The interval scheduling part felt familiar but the strict assignment policy is where I got tripped up.
Clarify the deterministic policy and edge cases, then outline an efficient algorithm using sorting and a min-heap of free car numbers. Simulate the assignment process while tracking booking counts per car, and finally return the car with the most bookings (smallest index on tie).
Pro tip: Mention that the half-open interval [start, end) means a car is free at the exact end time, so when processing bookings sorted by start, you must release cars whose end <= current start. Also, emphasize that the deterministic tie-breaking (start, end, index) ensures consistent output, which is crucial for testing.
Confirm the sorting criteria, tie-breaking rules, and interval semantics (half-open). Discuss edge cases like empty input, simultaneous start/end, and multiple bookings with identical start and end.
Sort bookings by (start, end, original index). Use a min-heap to track free car numbers and a min-heap (or sorted structure) to track busy cars by end time. Simulate assignments, releasing cars when their end <= current start.
Iterate through sorted bookings: release all cars with end <= current start, assign the lowest-numbered free car (or create a new one if none free), and increment that car's booking count. Record the car's end time in the busy heap.
After processing all bookings, find the car with the maximum booking count. If multiple cars tie, return the smallest car number.
State time complexity O(n log n) due to sorting and heap operations, and space O(n). Walk through a small example to verify correctness, including tie-breaking.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.