import random


class MahjongConnect:
    """
    MahjongConnect is a class representing a game board for Mahjong Connect with features like creating the board, checking valid moves, finding paths, removing icons, and checking if the game is over.
    """
    def __init__(self, BOARD_SIZE, ICONS):
        self.BOARD_SIZE = BOARD_SIZE
        self.ICONS = ICONS
        self.board = self.create_board()

    def create_board(self):
        """
        create the game board with the given board size and icons
        :return: 2-dimensional list, the game board
        >>> mc = MahjongConnect([4, 4], ['a', 'b', 'c'])
        >>> mc.create_board()
        mc.board = [['a', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a']]
        """

        board = [[random.choice(self.ICONS) for _ in range(self.BOARD_SIZE[1])] for _ in range(self.BOARD_SIZE[0])]
        return board

    def has_path(self, pos1, pos2):
        """
        check if there is a path between two icons
        :param pos1: position tuple(x, y) of the first icon
        :param pos2: position tuple(x, y) of the second icon
        :return: True or False ,representing whether there is a path between two icons
        >>> mc = MahjongConnect([4, 4], ['a', 'b', 'c'])
        mc.board = [['a', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a']]
        >>> mc.is_valid_move((0, 0), (1, 0))
        True
        """

        visited = set()
        stack = [pos1]

        while stack:
            current_pos = stack.pop()
            if current_pos == pos2:
                return True

            if current_pos in visited:
                continue

            visited.add(current_pos)
            x, y = current_pos

            # Check adjacent positions (up, down, left, right)
            for dx, dy in [(0, 1), (0, -1), (1, 0), (-1, 0)]:
                new_x, new_y = x + dx, y + dy
                if 0 <= new_x < self.BOARD_SIZE[0] and 0 <= new_y < self.BOARD_SIZE[1]:
                    if (new_x, new_y) not in visited and self.board[new_x][new_y] == self.board[x][y]:
                        stack.append((new_x, new_y))

        return False

    def remove_icons(self, pos1, pos2):
        """
        remove the connected icons on the game board
        :param pos1: position tuple(x, y) of the first icon to be removed
        :param pos2: position tuple(x, y) of the second icon to be removed
        :return: None
        >>> mc = MahjongConnect([4, 4], ['a', 'b', 'c'])
        mc.board = [['a', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a']]
        >>> mc.remove_icons((0, 0), (1, 0))
        mc.board = [[' ', 'b', 'c', 'a'],
                    [' ', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a'],
                    ['a', 'b', 'c', 'a']]
        """

        x1, y1 = pos1
        x2, y2 = pos2
        self.board[x1][y1] = ' '
        self.board[x2][y2] = ' '

    def is_game_over(self):
        """
        Check if the game is over (i.e., if there are no more icons on the game board)
        :return: True or False ,representing whether the game is over
        >>> mc = MahjongConnect([4, 4] ['a', 'b', 'c'])
        >>> mc.board = [[' ', ' ', ' ', ' '],
        >>>         [' ', ' ', ' ', ' '],
        >>>         [' ', ' ', ' ', ' '],
        >>>         [' ', ' ', ' ', ' ']]
        >>> mc.is_game_over()
        True
        """

        for row in self.board:
            if any(icon != ' ' for icon in row):
                return False
        return True

Method:
def is_valid_move(self, pos1, pos2):
        x1, y1 = pos1
        x2, y2 = pos2

        # Check if positions are within the game board range
        if not (0 <= x1 < self.BOARD_SIZE[0] and 0 <= y1 < self.BOARD_SIZE[1] and 0 <= x2 < self.BOARD_SIZE[
            0] and 0 <= y2 <
                self.BOARD_SIZE[1]):
            return False

        # Check if the two positions are the same
        if pos1 == pos2:
            return False

        # Check if the two positions have the same icon
        if self.board[x1][y1] != self.board[x2][y2]:
            return False

        # Check if there is a valid path between the two positions
        if not self.has_path(pos1, pos2):
            return False

        return True

Summary: check if the move of two icons is valid (i.e. positions are within the game board range, the two positions are not the same, the two positions have the same icon, and there is a valid path between the two positions)