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def minimax(board, depth, alpha, beta, maximizing_player, player):
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    terminal, score = is_terminal(board, player)
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    if depth == 0 or terminal:
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        return score if terminal else evaluate(board, player)
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    possible_moves = get_possible_moves(board)
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    if maximizing_player:  # AI（最大化玩家）
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        max_eval = -float('inf')
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        for move in possible_moves:
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            i, j = move
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            board[i][j] = player
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            eval_score = minimax(board, depth - 1, alpha, beta, False, player)
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            board[i][j] = 0  # 回溯
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            max_eval = max(max_eval, eval_score)
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            alpha = max(alpha, eval_score)
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            if beta <= alpha:
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                break  # Alpha-Beta剪枝
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        return max_eval
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    else:
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        min_eval = float('inf')
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        for move in possible_moves:
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            i, j = move
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            board[i][j] = -player
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            eval_score = minimax(board, depth - 1, alpha, beta, True, player)
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            board[i][j] = 0
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            min_eval = min(min_eval, eval_score)
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            beta = min(beta, eval_score)
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            if beta <= alpha:
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                break
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        return min_eval