我正在尝试实现一个极小极大算法来创建一个井字游戏机器人，但我遇到了递归错误

Question

I'm trying to implement a minimax algorithm to create a tic-tac-toe bot, but i'm getting RecursionError: maximum recursion depth exceeded in comparison error. I have the code below. I've added comments that mention what a function is supposed to do. I last Can you take a look at the code below. Thank you

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.
    """
    o_counter = 0
    x_counter = 0
    for i in board:
        for j in i:
            if j == 'X':
                x_counter += 1
            elif j == 'O':
                o_counter += 1
    if x_counter == 0 and o_counter == 0:
        return 'O'
    elif x_counter > o_counter:
        return 'O'
    elif o_counter > x_counter:
        return 'X'



def actions(board):
    """
    Returns set of all possible actions (i, j) available on the board.
    """
    action = []
    for i in range(3):
        for j in range(3):
            if board[i][j] is None:
                action.append([i, j])
    return action


def result(board, action):
    """
    Returns the board that results from making move (i, j) on the board.
    """
    p = player(board)
    i, j = action
    board[i][j] = p
    return board


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

        elif board[0][0] == board[1][0] == board[2][0] and (board[0][0] == 'X' or board[0][0] == 'O'):
            return board[0][0]
        elif board[0][i] == board[1][i] == board[2][i] and (board[0][i] == 'X' or board[0][i] == 'O'):
            return board[0][i]
        elif board[0][2] == board[1][2] == board[2][2] and (board[0][2] == 'X' or board[0][2] == 'O'):
            return board[0][2]

def terminal(board):
    """
    Returns True if game is over, False otherwise.
    """
    check = True
    if winner(board) == 'X' or winner(board) == 'O':
        return True
    elif check:
        for i in board:
            for j in i:
                if j is None:
                    check = False
                    return False
        if check:
            return True
    else:
        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 maximum(board):
    if terminal(board):
        return utility(board)
    v = -9999999999999999999999
    for action in actions(board):
        m = minimum(result(board, action))
        if m > v:
            v = m
    return v


def minimum(board):
    if terminal(board):
        return utility(board)
    v = 9999999999999999999999
    for action in actions(board):
        m = maximum(result(board, action))
        if m < v:
            v = m
    return v


def minimax(board):
    """
    Returns the optimal action for the current player on the board.
    """
    return_action = None
    curr_player = player(board)
    states = actions(board)
    temp_board = board.copy()
    score = 0
    temp_score = 0
    for state in states:
        i, j = state
        if curr_player == 'X':
            temp_board[i][j] = curr_player
            temp_score = maximum(temp_board)
        elif curr_player == 'O':
            temp_board[i][j] = curr_player
            temp_score = minimum(temp_board)
        if curr_player == 'X':
            if temp_score > score:
                score = temp_score
                return_action = state
        elif curr_player == 'O':
            if temp_score < score:
                score = temp_score
                return_action = state

    return  return_action

Answer 1

Your issue is your stuck in an infinite condition which means you keep recursively calling the function till you reach the recursion limit. Your issue comes in your player function and how you decide whos turn is next. After O plays in position 0,0 and X plays in position 0,1 you then try to decide who is next to play

So you count and both O and X have placed 1 token each. However your logic to decide who is next doesnt cater for this board state.

    if x_counter == 0 and o_counter == 0:
        return 'O'
    elif x_counter > o_counter:
        return 'O'
    elif o_counter > x_counter:
        return 'X'

so when x_counter and y_counter are equal but are not 0 you dont return anything. This results in None being returned by the function So your stuck and never then place a token in position 0,2. If O always goes first then any time x_counter == o_counter you should return '0' so change it to

    if x_counter == o_counter:
        return 'O'
    elif x_counter > o_counter:
        return 'O'
    elif o_counter > x_counter:
        return 'X'