问题

代码中的问题在于，max_value 和 min_value 函数的递归调用可能返回 None，这会导致比较操作出错。为了解决这个问题，你可以在递归调用之前添加条件，以确保不会返回 None。以下是修改后的代码：

def player(board):
    if Terminal(board) != False:
        return None
    else:
        if turn(board) == "X":
            value, move = max_value(board)
            return move
        else:
            value, move = min_value(board)
            return move

def max_value(board):
    if Terminal(board) != False:
        return Utility(board), None
    else:
        v = -1000
        move = None
        for action in Actions(board):
            aux, act = min_value(Result(board, action))
            print(aux)
            if aux is not None and aux > v:
                v = aux
                move = action
                if v == 1:
                    return v, move
        return v, move

def min_value(board):
    if Terminal(board) != False:
        return Utility(board), None
    else:
        v = 1000
        move = None
        for action in Actions(board):
            aux, act = max_value(Result(board, action))
            print(aux)
            if aux is not None and aux < v:
                v = aux
                move = action
                if v == -1:
                    return v, move
        return v, move

这样，当 aux 为 None 时，不会执行比较操作，从而避免了出现 '>' not supported between instances of 'NoneType' and 'int' 错误。

def player(board):
    if Terminal(board) != False:
        return None
    else:
        if turn(board) == "X":
            value,move = max_value(board)
            return move
        else:
            value,move = min_value(board)
            return move
        
def max_value(board):
    if Terminal(board) != False:
        return Utility(board),None
    else:
        v = -1000
        move = None
        for action in Actions(board):
            aux,act = min_value(Result(board,action))
            print(aux)
            if aux > v:
                v = aux
                move = action
                if v == 1:
                    return v,move
        return v,move

def min_value(board):
    if Terminal(board) != False:
        return Utility(board),None
    else:
        v = 1000
        move = None
        for action in Actions(board):
            aux,act = max_value(Result(board,action))
            print(aux)
            if aux < v:
                v = aux
                move = action
                if v == -1:
                    return v,move
        return v,move

答案1

得分: 0

以下是您要翻译的内容的翻译部分：

"The code you have shared is fine.

The error message indicates that Utility returns None when you call it. This should not happen. Utility should always return an integer when the game is over, and looking at your code it should return -1, 0 or 1.

There is also the possibility that Utility returns None when the game is not over, but that Terminal has a bug such that it returns something else than False even when the game is not over.

Here is an implementation of the functions Terminal and Utility that do not produce the error you got, but make it work as expected.

In fact, I added all missing functions based on a board representation that is a string of 9 characters, and a game loop so you can play against the minimax algorithm:

<details>
<summary>英文:</summary>

The code you have shared is fine. 

The error message indicates that `Utility` returns `None` when you call it. This should not happen. `Utility` should **always** return an integer when the game is over, and looking at your code it should return -1, 0 or 1.

There is also the possibility that `Utility` returns None when the game is not over, but that `Terminal` has a bug such that it returns something else than `False` even when the game is not over.

Here is an implementation of the functions `Terminal` and `Utility` that do not produce the error you got, but make it work as expected.

In fact, I added all missing functions based on a board representation that is a string of 9 characters, and a game loop so you can play against the minimax algorithm:

import re

def Utility(board):
m = re.findall(r"([XO])(?:\1\1(?:...)*$|..\1..\1|...\1...\1|.\1.\1..$)", board)
return -1 if "O" in m else len(m)

def Terminal(board):
return "O X"[Utility(board)+1].strip() or not board.count(".") and "draw"

def turn(board):
return "OX"[board.count(".") % 2]

def Actions(board):
return (i for i in range(9) if board[i] == ".")

def Result(board, action):
return board[:action] + turn(board) + board[action+1:]

board = "." * 9
while True: # Interactive game between human and minimax
print(f"{board[:3]}\n{board[3:6]}\n{board[6:]}")
winner = Terminal(board)
if winner:
print(f"Winner: {winner}")
break
if turn(board) == "X":
action = int(input("Your move (0..8)? "))
if board[action] != ".":
print("Invalid move. Try again.")
continue
else:
action = player(board)
print("minimax chooses", action)
board = Result(board, action)

</details>