在编程计算机下棋时如何为棋盘建模？

class Gomoku:
    def __init__(self, size=15):
        self.size = size
        self.board = [[0] * size for _ in range(size)]
        self.players = [1, 2]
        self.winning_length = 5

    def is_valid_move(self, x, y, player):
        if self.board[x][y] != 0:
            return False
        self.board[x][y] = player
        if self.check_winner(x, y, player):
            return True
        self.board[x][y] = 0
        return False

    def check_winner(self, x, y, player):
        directions = [(0, 1), (1, 0), (1, 1), (1, -1)]
        for dx, dy in directions:
            count = 1
            for direction in [-1, 1]:
                for step in range(1, self.winning_length):
                    row, col = x + step * dx * direction, y + step * dy * direction
                    if (
                        row < 0
                        or row >= self.size
                        or col < 0
                        or col >= self.size
                        or self.board[row][col] != player
                    ):
                        break
                    count += 1
            if count >= self.winning_length:
                return True
        return False

    def print_board(self):
        print("   ", end="")
        for i in range(self.size):
            print(chr(ord("a") + i), end=" ")
        print()
        for i in range(self.size):
            print("{:2d}".format(i + 1), end=" ")
            for j in range(self.size):
                if self.board[i][j] == 0:
                    print(".", end=" ")
                elif self.board[i][j] == 1:
                    print("X", end=" ")
                else:
                    print("O", end=" ")
            print()

    def play(self):
        current_player = 0
        while True:
            self.print_board()
            x, y = map(int, input("Player {} enters row and col (1-15): ".format(self.players[current_player])).split())
            x -= 1
            y -= 1
            if self.is_valid_move(x, y, self.players[current_player]):
                self.print_board()
                if self.check_winner(x, y, self.players[current_player]):
                    print("Player {} wins!".format(self.players[current_player]))
                    break
                if current_player == 0:
                    current_player = 1
                else:
                    current_player = 0
            else:
                print("Invalid move, try again.")