 | # Start with an empty board 150 | if not np.array_equal(game[0], np.zeros((3, 3))): 151 | return False 152 | 153 | for i in range(1, game.shape[0]): 154 | # Check the sum for odd and even turns 155 | if np.sum(game[i]) != i % 2: 156 | return False 157 | 158 | # Check that there is exactly one difference from the previous turn 159 | if np.sum(np.abs(game[i] - game[i - 1])) != 1: 160 | return False 161 | 162 | return True 163 | 164 | 165 | def check_win_status(game): 166 | """ 167 | Check if a Tic-Tac-Toe game is over and if so, who won 168 | 169 | :param game: A 3D NumPy array representing a Tic-Tac-Toe game (nx3x3). 170 | :return: -1 if X's win, 1 if O's win, and 0 if draw; False if not over 171 | """ 172 | game = square_format(game) 173 | 174 | last_board = game[-1] 175 | if check_win(last_board, 1): 176 | return 1 # O wins 177 | elif check_win(last_board, -1): 178 | return -1 # X wins 179 | elif np.sum(np.abs(last_board)) == 9: 180 | return 0 # draw 181 | else: 182 | return None # unfinished 183 | 184 | 185 | def is_game_over(game): 186 | """ 187 | Check if a Tic-Tac-Toe game is over by examining the last frame. 188 | 189 | :param game: A 3D NumPy array representing a Tic-Tac-Toe game (nx3x3). 190 | :return: True if the game is over (win or draw), False otherwise. 191 | """ 192 | game = square_format(game) 193 | return check_win_status(game) is not None 194 | 195 | 196 | def _find_differing_indices(tuple1, tuple2): 197 | return [i for i, (x, y) in enumerate(zip(tuple1, tuple2)) if x != y] 198 | 199 | 200 | def get_move_sequence(game): 201 | game = tuple_format(game) 202 | return tuple(_find_differing_indices(game[i], game[i+1])[0] for i in range(len(game) - 1)) 203 | 204 | # ---------------------------------------- stats ---------------------------------------------- 205 | 206 | 207 | def summarize_games(games): 208 | total_games = len(games) 209 | first_player_wins = len([x for x in games if check_win_status(x) == 1]) 210 | second_player_wins = len([x for x in games if check_win_status(x) == -1]) 211 | ties = len([x for x in games if check_win_status(x) == 0]) 212 | return total_games, first_player_wins, second_player_wins, ties 213 | 214 | 215 | def print_games_summary(games): 216 | total_games, first_player_wins, second_player_wins, ties = summarize_games(games) 217 | print(f"{total_games} total games") 218 | print(f"First player wins {first_player_wins} games ({first_player_wins/total_games:.1%})") 219 | print(f"Second player wins {second_player_wins} games ({second_player_wins/total_games:.1%})") 220 | print(f"Tied {ties} games ({ties/total_games:.1%})") -------------------------------------------------------------------------------- /draw_game_states.py: -------------------------------------------------------------------------------- 1 | import pygame 2 | import numpy as np 3 | from boardstates import BoardStatesList 4 | from utils import square_format 5 | 6 | 7 | pygame.init() 8 | 9 | WIDTH, HEIGHT = 1920, 1080 10 | 11 | screen = pygame.display.set_mode((WIDTH, HEIGHT), pygame.FULLSCREEN | pygame.HWSURFACE | pygame.DOUBLEBUF) 12 | pygame.display.set_caption("Tic Tac Toe States") 13 | 14 | clock = pygame.time.Clock() 15 | 16 | LINE_WIDTH = 12 17 | BOARD_ROWS, BOARD_COLS = 3, 3 18 | SQUARE_SIZE = WIDTH // BOARD_COLS 19 | WHITE = (255, 255, 255) 20 | BLACK = (0, 0, 0) 21 | O_COLOR = (0, 255, 0) 22 | X_COLOR = (255, 150, 50) 23 | 24 | 25 | def draw_board(x0, y0, width, height): 26 | square_size = width // BOARD_COLS 27 | screen.fill(BLACK, rect=(x0, y0, width, height)) 28 | for row in range(1, BOARD_ROWS): 29 | pygame.draw.line(screen, WHITE, (x0, row * square_size), (width, row * square_size), LINE_WIDTH) 30 | for col in range(1, BOARD_COLS): 31 | pygame.draw.line(screen, WHITE, (col * square_size, y0), (col * square_size, height), LINE_WIDTH) 32 | 33 | 34 | def check_winner(game_state): 35 | """ 36 | Returns the coordinates of the start and end of the winning line, or (None, None) if no winning line 37 | Kinda a weird way of formatting this information? 38 | """ 39 | # Check rows and columns 40 | for i in range(3): 41 | if abs(game_state[i, :].sum()) == 3: # Check rows 42 | return ((i, 0), (i, 2)), game_state[i, 0] 43 | if abs(game_state[:, i].sum()) == 3: # Check columns 44 | return ((0, i), (2, i)), game_state[0, i] 45 | 46 | # Check diagonals 47 | if abs(np.diag(game_state).sum()) == 3: 48 | return ((0, 0), (2, 2)), game_state[0, 0] 49 | if abs(np.diag(np.fliplr(game_state)).sum()) == 3: 50 | return ((0, 2), (2, 0)), game_state[0, 2] 51 | 52 | return None, None # No winner 53 | 54 | 55 | def is_winning_square(row, col, winning_line): 56 | """ 57 | Checks if this square is on the given winning line. 58 | """ 59 | if not winning_line: 60 | return False 61 | ((start_row, start_col), (end_row, end_col)) = winning_line 62 | if start_row == end_row: # Winning row 63 | return row == start_row 64 | elif start_col == end_col: # Winning column 65 | return col == start_col 66 | elif start_row < end_row and start_col < end_col: # Diagonal from top-left to bottom-right 67 | return row == col 68 | else: # Diagonal from top-right to bottom-left 69 | return row + col == 2 70 | 71 | 72 | def draw_board(x0, y0, width, height): 73 | square_size = width // BOARD_COLS 74 | screen.fill((0, 0, 0), rect=(x0, y0, width, height)) 75 | for row in range(1, BOARD_ROWS): 76 | pygame.draw.line(screen, WHITE, (x0, y0 + row * square_size), (x0 + width, y0 + row * square_size), LINE_WIDTH) 77 | for col in range(1, BOARD_COLS): 78 | pygame.draw.line(screen, WHITE, (x0 + col * square_size, y0), (x0 + col * square_size, y0 + height), LINE_WIDTH) 79 | 80 | 81 | def draw_xo(game_state, x0, y0, width, height, winning_line=None, winning_player=None): 82 | square_size = width // BOARD_COLS 83 | for row in range(BOARD_ROWS): 84 | for col in range(BOARD_COLS): 85 | center = (int(x0 + col * square_size + square_size // 2), int(y0 + row * square_size + square_size // 2)) 86 | if game_state[row][col] == -1: 87 | color = O_COLOR if (winning_player == -1 and is_winning_square(row, col, winning_line)) else WHITE 88 | pygame.draw.circle(screen, color, center, square_size * 0.4, LINE_WIDTH) 89 | elif game_state[row][col] == 1: 90 | color = X_COLOR if (winning_player == 1 and is_winning_square(row, col, winning_line)) else WHITE 91 | margin = square_size * 0.1 92 | pygame.draw.line(screen, color, (x0 + col * square_size + margin, y0 + row * square_size + margin), 93 | (x0 + col * square_size + square_size - margin, 94 | y0 + row * square_size + square_size - margin), int(LINE_WIDTH * 1.2)) 95 | pygame.draw.line(screen, color, 96 | (x0 + col * square_size + margin, y0 + row * square_size + square_size - margin), 97 | (x0 + col * square_size + square_size - margin, y0 + row * square_size + margin), 98 | int(LINE_WIDTH * 1.2)) 99 | 100 | 101 | def calculate_image_positions(canvas_width, canvas_height, num_images, overall_padding, inter_rect_padding_percent): 102 | """ 103 | From ChatGPT. overall_padding is in px, inter_rect_padding_percent is in % of rect_width 104 | """ 105 | if not hasattr(overall_padding, '__len__'): 106 | overall_padding = (overall_padding, overall_padding) 107 | 108 | if len(overall_padding) < 4: 109 | overall_padding *= 2 110 | 111 | # Adjust canvas size for overall padding 112 | adj_width = canvas_width - overall_padding[0] - overall_padding[2] 113 | adj_height = canvas_height - overall_padding[1] - overall_padding[3] 114 | 115 | # Find the best fit for rows and columns 116 | best_layout = (0, 0) 117 | max_size = 0 118 | for rows in range(1, num_images + 1): 119 | cols = -(-num_images // rows) # Ceiling division 120 | if rows * cols >= num_images: 121 | # Calculate size considering inter-rectangle padding 122 | size = min(adj_width // cols, 123 | adj_height // rows) 124 | if size > max_size: 125 | max_size = size 126 | best_layout = (rows, cols) 127 | 128 | rows, cols = best_layout 129 | inter_rect_padding = inter_rect_padding_percent * max_size 130 | size = min((adj_width - (cols - 1) * inter_rect_padding) // cols, 131 | (adj_height - (rows - 1) * inter_rect_padding) // rows) 132 | 133 | # Centering adjustment 134 | total_width = cols * size + (cols - 1) * inter_rect_padding 135 | total_height = rows * size + (rows - 1) * inter_rect_padding 136 | start_x = overall_padding[0] + (adj_width - total_width) // 2 137 | start_y = overall_padding[1] + (adj_height - total_height) // 2 138 | 139 | # Generate coordinates for each image 140 | positions = [] 141 | for i in range(num_images): 142 | row = i // cols 143 | col = i % cols 144 | x = start_x + col * (size + inter_rect_padding) 145 | y = start_y + row * (size + inter_rect_padding) 146 | positions.append((x, y, size, size)) 147 | 148 | return positions 149 | 150 | 151 | font = pygame.font.Font(None, 80) 152 | 153 | 154 | def draw_states(which_move): 155 | global LINE_WIDTH 156 | screen.fill((0, 0, 0)) 157 | states_to_draw = square_format(all_board_states.board_states[which_move]) 158 | 159 | board_rects = calculate_image_positions(WIDTH, HEIGHT, len(states_to_draw), (150, 120, 150, 40), 0.1) 160 | LINE_WIDTH = max(1, int(12 * board_rects[0][3] / HEIGHT)) 161 | 162 | text = font.render(f"Move {current_state} {len(all_board_states.board_states[current_state])} state" + ("s" if len(all_board_states.board_states[current_state]) > 1 else ""), True, (255, 255, 255)) 163 | screen.blit(text, ((WIDTH - text.get_width()) / 2, 30)) 164 | 165 | for board_state, rect in zip(states_to_draw, board_rects): 166 | draw_board(*rect) 167 | winning_line, winning_player = check_winner(board_state) 168 | draw_xo(board_state, *rect, winning_line, winning_player) 169 | pygame.display.update() 170 | 171 | 172 | all_board_states = BoardStatesList.complete().standard_forms_only() 173 | current_state = 0 174 | draw_states(current_state) 175 | 176 | running = True 177 | while running: 178 | for event in pygame.event.get(): 179 | if event.type == pygame.QUIT: 180 | running = False 181 | # Check for keypress event 182 | if event.type == pygame.KEYDOWN: 183 | # Here you can check which key was pressed 184 | if event.key == pygame.K_ESCAPE: 185 | running = False # Exit the loop if ESC is pressed 186 | elif event.key == pygame.K_SPACE: 187 | current_state += 1 188 | try: 189 | draw_states(current_state) 190 | except IndexError: 191 | running = False 192 | break 193 | else: 194 | print(f"Key {pygame.key.name(event.key)} pressed") 195 | 196 | clock.tick(60) 197 | -------------------------------------------------------------------------------- /draw_states_tree.py: -------------------------------------------------------------------------------- 1 | import dataclasses 2 | 3 | from boardstates import BoardStatesList, get_standard_form 4 | from game_extrapolation import (extrapolate_all_games, remove_near_duplicates, start_game, start_with_center, 5 | check_win_status) 6 | from utils import tuple_format, square_format, get_move_sequence 7 | import numpy as np 8 | import time 9 | 10 | 11 | FRAME_DUR = 0.18 12 | 13 | games = [tuple_format(game) for game in extrapolate_all_games([start_game], skill=7)] 14 | # Start with center truncated vs non-truncated is very interesting/revealing 15 | 16 | used_states = BoardStatesList.from_games(games) 17 | used_states_standard_forms = used_states.standard_forms_only() 18 | 19 | games_state_indices = [tuple(used_states_standard_forms.get_state_index(get_standard_form(board_state))[1] 20 | for board_state in game) 21 | for game in games] 22 | 23 | highlighted_games = [-1] 24 | 25 | # ---------------- Filter down games by paring down games that have the same standardized index sequence ------------- 26 | 27 | pared_down_indices = [] 28 | pared_down_games = [] 29 | index_set = set() 30 | 31 | for game, state_index in zip(games, games_state_indices): 32 | if state_index not in index_set: 33 | pared_down_indices.append(state_index) 34 | pared_down_games.append(game) 35 | index_set.add(state_index) 36 | 37 | games_state_indices = pared_down_indices 38 | games = pared_down_games 39 | 40 | # --------------------------------- win statuses and game moves -------------------------------------- 41 | 42 | game_win_statuses = [check_win_status(game) for game in games] 43 | game_move_sequences = [get_move_sequence(game) for game in games] 44 | 45 | 46 | # --------------------------------------- truncate --------------------------------------------- 47 | 48 | def truncate_sequences(game_sequences, game_results): 49 | prefix_map = {} 50 | 51 | # Step 1: Create initial prefix map 52 | for sequence, result in zip(game_sequences, game_results): 53 | for i in range(1, len(sequence) + 1): 54 | prefix = sequence[:i] 55 | if prefix in prefix_map: 56 | prefix_map[prefix].add(result) 57 | else: 58 | prefix_map[prefix] = {result} 59 | 60 | # Step 2: Truncate sequences 61 | truncated_sequences = {} 62 | for sequence, result in zip(game_sequences, game_results): 63 | for i in range(1, len(sequence) + 1): 64 | prefix = sequence[:i] 65 | if len(prefix_map[prefix]) == 1 and result in prefix_map[prefix]: 66 | truncated_sequences[prefix] = result 67 | break 68 | 69 | return truncated_sequences 70 | 71 | 72 | truncated_sequence_dict = truncate_sequences(games_state_indices, game_win_statuses) 73 | 74 | truncated_game_state_indices = list(truncated_sequence_dict.keys()) 75 | truncated_game_win_statuses = list(truncated_sequence_dict.values()) 76 | truncated_games = [used_states_standard_forms.index_sequence_to_board_sequence(truncated_game_state_index_sequence) 77 | for truncated_game_state_index_sequence in truncated_game_state_indices] 78 | 79 | original_game_stata_indices = games_state_indices 80 | original_game_win_statuses = game_win_statuses 81 | original_games = games 82 | 83 | # ------------------------------ pygame ---------------------------------- 84 | 85 | import pygame 86 | import pygame.draw 87 | 88 | # Initialize Pygame 89 | pygame.init() 90 | 91 | # Get the screen resolution of your monitor 92 | infoObject = pygame.display.Info() 93 | SCREEN_WIDTH, SCREEN_HEIGHT = infoObject.current_w, infoObject.current_h 94 | 95 | WORLD_WIDTH, WORLD_HEIGHT = 16, 9 96 | CELL_SIZE = SCREEN_WIDTH / 16 97 | 98 | # Zoom and pan variables 99 | zoom = 1 100 | pan_x = 0 101 | pan_y = 0 102 | 103 | 104 | # --------------------- world drawing utilities --------------------- 105 | 106 | # Function to convert world coordinates to screen coordinates 107 | def world_to_screen(x, y): 108 | screen_x = x * CELL_SIZE * zoom + pan_x 109 | screen_y = y * CELL_SIZE * zoom + pan_y 110 | return int(screen_x), int(screen_y) 111 | 112 | 113 | def world_to_screen_width(width): 114 | return max(1, int(width * CELL_SIZE * zoom)) 115 | 116 | 117 | # Wrapper for rect 118 | def world_rect(surface, color, world_rect, width=0, **kwargs): 119 | screen_rect = pygame.Rect( 120 | world_to_screen(world_rect[0], world_rect[1]), 121 | (world_rect[2] * CELL_SIZE * zoom, world_rect[3] * CELL_SIZE * zoom) 122 | ) 123 | return pygame.draw.rect(surface, color, screen_rect, world_to_screen_width(width), **kwargs) 124 | 125 | 126 | # Wrapper for line 127 | def world_line(surface, color, start_pos, end_pos, width=1): 128 | screen_start = world_to_screen(*start_pos) 129 | screen_end = world_to_screen(*end_pos) 130 | return pygame.draw.line(surface, color, screen_start, screen_end, world_to_screen_width(width)) 131 | 132 | 133 | # Wrapper for circle 134 | def world_circle(surface, color, center, radius, width=0, **kwargs): 135 | screen_center = world_to_screen(*center) 136 | screen_radius = radius * CELL_SIZE * zoom 137 | return pygame.draw.circle(surface, color, screen_center, screen_radius, world_to_screen_width(width), **kwargs) 138 | 139 | 140 | # Wrapper for ellipse 141 | def world_ellipse(surface, color, world_rect, width=0): 142 | # Convert the world rectangle to screen rectangle 143 | screen_rect = pygame.Rect( 144 | world_to_screen(world_rect[0], world_rect[1]), 145 | (world_rect[2] * CELL_SIZE * zoom, world_rect[3] * CELL_SIZE * zoom) 146 | ) 147 | return pygame.draw.ellipse(surface, color, screen_rect, width) 148 | 149 | 150 | # Wrapper for polygon 151 | def world_polygon(surface, color, points, width=0, **kwargs): 152 | screen_points = [world_to_screen(*point) for point in points] 153 | return pygame.draw.polygon(surface, color, screen_points, world_to_screen_width(width), **kwargs) 154 | 155 | # ------------------ game animation ------------------------- 156 | 157 | ORIGIN = 60, SCREEN_HEIGHT * 0.65 - 60 158 | WIDTH, HEIGHT = SCREEN_HEIGHT * 0.35, SCREEN_HEIGHT * 0.35 159 | LINE_WIDTH = 5 160 | BOARD_ROWS, BOARD_COLS = 3, 3 161 | SQUARE_SIZE = WIDTH // BOARD_COLS 162 | WHITE = (255, 255, 255) 163 | BLACK = (0, 0, 0) 164 | O_COLOR = (0, 255, 0) 165 | X_COLOR = (255, 150, 50) 166 | 167 | 168 | def draw_board(x0, y0, width, height): 169 | square_size = width // BOARD_COLS 170 | screen.fill((0, 0, 0), rect=(x0, y0, width, height)) 171 | for row in range(1, BOARD_ROWS): 172 | pygame.draw.line(screen, WHITE, (x0, y0 + row * square_size), (x0 + width, y0 + row * square_size), LINE_WIDTH) 173 | for col in range(1, BOARD_COLS): 174 | pygame.draw.line(screen, WHITE, (x0 + col * square_size, y0), (x0 + col * square_size, y0 + height), LINE_WIDTH) 175 | 176 | 177 | def draw_xo(game_state, x0, y0, width, height, winning_line=None, winning_player=None): 178 | square_size = width // BOARD_COLS 179 | for row in range(BOARD_ROWS): 180 | for col in range(BOARD_COLS): 181 | center = (int(x0 + col * square_size + square_size // 2), int(y0 + row * square_size + square_size // 2)) 182 | if game_state[row][col] == -1: 183 | color = O_COLOR if (winning_player == -1 and is_winning_square(row, col, winning_line)) else WHITE 184 | pygame.draw.circle(screen, color, center, square_size * 0.4, LINE_WIDTH) 185 | elif game_state[row][col] == 1: 186 | color = X_COLOR if (winning_player == 1 and is_winning_square(row, col, winning_line)) else WHITE 187 | margin = square_size * 0.1 188 | pygame.draw.line(screen, color, (x0 + col * square_size + margin, y0 + row * square_size + margin), 189 | (x0 + col * square_size + square_size - margin, 190 | y0 + row * square_size + square_size - margin), int(LINE_WIDTH * 1.2)) 191 | pygame.draw.line(screen, color, 192 | (x0 + col * square_size + margin, y0 + row * square_size + square_size - margin), 193 | (x0 + col * square_size + square_size - margin, y0 + row * square_size + margin), 194 | int(LINE_WIDTH * 1.2)) 195 | 196 | 197 | def check_winner(game_state): 198 | # Check rows and columns 199 | for i in range(3): 200 | if abs(game_state[i, :].sum()) == 3: # Check rows 201 | return ((i, 0), (i, 2)), game_state[i, 0] 202 | if abs(game_state[:, i].sum()) == 3: # Check columns 203 | return ((0, i), (2, i)), game_state[0, i] 204 | 205 | # Check diagonals 206 | if abs(np.diag(game_state).sum()) == 3: 207 | return ((0, 0), (2, 2)), game_state[0, 0] 208 | if abs(np.diag(np.fliplr(game_state)).sum()) == 3: 209 | return ((0, 2), (2, 0)), game_state[0, 2] 210 | 211 | return None, None # No winner 212 | 213 | 214 | def is_winning_square(row, col, winning_line): 215 | if not winning_line: 216 | return False 217 | ((start_row, start_col), (end_row, end_col)) = winning_line 218 | if start_row == end_row: # Winning row 219 | return row == start_row 220 | elif start_col == end_col: # Winning column 221 | return col == start_col 222 | elif start_row < end_row and start_col < end_col: # Diagonal from top-left to bottom-right 223 | return row == col 224 | else: # Diagonal from top-right to bottom-left 225 | return row + col == 2 226 | 227 | 228 | from scamp import * 229 | 230 | s = Session().run_as_server() 231 | ohs = s.new_midi_part("midi through Port-0") 232 | exes = s.new_midi_part("midi through Port-1") 233 | ohs_long = s.new_midi_part("midi through Port-2") 234 | exes_long = s.new_midi_part("midi through Port-3") 235 | 236 | 237 | def coords_to_pitch(coords): 238 | return 70 - 4.98 * coords[1] + 3.86 * coords[0] 239 | 240 | 241 | def roll_chord(inst, pitches, volume=1, spacing=0.07, length=1): 242 | length_left = length 243 | for pitch in pitches: 244 | inst.play_note(pitch, volume, length_left, blocking=False) 245 | wait(spacing) 246 | length_left -= spacing 247 | wait_for_children_to_finish() 248 | 249 | 250 | @dataclasses.dataclass 251 | class GameAnimation: 252 | game_state: np.ndarray 253 | winning_line: tuple 254 | winning_player: int 255 | 256 | def draw(self): 257 | draw_board(*ORIGIN, WIDTH, HEIGHT) 258 | draw_xo(self.game_state, *ORIGIN, WIDTH, HEIGHT, self.winning_line, self.winning_player) 259 | 260 | i, game_state_index = used_states_standard_forms.get_state_index(get_standard_form(self.game_state)) 261 | num_states_this_move = used_states_standard_forms.sizes_per_move()[i] 262 | x_step, y_step = DRAW_BOX[2] / 9, DRAW_BOX[3] / num_states_this_move 263 | this_point = DRAW_BOX[0] + i * x_step, DRAW_BOX[1] + game_state_index * y_step 264 | world_ellipse(screen, (255, 255, 0), (this_point[0] - 0.07, this_point[1] - 0.07, 0.14, 0.14)) 265 | 266 | 267 | game_animation: GameAnimation = None 268 | 269 | 270 | def animate_game(game, frame_dur): 271 | global game_animation 272 | last_state = None 273 | for game_state in game: 274 | winning_line, winning_player = check_winner(game_state) 275 | if last_state is not None: 276 | delta = game_state - last_state 277 | coords = list(zip(*np.where(delta != 0)))[0] 278 | if winning_line: 279 | inst = ohs_long if np.sum(delta) == -1 else exes_long 280 | coords1, coords3 = winning_line 281 | coords2 = ((coords1[0] + coords3[0]) / 2, (coords1[1] + coords3[1]) / 2) 282 | chord = [coords_to_pitch(coord) for coord in (coords1, coords2, coords3)] 283 | inst.play_chord(chord, [0.2, 1.0], frame_dur / 3) 284 | else: 285 | inst = ohs if np.sum(delta) == -1 else exes 286 | inst.play_note(coords_to_pitch(coords), 0.6, frame_dur / 3) 287 | game_animation = GameAnimation(game_state, winning_line, winning_player) 288 | last_state = game_state 289 | 290 | wait(frame_dur) 291 | wait(frame_dur * 2) 292 | game_animation = None 293 | 294 | 295 | # ------------------- line drawings ------------------------ 296 | 297 | DRAW_BOX = (1, 0.5, 14, 8) 298 | 299 | 300 | def draw_game_state_sequence(state_sequence, surface, color=(255, 255, 255), cap_color=(255, 255, 255), width=0.02): 301 | last_point = None 302 | x_step = DRAW_BOX[2] / 9 303 | for i, (game_state_index, num_states_this_move) in enumerate(zip(state_sequence, used_states_standard_forms.sizes_per_move())): 304 | y_step = DRAW_BOX[3] / num_states_this_move 305 | this_point = DRAW_BOX[0] + i * x_step, DRAW_BOX[1] + game_state_index * y_step 306 | if last_point: 307 | world_line(surface, color, last_point, this_point, width=width) 308 | world_ellipse(surface, color, (this_point[0] - 0.03, this_point[1] - 0.03, 0.06, 0.06)) 309 | last_point = this_point 310 | world_ellipse(surface, cap_color, (this_point[0] - 0.05, this_point[1] - 0.05, 0.1, 0.1)) 311 | 312 | 313 | def draw_games(screen): 314 | highlights = [] 315 | for i, (this_game_indices, win_status) in enumerate(zip(games_state_indices, game_win_statuses)): 316 | cap_color = (255, 150, 50) if win_status == 1 else \ 317 | (0, 255, 0) if win_status == -1 else \ 318 | (255, 255, 255) 319 | if i in highlighted_games: 320 | highlights.append((i, (this_game_indices, win_status))) 321 | continue 322 | draw_game_state_sequence(this_game_indices, screen, cap_color=cap_color, width=0.005) 323 | 324 | for i, (this_game_indices, win_status) in highlights: 325 | cap_color = (255, 150, 50) if win_status == 1 else \ 326 | (0, 255, 0) if win_status == -1 else \ 327 | (255, 255, 255) 328 | draw_game_state_sequence(this_game_indices, screen, color=(255, 255, 0), cap_color=cap_color, width=0.02) 329 | 330 | 331 | # ------------------- pygame main --------------------------- 332 | 333 | clock = pygame.time.Clock() 334 | 335 | # Set up the display 336 | screen = pygame.display.set_mode((SCREEN_WIDTH, SCREEN_HEIGHT), pygame.FULLSCREEN | pygame.HWSURFACE | pygame.DOUBLEBUF) 337 | 338 | KEY_REPEAT_DELAY = 500 339 | KEY_REPEAT_INTERVAL = 100 340 | key_repeat_countdown = None 341 | 342 | # Main loop 343 | running = True 344 | while running: 345 | for event in pygame.event.get(): 346 | if event.type == pygame.QUIT: 347 | running = False 348 | 349 | elif event.type == pygame.MOUSEWHEEL: 350 | if pygame.key.get_mods() & pygame.KMOD_CTRL: 351 | # Capture the current mouse position 352 | mouse_x, mouse_y = pygame.mouse.get_pos() 353 | 354 | # Convert mouse position to world coordinates before zoom 355 | world_mouse_x_before = (mouse_x - pan_x) / (CELL_SIZE * zoom) 356 | world_mouse_y_before = (mouse_y - pan_y) / (CELL_SIZE * zoom) 357 | 358 | # Calculate the zoom factor 359 | old_zoom = zoom 360 | zoom *= 1 + event.y * (0.09 if pygame.key.get_mods() & pygame.KMOD_SHIFT else 0.03) 361 | zoom = max(0.01, min(zoom, 50)) 362 | 363 | # Convert mouse position to world coordinates after zoom 364 | world_mouse_x_after = (mouse_x - pan_x) / (CELL_SIZE * zoom) 365 | world_mouse_y_after = (mouse_y - pan_y) / (CELL_SIZE * zoom) 366 | 367 | # Adjust pan to keep the mouse position constant in world coordinates 368 | pan_x += (world_mouse_x_after - world_mouse_x_before) * CELL_SIZE * zoom 369 | pan_y += (world_mouse_y_after - world_mouse_y_before) * CELL_SIZE * zoom 370 | else: 371 | pan_x += -event.x * 20 * zoom ** 0.5 372 | pan_y += event.y * 20 * zoom ** 0.5 373 | 374 | dt = clock.tick(60) 375 | 376 | keys = pygame.key.get_pressed() 377 | 378 | if not any(pygame.key.get_pressed()): 379 | key_repeat_countdown = None 380 | elif key_repeat_countdown is None or key_repeat_countdown < 0: 381 | if keys[pygame.K_UP]: 382 | highlighted_games[0] = len(games) - 1 383 | elif keys[pygame.K_DOWN]: 384 | highlighted_games[0] = 0 385 | elif keys[pygame.K_LEFT]: 386 | highlighted_games[0] = max(highlighted_games[0] - 1, -1) 387 | elif keys[pygame.K_RIGHT]: 388 | highlighted_games[0] = min(highlighted_games[0] + 1, len(games) - 1) 389 | elif keys[pygame.K_t]: 390 | if games_state_indices == original_game_stata_indices: 391 | games_state_indices = truncated_game_state_indices 392 | game_win_statuses = truncated_game_win_statuses 393 | games = truncated_games 394 | highlighted_games = [-1] 395 | else: 396 | games_state_indices = original_game_stata_indices 397 | game_win_statuses = original_game_win_statuses 398 | games = original_games 399 | highlighted_games = [-1] 400 | 401 | elif keys[pygame.K_SPACE]: 402 | s.fork(animate_game, (square_format(games[highlighted_games[0]]), FRAME_DUR)) 403 | key_repeat_countdown = KEY_REPEAT_DELAY if key_repeat_countdown is None else KEY_REPEAT_INTERVAL 404 | 405 | if key_repeat_countdown is not None: 406 | key_repeat_countdown -= dt 407 | 408 | # Clear screen 409 | screen.fill((0, 0, 0)) 410 | 411 | # draw_games_state_tree(screen) 412 | draw_games(screen) 413 | 414 | if game_animation: 415 | game_animation.draw() 416 | 417 | # Update the display 418 | pygame.display.flip() 419 | 420 | # Quit Pygame 421 | pygame.quit() 422 | -------------------------------------------------------------------------------- /LICENSE.txt: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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No Surrender of Others' Freedom. 541 | 542 | If conditions are imposed on you (whether by court order, agreement or 543 | otherwise) that contradict the conditions of this License, they do not 544 | excuse you from the conditions of this License. If you cannot convey a 545 | covered work so as to satisfy simultaneously your obligations under this 546 | License and any other pertinent obligations, then as a consequence you may 547 | not convey it at all. For example, if you agree to terms that obligate you 548 | to collect a royalty for further conveying from those to whom you convey 549 | the Program, the only way you could satisfy both those terms and this 550 | License would be to refrain entirely from conveying the Program. 551 | 552 | 13. Use with the GNU Affero General Public License. 553 | 554 | Notwithstanding any other provision of this License, you have 555 | permission to link or combine any covered work with a work licensed 556 | under version 3 of the GNU Affero General Public License into a single 557 | combined work, and to convey the resulting work. The terms of this 558 | License will continue to apply to the part which is the covered work, 559 | but the special requirements of the GNU Affero General Public License, 560 | section 13, concerning interaction through a network will apply to the 561 | combination as such. 562 | 563 | 14. Revised Versions of this License. 564 | 565 | The Free Software Foundation may publish revised and/or new versions of 566 | the GNU General Public License from time to time. Such new versions will 567 | be similar in spirit to the present version, but may differ in detail to 568 | address new problems or concerns. 569 | 570 | Each version is given a distinguishing version number. If the 571 | Program specifies that a certain numbered version of the GNU General 572 | Public License "or any later version" applies to it, you have the 573 | option of following the terms and conditions either of that numbered 574 | version or of any later version published by the Free Software 575 | Foundation. If the Program does not specify a version number of the 576 | GNU General Public License, you may choose any version ever published 577 | by the Free Software Foundation. 578 | 579 | If the Program specifies that a proxy can decide which future 580 | versions of the GNU General Public License can be used, that proxy's 581 | public statement of acceptance of a version permanently authorizes you 582 | to choose that version for the Program. 583 | 584 | Later license versions may give you additional or different 585 | permissions. However, no additional obligations are imposed on any 586 | author or copyright holder as a result of your choosing to follow a 587 | later version. 588 | 589 | 15. Disclaimer of Warranty. 590 | 591 | THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY 592 | APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT 593 | HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY 594 | OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, 595 | THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR 596 | PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM 597 | IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF 598 | ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 599 | 600 | 16. Limitation of Liability. 601 | 602 | IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING 603 | WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS 604 | THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY 605 | GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE 606 | USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF 607 | DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD 608 | PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), 609 | EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF 610 | SUCH DAMAGES. 611 | 612 | 17. Interpretation of Sections 15 and 16. 613 | 614 | If the disclaimer of warranty and limitation of liability provided 615 | above cannot be given local legal effect according to their terms, 616 | reviewing courts shall apply local law that most closely approximates 617 | an absolute waiver of all civil liability in connection with the 618 | Program, unless a warranty or assumption of liability accompanies a 619 | copy of the Program in return for a fee. 620 | 621 | END OF TERMS AND CONDITIONS 622 | 623 | How to Apply These Terms to Your New Programs 624 | 625 | If you develop a new program, and you want it to be of the greatest 626 | possible use to the public, the best way to achieve this is to make it 627 | free software which everyone can redistribute and change under these terms. 628 | 629 | To do so, attach the following notices to the program. It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | --------------------------------------------------------------------------------