tictactoe.py

"""
Tic Tac Toe Player
"""

import math

X = "X"
O = "O"
EMPTY = None


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.
    """
    x_count = 0
    o_count = 0
    for row in board:
        for cell in row:
            if cell == X:
                x_count += 1
            elif cell == 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.
    """
    possible_actions = set()
    for i in range(3):
        for j in range(3):
            if board[i][j] == EMPTY:
                possible_actions.add((i, j))
    return possible_actions


def result(board, action):
    """
    Returns the board that results from making move (i, j) on the board.
    """
    if action[0] < 0 or action[0] > 2 or action[1] < 0 or action[1] > 2:
        raise Exception("Invalid move: out of bounds")
    new_board = [row.copy() for row in board]
    if new_board[action[0]][action[1]] != EMPTY:
        raise Exception("Invalid move: cell already occupied")
    new_board[action[0]][action[1]] = player(board)
    return new_board


def winner(board):
    """
    Returns the winner of the game, if there is one.
    """
    # Check rows
    for row in board:
        if row.count(row[0]) == 3 and row[0] != EMPTY:
            return row[0]

    # Check columns
    for col in range(3):
        check = []
        for row in board:
            check.append(row[col])
        if check.count(check[0]) == 3 and check[0] != EMPTY:
            return check[0]

    # Check diagonals
    if board[0][0] == board[1][1] == board[2][2] and board[0][0] != EMPTY:
        return board[0][0]
    if board[0][2] == board[1][1] == board[2][0] and board[0][2] != EMPTY:
        return board[0][2]

    return None


def terminal(board):
    """
    Returns True if game is over, False otherwise.
    """
    if winner(board) is not None:
        return True
    for row in board:
        if EMPTY in row:
            return False
    return True


def utility(board):
    """
    Returns 1 if X has won the game, -1 if O has won, 0 otherwise.
    """
    winner_result = winner(board)
    if winner_result == X:
        return 1
    elif winner_result == O:
        return -1
    else:
        return 0


def minimax(board):
    """
    Returns the optimal action for the current player on the board.
    """
    if terminal(board):
        return None

    current_player = player(board)
    if current_player == X:
        best_value = -math.inf
        best_action = None
        for action in actions(board):
            new_board = result(board, action)
            value = min_value(new_board)
            if value > best_value:
                best_value = value
                best_action = action
        return best_action
    else:
        best_value = math.inf
        best_action = None
        for action in actions(board):
            new_board = result(board, action)
            value = max_value(new_board)
            if value < best_value:
                best_value = value
                best_action = action
        return best_action


def max_value(board):
    if terminal(board):
        return utility(board)
    value = -math.inf
    for action in actions(board):
        new_board = result(board, action)
        value = max(value, min_value(new_board))
    return value


def min_value(board):
    if terminal(board):
        return utility(board)
    value = math.inf
    for action in actions(board):
        new_board = result(board, action)
        value = min(value, max_value(new_board))
    return value