from enum import IntEnum, auto

type Coordinate = tuple[int, int]


class PieceType(IntEnum):
    T_JUNCTION = auto()  # Direction is the piece at the "stem" of the T
    STRAIGHT = auto()
    CORNER = auto()  # Direction is the more counter-clockwise connection
    NODE = auto()


class Direction(IntEnum):
    UP = 0
    RIGHT = auto()
    DOWN = auto()
    LEFT = auto()

    @staticmethod
    def from_offset(dx: int, dy: int) -> Direction:
        if (dx != 0 and dy != 0) or abs(dx + dy) != 1:
            raise ValueError(f"({dx}, {dy}) is not a valid direction offset")
        if dx != 0:
            return Direction(dx % 4)
        else:
            return Direction(dy + 1)

    def flip(self) -> Direction:
        return Direction((self + 2) % 4)


class Piece:
    type: PieceType
    direction: Direction
    locked: bool = False

    def __init__(self, type: PieceType, direction: Direction = Direction.UP) -> None:
        self.type = type
        self.direction = direction

    def connected_directions(self) -> list[Direction]:
        match self.type:
            case PieceType.NODE:
                return [self.direction]
            case PieceType.CORNER:
                return [self.direction, Direction((self.direction + 1) % 4)]
            case PieceType.STRAIGHT:
                return [self.direction, Direction((self.direction + 2) % 4)]
            case PieceType.T_JUNCTION:
                return [
                    self.direction,
                    Direction((self.direction + 1) % 4),
                    Direction((self.direction - 1) % 4),
                ]

    def turn_cw(self) -> None:
        if self.locked:
            return
        self.direction = Direction((self.direction + 1) % 4)

    def turn_ccw(self) -> None:
        if self.locked:
            return
        self.direction = Direction((self.direction - 1) % 4)