tictactoe.py

"""
Tic Tac Toe Player
"""

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.
    """
    numX, numO = 0, 0
    for row in board:
        for cell in row:
            if cell == X:
                numX += 1
            elif cell == O:
                numO += 1
    
    if numX > numO:
        return O
    elif not terminal(board) and numX == numO:
        return X
    else:
        return None

def actions(board):
    """
    Returns set of all possible actions (i, j) available on the board.
    """
    result = set()

    for i in range(3):
        for j in range(3):
            if board[i][j] == EMPTY:
                result.add((i, j))
    return result

def result(board, action):
    """
    Returns the board that results from making move (i, j) on the board.
    """

    if terminal(board):
        raise ValueError("Game over.")
    elif action not in actions(board):
        raise ValueError("Invalid action.")
    else:
        p = player(board)
        result_board = copy.deepcopy(board)
        (i, j) = action
        result_board[i][j] = p

    return result_board

def winner(board):
    """
    Returns the winner of the game, if there is one.
    """
    
    if board[0][0] == board[0][1] == board[0][2] != None:
        if board[0][0] == X:
            return X
        else:
            return O
    elif board[1][0] == board[1][1] == board[1][2] != None: 
        if board[1][0] == X:
            return X
        else:
            return O
    elif board[2][0] == board[2][1] == board[2][2] != None:
        if board[2][0] == X:
            return X
        else:
            return O
    elif board[0][0] == board[1][0] == board[2][0] != None:
        if board[0][0] == X:
            return X
        else:
            return O
    elif board[0][1] == board[1][1] == board[2][1] != None:
        if board[0][1] == X:
            return X
        else:
            return O
    elif board[0][2] == board[1][2] == board[2][2] != None:
        if board[0][2] == X:
            return X
        else:
            return O
    elif board[0][0] == board[1][1] == board[2][2] != None:
        if board[0][0] == X:
            return X
        else:
            return O
    elif board[0][2] == board[1][1] == board[2][0] != None:
        if board[0][2] == X:
            return X
        else:
            return O
    else:
        return None

def terminal(board):
    """
    Returns True if game is over, False otherwise.
    """

    # Someone won
    if winner(board) != None:
        return True
    
    # All cells were filled
    for row in board:
        for cell in row:
            if cell == EMPTY:
                return False
    return True


def utility(board):
    """
    Returns 1 if X has won the game, -1 if O has won, 0 otherwise.
    """

    w = winner(board)
    if w == X:
        return 1
    elif w == O:
        return -1
    else:
        return 0


def minimax(board):
    """
    Returns the optimal action for the current player on the board.
    """
    p = player(board)

    # If empty board is provided as input, return corner.
    if board == [[EMPTY]*3]*3:
        return (0,0)

    if p == X:
        v = float("-inf")
        selected_action = None
        for action in actions(board):
            minValueResult = minValue(result(board, action))
            if minValueResult > v:
                v = minValueResult
                selected_action = action
    elif p == O:
        v = float("inf")
        selected_action = None
        for action in actions(board):
            maxValueResult = maxValue(result(board, action))
            if maxValueResult < v:
                v = maxValueResult
                selected_action = action

    return selected_action
    
def maxValue(board):
    if terminal(board):
        return utility(board)
    v = float("-inf")
    for action in actions(board):
        v = max(v, minValue(result(board, action)))
    
    return v

def minValue(board):
    if terminal(board):
        return utility(board)
    v = float("inf")
    for action in actions(board):
        v = min(v, maxValue(result(board, action)))

    return v