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minimax_tictactoe.py
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minimax_tictactoe.py
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"""
Tic Tac Toe Player
"""
import copy
import math
import random
X = "X"
O = "O"
EMPTY = None
def all_cells_filled(board):
count = 0
for i in range(3):
for j in range(3):
if (board[i][j]) != EMPTY:
count += 1
if count == 9:
return True
return False
def initial_state():
"""
Returns starting state of the board.
"""
return [[EMPTY, EMPTY, EMPTY],
[EMPTY, EMPTY, EMPTY],
[EMPTY, EMPTY, EMPTY]]
def player(board):
"""
Returns player who has the next turn on a board.
"""
if board == initial_state():
return X
x_count = 0
o_count = 0
for i in range(3):
for j in range(3):
if board[i][j] == X:
x_count += 1
elif board[i][j] == O:
o_count += 1
if x_count == o_count:
return X
else:
return O
def actions(board):
"""
Returns set of all possible actions (i, j) available on the board.
"""
actions = []
for i in range(3):
for j in range(3):
if board[i][j] == EMPTY:
actions.append((i,j))
return actions
def result(board, action):
"""
Returns the board that results from making move (i, j) on the board.
"""
board_copy = copy.deepcopy(board)
try:
if board_copy[action[0]][action[1]] == EMPTY:
board_copy[action[0]][action[1]] = player(board)
return board_copy
except:
raise Exception("Invalid Move")
def winner(board):
"""
Returns the winner of the game, if there is one.
"""
# Horizontal
for row in board:
x_count = row.count(X)
o_count = row.count(O)
if x_count == 3:
return X
elif o_count == 3:
return O
# Vertical
for i in range(3):
x_count = 0
o_count = 0
for j in range(3):
if board[j][i] == X:
x_count += 1
elif board[j][i] == O:
o_count += 1
if x_count == 3:
return X
elif o_count == 3:
return O
# Diagonals
if board[0][0] == board[1][1] == board[2][2] == X:
return X
elif board[0][0] == board[1][1] == board[2][2] == O:
return O
elif board[0][2] == board[1][1] == board[2][0] == X:
return X
elif board[0][2] == board[1][1] == board[2][0] == O:
return O
return None
def terminal(board):
"""
Returns True if game is over, False otherwise.
"""
if all_cells_filled(board) and winner(board) == None:
return True
if winner(board) == X or winner(board) == O:
return True
elif winner(board) is not None:
return False
def utility(board):
"""
Returns 1 if X has won the game, -1 if O has won, 0 otherwise.
"""
if winner(board) == X:
return 1
elif winner(board) == O:
return -1
else:
return 0
def minimax(board):
"""
Returns the optimal action for the current player on the board.
"""
act = None
if board == initial_state():
act = random.choice(actions(board))
return act
elif player(board) == X:
v = -math.inf
for action in actions(board):
v_new = min_value(result(board, action))
if v_new > v:
v = v_new
act = action
else:
v = math.inf
for action in actions(board):
v_new = max_value(result(board, action))
if v_new < v:
v = v_new
act = action
return act
def max_value(board):
if terminal(board):
return utility(board)
v = -math.inf
for action in actions(board):
v = max(v, min_value(result(board, action)))
return v
def min_value(board):
if terminal(board):
return utility(board)
v = math.inf
for action in actions(board):
v = min(v, max_value(result(board, action)))
return v