Assign bookings to minimum tennis courts

You are given a list of tennis court bookings. Each booking has a start time and an end time.

Task

Return an assignment plan that:

1. Assigns each booking to a specific court (e.g., court IDs 1..k ).
2. Ensures no court has overlapping bookings .
3. Uses the minimum number of courts (assume unlimited courts are available).

You may return:

• The minimum number of courts needed, and
• An array of court IDs aligned with the input bookings (i.e., assignment[i] is the court used by booking i ).

Follow-up: Maintenance buffer

After a booking ends, the court is unavailable for a fixed maintenance time M (e.g., minutes). That means a booking [s2, e2] can reuse the same court after booking [s1, e1] only if:

• s2 >= e1 + M

Update your approach to support this requirement.

Notes / Assumptions

• Time can be treated as integers.
• You should aim for an efficient solution (e.g., for large n ).