aima-python/games.py at master · aaronsgithub/aima-python · GitHub

History

590 lines (479 loc) · 20.5 KB

Raw

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492

493

494

495

496

497

498

499

500

501

502

503

504

505

506

507

508

509

510

511

512

513

514

515

516

517

518

519

520

521

522

523

524

525

526

527

528

529

530

531

532

533

534

535

536

537

538

539

540

541

542

543

544

545

546

547

548

549

550

551

552

553

554

555

556

557

558

559

560

561

562

563

564

565

566

567

568

569

570

571

572

573

574

575

576

577

578

579

580

581

582

583

584

585

586

587

588

589

590

"""Games or Adversarial Search (Chapter 5)"""

import copy

import itertools

import random

from collections import namedtuple

import numpy as np

from utils import vector_add

GameState = namedtuple('GameState', 'to_move, utility, board, moves')

StochasticGameState = namedtuple('StochasticGameState', 'to_move, utility, board, moves, chance')

# ______________________________________________________________________________

# MinMax Search

def minmax_decision(state, game):

"""Given a state in a game, calculate the best move by searching

forward all the way to the terminal states. [Figure 5.3]"""

player = game.to_move(state)

def max_value(state):

if game.terminal_test(state):

return game.utility(state, player)

v = -np.inf

for a in game.actions(state):

v = max(v, min_value(game.result(state, a)))

return v

def min_value(state):

if game.terminal_test(state):

return game.utility(state, player)

v = np.inf

for a in game.actions(state):

v = min(v, max_value(game.result(state, a)))

return v

# Body of minmax_decision:

return max(game.actions(state), key=lambda a: min_value(game.result(state, a)))

# ______________________________________________________________________________

def expect_minmax(state, game):

"""

[Figure 5.11]

Return the best move for a player after dice are thrown. The game tree

includes chance nodes along with min and max nodes.

"""

player = game.to_move(state)

def max_value(state):

v = -np.inf

for a in game.actions(state):

v = max(v, chance_node(state, a))

return v

def min_value(state):

v = np.inf

for a in game.actions(state):

v = min(v, chance_node(state, a))

return v

def chance_node(state, action):

res_state = game.result(state, action)

if game.terminal_test(res_state):

return game.utility(res_state, player)

sum_chances = 0

num_chances = len(game.chances(res_state))

for chance in game.chances(res_state):

res_state = game.outcome(res_state, chance)

util = 0

if res_state.to_move == player:

util = max_value(res_state)

else:

util = min_value(res_state)

sum_chances += util * game.probability(chance)

return sum_chances / num_chances

# Body of expect_minmax:

return max(game.actions(state), key=lambda a: chance_node(state, a), default=None)

def alpha_beta_search(state, game):

"""Search game to determine best action; use alpha-beta pruning.

As in [Figure 5.7], this version searches all the way to the leaves."""

player = game.to_move(state)

# Functions used by alpha_beta

def max_value(state, alpha, beta):

if game.terminal_test(state):

return game.utility(state, player)

v = -np.inf

for a in game.actions(state):

v = max(v, min_value(game.result(state, a), alpha, beta))

if v >= beta:

return v

alpha = max(alpha, v)

return v

def min_value(state, alpha, beta):

if game.terminal_test(state):

return game.utility(state, player)

v = np.inf

for a in game.actions(state):

v = min(v, max_value(game.result(state, a), alpha, beta))

if v <= alpha:

return v

beta = min(beta, v)

return v

# Body of alpha_beta_search:

best_score = -np.inf

beta = np.inf

best_action = None

for a in game.actions(state):

v = min_value(game.result(state, a), best_score, beta)

if v > best_score:

best_score = v

best_action = a

return best_action

def alpha_beta_cutoff_search(state, game, d=4, cutoff_test=None, eval_fn=None):

"""Search game to determine best action; use alpha-beta pruning.

This version cuts off search and uses an evaluation function."""

player = game.to_move(state)

# Functions used by alpha_beta

def max_value(state, alpha, beta, depth):

if cutoff_test(state, depth):

return eval_fn(state)

v = -np.inf

for a in game.actions(state):

v = max(v, min_value(game.result(state, a), alpha, beta, depth + 1))

if v >= beta:

return v

alpha = max(alpha, v)

return v

def min_value(state, alpha, beta, depth):

if cutoff_test(state, depth):

return eval_fn(state)

v = np.inf

for a in game.actions(state):

v = min(v, max_value(game.result(state, a), alpha, beta, depth + 1))

if v <= alpha:

return v

beta = min(beta, v)

return v

# Body of alpha_beta_cutoff_search starts here:

# The default test cuts off at depth d or at a terminal state

cutoff_test = (cutoff_test or (lambda state, depth: depth > d or game.terminal_test(state)))

eval_fn = eval_fn or (lambda state: game.utility(state, player))

best_score = -np.inf

beta = np.inf

best_action = None

for a in game.actions(state):

v = min_value(game.result(state, a), best_score, beta, 1)

if v > best_score:

best_score = v

best_action = a

return best_action

# ______________________________________________________________________________

# Players for Games

def query_player(game, state):

"""Make a move by querying standard input."""

print("current state:")

game.display(state)

print("available moves: {}".format(game.actions(state)))

print("")

move = None

if game.actions(state):

move_string = input('Your move? ')

try:

move = eval(move_string)

except NameError:

move = move_string

else:

print('no legal moves: passing turn to next player')

return move

def random_player(game, state):

"""A player that chooses a legal move at random."""

return random.choice(game.actions(state)) if game.actions(state) else None

def alpha_beta_player(game, state):

return alpha_beta_search(state, game)

def minmax_player(game,state):

return minmax_decision(state,game)

def expect_minmax_player(game, state):

return expect_minmax(state, game)

# ______________________________________________________________________________

# Some Sample Games

class Game:

"""A game is similar to a problem, but it has a utility for each

state and a terminal test instead of a path cost and a goal

test. To create a game, subclass this class and implement actions,

result, utility, and terminal_test. You may override display and

successors or you can inherit their default methods. You will also

need to set the .initial attribute to the initial state; this can

be done in the constructor."""

def actions(self, state):

"""Return a list of the allowable moves at this point."""

raise NotImplementedError

def result(self, state, move):

"""Return the state that results from making a move from a state."""

raise NotImplementedError

def utility(self, state, player):

"""Return the value of this final state to player."""

raise NotImplementedError

def terminal_test(self, state):

"""Return True if this is a final state for the game."""

return not self.actions(state)

def to_move(self, state):

"""Return the player whose move it is in this state."""

return state.to_move

def display(self, state):

"""Print or otherwise display the state."""

print(state)

def __repr__(self):

return '<{}>'.format(self.__class__.__name__)

def play_game(self, *players):

"""Play an n-person, move-alternating game."""

state = self.initial

while True:

for player in players:

move = player(self, state)

state = self.result(state, move)

if self.terminal_test(state):

self.display(state)

return self.utility(state, self.to_move(self.initial))

class StochasticGame(Game):

"""A stochastic game includes uncertain events which influence

the moves of players at each state. To create a stochastic game, subclass

this class and implement chances and outcome along with the other

unimplemented game class methods."""

def chances(self, state):

"""Return a list of all possible uncertain events at a state."""

raise NotImplementedError

def outcome(self, state, chance):

"""Return the state which is the outcome of a chance trial."""

raise NotImplementedError

def probability(self, chance):

"""Return the probability of occurrence of a chance."""

raise NotImplementedError

def play_game(self, *players):

"""Play an n-person, move-alternating stochastic game."""

state = self.initial

while True:

for player in players:

chance = random.choice(self.chances(state))

state = self.outcome(state, chance)

move = player(self, state)

state = self.result(state, move)

if self.terminal_test(state):

self.display(state)

return self.utility(state, self.to_move(self.initial))

class Fig52Game(Game):

"""The game represented in [Figure 5.2]. Serves as a simple test case."""

succs = dict(A=dict(a1='B', a2='C', a3='D'),

B=dict(b1='B1', b2='B2', b3='B3'),

C=dict(c1='C1', c2='C2', c3='C3'),

D=dict(d1='D1', d2='D2', d3='D3'))

utils = dict(B1=3, B2=12, B3=8, C1=2, C2=4, C3=6, D1=14, D2=5, D3=2)

initial = 'A'

def actions(self, state):

return list(self.succs.get(state, {}).keys())

def result(self, state, move):

return self.succs[state][move]

def utility(self, state, player):

if player == 'MAX':

return self.utils[state]

else:

return -self.utils[state]

def terminal_test(self, state):

return state not in ('A', 'B', 'C', 'D')

def to_move(self, state):

return 'MIN' if state in 'BCD' else 'MAX'

class Fig52Extended(Game):

"""Similar to Fig52Game but bigger. Useful for visualisation"""

succs = {i: dict(l=i * 3 + 1, m=i * 3 + 2, r=i * 3 + 3) for i in range(13)}

utils = dict()

def actions(self, state):

return sorted(list(self.succs.get(state, {}).keys()))

def result(self, state, move):

return self.succs[state][move]

def utility(self, state, player):

if player == 'MAX':

return self.utils[state]

else:

return -self.utils[state]

def terminal_test(self, state):

return state not in range(13)

def to_move(self, state):

return 'MIN' if state in {1, 2, 3} else 'MAX'

class TicTacToe(Game):

"""Play TicTacToe on an h x v board, with Max (first player) playing 'X'.

A state has the player to move, a cached utility, a list of moves in

the form of a list of (x, y) positions, and a board, in the form of

a dict of {(x, y): Player} entries, where Player is 'X' or 'O'."""

def __init__(self, h=3, v=3, k=3):

self.h = h

self.v = v

self.k = k

moves = [(x, y) for x in range(1, h + 1)

for y in range(1, v + 1)]

self.initial = GameState(to_move='X', utility=0, board={}, moves=moves)

def actions(self, state):

"""Legal moves are any square not yet taken."""

return state.moves

def result(self, state, move):

if move not in state.moves:

return state # Illegal move has no effect

board = state.board.copy()

board[move] = state.to_move

moves = list(state.moves)

moves.remove(move)

return GameState(to_move=('O' if state.to_move == 'X' else 'X'),

utility=self.compute_utility(board, move, state.to_move),

board=board, moves=moves)

def utility(self, state, player):

"""Return the value to player; 1 for win, -1 for loss, 0 otherwise."""

return state.utility if player == 'X' else -state.utility

def terminal_test(self, state):

"""A state is terminal if it is won or there are no empty squares."""

return state.utility != 0 or len(state.moves) == 0

def display(self, state):

board = state.board

for x in range(1, self.h + 1):

for y in range(1, self.v + 1):

print(board.get((x, y), '.'), end=' ')

print()

def compute_utility(self, board, move, player):

"""If 'X' wins with this move, return 1; if 'O' wins return -1; else return 0."""

if (self.k_in_row(board, move, player, (0, 1)) or

self.k_in_row(board, move, player, (1, 0)) or

self.k_in_row(board, move, player, (1, -1)) or

self.k_in_row(board, move, player, (1, 1))):

return +1 if player == 'X' else -1

else:

return 0

def k_in_row(self, board, move, player, delta_x_y):

"""Return true if there is a line through move on board for player."""

(delta_x, delta_y) = delta_x_y

x, y = move

n = 0 # n is number of moves in row

while board.get((x, y)) == player:

n += 1

x, y = x + delta_x, y + delta_y

x, y = move

while board.get((x, y)) == player:

n += 1

x, y = x - delta_x, y - delta_y

n -= 1 # Because we counted move itself twice

return n >= self.k

class ConnectFour(TicTacToe):

"""A TicTacToe-like game in which you can only make a move on the bottom

row, or in a square directly above an occupied square. Traditionally

played on a 7x6 board and requiring 4 in a row."""

def __init__(self, h=7, v=6, k=4):

TicTacToe.__init__(self, h, v, k)

def actions(self, state):

return [(x, y) for (x, y) in state.moves

if x == self.h or (x + 1 , y ) in state.board]

class Gomoku(TicTacToe):

"""Also known as Five in a row."""

def __init__(self, h=15, v=16, k=5):

TicTacToe.__init__(self, h, v, k)

class Backgammon(StochasticGame):

"""A two player game where the goal of each player is to move all the

checkers off the board. The moves for each state are determined by

rolling a pair of dice."""

def __init__(self):

"""Initial state of the game"""

point = {'W': 0, 'B': 0}

board = [point.copy() for index in range(24)]

board[0]['B'] = board[23]['W'] = 2

board[5]['W'] = board[18]['B'] = 5

board[7]['W'] = board[16]['B'] = 3

board[11]['B'] = board[12]['W'] = 5

self.allow_bear_off = {'W': False, 'B': False}

self.direction = {'W': -1, 'B': 1}

self.initial = StochasticGameState(to_move='W',

utility=0,

board=board,

moves=self.get_all_moves(board, 'W'), chance=None)

def actions(self, state):

"""Return a list of legal moves for a state."""

player = state.to_move

moves = state.moves

if len(moves) == 1 and len(moves[0]) == 1:

return moves

legal_moves = []

for move in moves:

board = copy.deepcopy(state.board)

if self.is_legal_move(board, move, state.chance, player):

legal_moves.append(move)

return legal_moves

def result(self, state, move):

board = copy.deepcopy(state.board)

player = state.to_move

self.move_checker(board, move[0], state.chance[0], player)

if len(move) == 2:

self.move_checker(board, move[1], state.chance[1], player)

to_move = ('W' if player == 'B' else 'B')

return StochasticGameState(to_move=to_move,

utility=self.compute_utility(board, move, player),

board=board,

moves=self.get_all_moves(board, to_move), chance=None)

def utility(self, state, player):

"""Return the value to player; 1 for win, -1 for loss, 0 otherwise."""

return state.utility if player == 'W' else -state.utility

def terminal_test(self, state):

"""A state is terminal if one player wins."""

return state.utility != 0

def get_all_moves(self, board, player):

"""All possible moves for a player i.e. all possible ways of

choosing two checkers of a player from the board for a move

at a given state."""

all_points = board

taken_points = [index for index, point in enumerate(all_points)

if point[player] > 0]

if self.checkers_at_home(board, player) == 1:

return [(taken_points[0],)]

moves = list(itertools.permutations(taken_points, 2))

moves = moves + [(index, index) for index, point in enumerate(all_points)

if point[player] >= 2]

return moves

def display(self, state):

"""Display state of the game."""

board = state.board

player = state.to_move

print("current state : ")

for index, point in enumerate(board):

print("point : ", index, " W : ", point['W'], " B : ", point['B'])

print("to play : ", player)

def compute_utility(self, board, move, player):

"""If 'W' wins with this move, return 1; if 'B' wins return -1; else return 0."""

util = {'W': 1, 'B': -1}

for idx in range(0, 24):

if board[idx][player] > 0:

return 0

return util[player]

def checkers_at_home(self, board, player):

"""Return the no. of checkers at home for a player."""

sum_range = range(0, 7) if player == 'W' else range(17, 24)

count = 0

for idx in sum_range:

count = count + board[idx][player]

return count

def is_legal_move(self, board, start, steps, player):

"""Move is a tuple which contains starting points of checkers to be

moved during a player's turn. An on-board move is legal if both the destinations

are open. A bear-off move is the one where a checker is moved off-board.

It is legal only after a player has moved all his checkers to his home."""

dest1, dest2 = vector_add(start, steps)

dest_range = range(0, 24)

move1_legal = move2_legal = False

if dest1 in dest_range:

if self.is_point_open(player, board[dest1]):

self.move_checker(board, start[0], steps[0], player)

move1_legal = True

else:

if self.allow_bear_off[player]:

self.move_checker(board, start[0], steps[0], player)

move1_legal = True

if not move1_legal:

return False

if dest2 in dest_range:

if self.is_point_open(player, board[dest2]):

move2_legal = True

else:

if self.allow_bear_off[player]:

move2_legal = True

return move1_legal and move2_legal

def move_checker(self, board, start, steps, player):

"""Move a checker from starting point by a given number of steps"""

dest = start + steps

dest_range = range(0, 24)

board[start][player] -= 1

if dest in dest_range:

board[dest][player] += 1

if self.checkers_at_home(board, player) == 15:

self.allow_bear_off[player] = True

def is_point_open(self, player, point):

"""A point is open for a player if the no. of opponent's

checkers already present on it is 0 or 1. A player can

move a checker to a point only if it is open."""

opponent = 'B' if player == 'W' else 'W'

return point[opponent] <= 1

def chances(self, state):

"""Return a list of all possible dice rolls at a state."""

dice_rolls = list(itertools.combinations_with_replacement([1, 2, 3, 4, 5, 6], 2))

return dice_rolls

def outcome(self, state, chance):

"""Return the state which is the outcome of a dice roll."""

dice = tuple(map((self.direction[state.to_move]).__mul__, chance))

return StochasticGameState(to_move=state.to_move,

utility=state.utility,

board=state.board,

moves=state.moves, chance=dice)

def probability(self, chance):

"""Return the probability of occurrence of a dice roll."""

return 1 / 36 if chance[0] == chance[1] else 1 / 18

aima-python/games.py at master · aaronsgithub/aima-python · GitHub

Expand file tree

Breadcrumbs

games.py

Latest commit

History

Breadcrumbs

games.py

File metadata and controls