tictactoe.py

import math
import copy

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 = sum(row.count(X) for row in board)
    O_count = sum(row.count(O) for row in board)
    return X if X_count <= O_count else O


def actions(board):
    """
    Returns set of all possible actions (i, j) available on the board.
    """
    possible_set = set()
    for i in range(3):
        for j in range(3):
            if board[i][j] == EMPTY:
                possible_set.add((i, j))
    return possible_set


def result(board, action):
    """
    Returns the board that results from making move (i, j) on the board.
    """
    if board[action[0]][action[1]] != EMPTY:
        raise ValueError("Invalid action")

    new_board = copy.deepcopy(board)
    new_board[action[0]][action[1]] = player(board)
    return new_board


def winner(board):
    """
    Returns the winner of the game, if there is one.
    """
    for i in range(3):
        if board[i][0] == board[i][1] == board[i][2] and board[i][0] is not None:
            return board[i][0]
        if board[0][i] == board[1][i] == board[2][i] and board[0][i] is not None:
            return board[0][i]

    if board[0][0] == board[1][1] == board[2][2] and board[0][0] is not None:
        return board[0][0]
    if board[0][2] == board[1][1] == board[2][0] and board[0][2] is not None:
        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
    if all(cell is not EMPTY for row in board for cell in row):
        return True
    return False


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

    return move


def max_value(board):
    if terminal(board):
        return utility(board), None

    v = -math.inf
    best_move = None
    for action in actions(board):
        min_val, _ = min_value(result(board, action))
        if min_val > v:
            v = min_val
            best_move = action

    return v, best_move


def min_value(board):
    if terminal(board):
        return utility(board), None

    v = math.inf
    best_move = None
    for action in actions(board):
        max_val, _ = max_value(result(board, action))
        if max_val < v:
            v = max_val
            best_move = action

    return v, best_move


# Example usage:
current_board = initial_state()
optimal_move = minimax(current_board)
print(f"The optimal move is: {optimal_move}")