Classic sweep line problem but they wanted the full treatment.
Clarify the problem constraints and edge cases, then propose a sweep-line algorithm using events (start/end) sorted by time, handling ties by processing ends before starts to avoid counting drivers who are not simultaneously online. Implement the algorithm, analyze its O(N log N) time and O(N) space complexity, and discuss potential optimizations or trade-offs.
Pro tip: Mention that you would process end events before start events at the same timestamp to correctly handle intervals that touch but do not overlap, and explicitly state this assumption to show attention to detail.
Ask about interval inclusivity (e.g., whether [start, end] or [start, end) ), duplicate timestamps, and whether N can be very large (e.g., millions). Confirm that intervals are within a single day and that drivers can have multiple intervals.
Select a sweep-line approach: create events for each interval start (+1) and end (-1), sort events by time, and sweep through while maintaining a running count and tracking the maximum. Alternatively, use a difference array if timestamps are bounded and small.
When multiple events share the same timestamp, process all end events before start events to ensure that intervals that merely touch are not counted as overlapping. Also handle empty input, single interval, and all intervals overlapping.
Write clean code for the sweep-line algorithm, using a list of tuples (time, delta) and sorting. Test with provided examples and edge cases like duplicate timestamps and zero-length intervals.
State that sorting takes O(N log N) time and O(N) space for events. Compare with alternative approaches like difference array (O(N + T) time, O(T) space) and explain when each is preferable based on constraints.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the streaming model: are updates append-only or can they modify/delete existing intervals? Then outline a data structure that supports efficient insertion, deletion, and overlap queries under incremental updates, discussing trade-offs between simplicity and performance. Finally, address how to handle corrections (e.g., versioning or tombstones) and ensure the solution remains scalable and consistent.
Pro tip: Mention that you would first ask about the expected update frequency and query patterns to choose the right data structure—this shows you prioritize requirements over premature optimization. Also, highlight the importance of idempotency and ordering when dealing with corrections, as it's a common pitfall in streaming systems.
Ask about the nature of updates (append, modify, delete), expected throughput, latency requirements, and whether intervals have unique IDs. This determines the appropriate data structure and consistency model.
Propose a balanced BST (e.g., interval tree) or a skip list to support O(log n) insertions, deletions, and overlap queries. Discuss alternatives like segment trees or hash maps with sorted lists, and their trade-offs.
For corrections, use versioning or tombstones to mark old intervals as invalid, and ensure queries ignore them. Discuss how to handle out-of-order updates, possibly with a buffer or watermark.
Address partitioning, replication, and concurrency control if the system is distributed. Mention eventual consistency vs. strong consistency and how to maintain correctness under concurrent updates.
Compare the proposed approach with simpler solutions (e.g., rebuilding the index periodically) and explain when each is appropriate. Highlight the balance between complexity, performance, and maintainability.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.