Tic-Tac-Toe Problem.

"""
Tic Tac Toe Player
"""

import math, copy


X = "X"
O = "O"
EMPTY = None
turn = 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.
    """
    global turn
    x_count = 0
    o_count = 0

    if board == initial_state():
        turn = X
        print(X)
        return X

    for row in range(len(board)):
        for cell in range(len(board[row])):
            if board[row][cell] == X:
                x_count += 1
            elif board[row][cell] == O:
                o_count += 1

    if x_count > o_count:
        turn = O
        print(O)
        return O
    elif x_count < o_count:
        turn = X
        print(X)
        return X


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

    for row in range(len(board)):
        for cell in range(len(board[row])):
            if board[row][cell] == EMPTY:
                poss_actions.append((row, cell))

    return poss_actions


def result(board, action):
    """
    Returns the board that results from making move (i, j) on the board.
    """
    global turn
    copy_board = copy.deepcopy(board)
    row = action[0]
    cell = action[1]
    if turn == X:
        copy_board[row][cell] = X
    elif turn == O:
        copy_board[row][cell] = O
    return copy_board


def winner(board):
    """
    Returns the winner of the game, if there is one.
    """
    for i in range(len(board)):
        if board[i][0] and board[i][1] and board[i][2] == X:
            return X
        elif board[i][0] and board[i][1] and board[i][2] == O:
            return O
        elif board[0][i] and board[1][i] and board[2][i] == X:
            return X
        elif board[0][i] and board[1][i] and board[2][i] == O:
            return O
    if board[0][0] and board[1][1] and board[2][2] == X:
        return X
    elif board[0][0] and board[1][1] and board[2][2] == O:
        return O
    elif board[0][2] and board[1][1] and board[2][0] == X:
        return X
    elif board[0][2] and board[1][1] and board[2][0] == O:
        return O

    return None


def terminal(board):
    """
    Returns True if game is over, False otherwise.
    """
    for row in range(len(board)):
        for cell in range(len(board[row])):
            if board[row][cell] == EMPTY:
                return False

    return True


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
    elif winner(board) == None:
        return 0


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

    print("Called upon.")
    global turn
    current_turn = turn

    #iterate over every possible action in board, and use MAX and MIN VALUE functions
    possible_actions = actions(board)
    v = 0
    opt_action = None

    for action in possible_actions:
        if turn == X:
            maxval = MAX_VALUE(board, action)
            if maxval > v:
                v = maxval
                opt_action = action
            elif maxval == v:
                opt_action = action
        elif turn == O:
            minval = MIN_VALUE(board, action)
            if minval > v:
                v = minval
                opt_action = action
            elif minval == v:
                opt_action = action

    turn = current_turn
    return opt_action


def MAX_VALUE(board, action):
    """
    Returns the max value of the current action.
    """
    global turn
    turn = X
    v = float("-inf")
    new_board = result(board, action)
    pos_actions = actions(new_board)
    if not terminal(new_board):
        for action in pos_actions:
            min_value = MIN_VALUE(new_board, action)
            v = max(v, min_value)
    else:
        min_value = utility(new_board)
        v = max(v, min_value)
    return v


def MIN_VALUE(board, action):
    """
    Returns the min value of the current action.
    """
    global turn
    turn = O
    v = float("inf")
    new_board = result(board, action)
    pos_actions = actions(new_board)
    if not terminal(new_board):
        for action in pos_actions:
            max_value = MAX_VALUE(new_board, action)
            v = min(v, max_value)
    else:
        max_value = utility(new_board)
        v = min(v, max_value)
    return v