aima-python/games.py at aima3python2 · prango/aima-python · GitHub

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

"""

from utils import *

import random

#______________________________________________________________________________

# Minimax Search

def minimax_decision(state, game):

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

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

player = game.to_move(state)

def max_value(state):

if game.terminal_test(state):

return game.utility(state, player)

v = -infinity

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 = infinity

for a in game.actions(state):

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

return v

# Body of minimax_decision:

return argmax(game.actions(state),

lambda a: min_value(game.result(state, a)))

#______________________________________________________________________________

def alphabeta_full_search(state, game):

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

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

player = game.to_move(state)

def max_value(state, alpha, beta):

if game.terminal_test(state):

return game.utility(state, player)

v = -infinity

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 = infinity

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 alphabeta_search:

return argmax(game.actions(state),

lambda a: min_value(game.result(state, a),

-infinity, infinity))

def alphabeta_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)

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

if cutoff_test(state, depth):

return eval_fn(state)

v = -infinity

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 = infinity

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 alphabeta_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))

return argmax(game.actions(state),

lambda a: min_value(game.result(state, a),

-infinity, infinity, 0))

#______________________________________________________________________________

# Players for Games

def query_player(game, state):

"Make a move by querying standard input."

game.display(state)

return num_or_str(raw_input('Your move? '))

def random_player(game, state):

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

return random.choice(game.actions(state))

def alphabeta_player(game, state):

return alphabeta_search(state, game)

def play_game(game, *players):

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

>>> play_game(Fig52Game(), alphabeta_player, alphabeta_player)

"""

state = game.initial

while True:

for player in players:

move = player(game, state)

state = game.result(state, move)

if game.terminal_test(state):

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

#______________________________________________________________________________

# 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."

abstract

def result(self, state, move):

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

abstract

def utility(self, state, player):

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

abstract

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 '<%s>' % self.__class__.__name__

class Fig52Game(Game):

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

>>> g = Fig52Game()

>>> minimax_decision('A', g)

'a1'

>>> alphabeta_full_search('A', g)

'a1'

>>> alphabeta_search('A', g)

'a1'

"""

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 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 if_(state in 'BCD', 'MIN', '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):

update(self, h=h, v=v, k=k)

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

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

self.initial = Struct(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 Struct(to_move=if_(state.to_move == 'X', 'O', '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 if_(player == 'X', state.utility, -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), '.'),

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

"If X wins with this move, return 1; if O 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 if_(player == 'X', +1, -1)

else:

return 0

def k_in_row(self, board, move, player, (delta_x, delta_y)):

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

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 y == 0 or (x, y-1) in state.board]

__doc__ += random_tests("""

>>> play_game(Fig52Game(), random_player, random_player)

>>> play_game(TicTacToe(), random_player, random_player)

""")

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