Room Availability Queries

Meeting rooms: using provided methods, identify which rooms are free and when.

Asked in the Phone interview stage. Also asked to identify free time for query ingestion and sort intervals to minimize LLM processing time.

Output

1. One row per room and free time interval.
2. Return room_name, free_start, and free_end.
3. Include only gaps where the room is not booked.
4. Sort by room_name, then free_start, then free_end.
5. If a room has no bookings, return its full available day as one free interval.