async def create(conn):
    # Households table
    await conn.execute(
        """
        CREATE TABLE IF NOT EXISTS Household (
            id INTEGER PRIMARY KEY,
            name TEXT NOT NULL,
            slug TEXT NOT NULL UNIQUE
        );
        """
    )

    # Membership table
    await conn.execute(
        """
        CREATE TABLE IF NOT EXISTS HouseholdMember (
            user_id INTEGER NOT NULL,
            household_id INTEGER NOT NULL,
            role TEXT NOT NULL,
            PRIMARY KEY (user_id, household_id),
            FOREIGN KEY(user_id) REFERENCES User(id) ON DELETE CASCADE,
            FOREIGN KEY(household_id) REFERENCES Household(id) ON DELETE CASCADE
        );
        """
    )

    # Invitations table
    await conn.execute(
        """
        CREATE TABLE IF NOT EXISTS HouseholdInvitation (
            id INTEGER PRIMARY KEY,
            household_id INTEGER NOT NULL,
            email TEXT NOT NULL,
            invited_by_user_id INTEGER NOT NULL,
            token TEXT NOT NULL UNIQUE,
            expires_at DATETIME NOT NULL,
            status TEXT NOT NULL,
            FOREIGN KEY(household_id) REFERENCES Household(id) ON DELETE CASCADE,
            FOREIGN KEY(invited_by_user_id) REFERENCES User(id) ON DELETE SET NULL
        );
        """
    )

    # Indices
    await conn.execute("CREATE INDEX IF NOT EXISTS idx_household_slug ON Household(slug);")
    await conn.execute(
        "CREATE INDEX IF NOT EXISTS idx_household_member_household ON HouseholdMember(household_id);"
    )


async def member_ids_in_household(conn, household_id: int, user_ids: list[int]) -> set[int]:
    """Return the subset of user_ids that are members of the given household.

    Uses HouseholdMember join User to ensure users exist.
    """
    if not user_ids:
        return set()
    placeholders = ",".join(["?"] * len(user_ids))
    query = f"""
        SELECT u.id
        FROM HouseholdMember hm
        JOIN User u ON u.id = hm.user_id
        WHERE hm.household_id = ? AND u.id IN ({placeholders})
    """
    valid: set[int] = set()
    async with conn.execute(query, (household_id, *sorted(user_ids))) as c:
        async for row in c:
            valid.add(int(row[0]))
    return valid


async def are_members(conn, household_id: int, user_ids: list[int]) -> bool:
    """True only if all provided user_ids are members of the household."""
    if not user_ids:
        return True
    found = await member_ids_in_household(conn, household_id, user_ids)
    return found == set(user_ids)