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I went with a sorted map per court keyed by start time, which let me do a predecessor lookup to check for overlap in O(log n).
Start by clarifying requirements and assumptions (e.g., granularity, time zones, concurrency). Then propose a per-court data structure that maintains non-overlapping intervals, such as a balanced BST or sorted list, and analyze the time complexity of booking, cancelling, and querying. Finally, discuss trade-offs and potential optimizations for scale.
Pro tip: Mention that using a balanced BST (e.g., TreeMap in Java) allows O(log n) operations and that you'd handle concurrency with per-court locks or optimistic concurrency to avoid race conditions.
Ask about expected load, time granularity, whether bookings can span multiple courts, and if concurrent access is a concern. This shows you think about real-world constraints.
Propose a per-court balanced BST (or sorted list) storing intervals keyed by start time. Explain that this keeps intervals ordered and allows efficient overlap checks.
Detail how to implement booking (check for overlap with predecessor/successor, then insert), cancellation (find and remove exact interval), and query (find interval containing the time).
State that all operations are O(log n) for balanced BST, or O(n) for sorted list if using linear search. Mention that query can be O(log n) with binary search.
Compare BST vs. interval tree vs. hash map with bucketing. Address concurrency, persistence, and scaling to multiple courts (e.g., sharding by court ID).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
This is where I started running out of steam.
Start by clarifying the data model and constraints (e.g., court schedules, booking durations, time granularity) and then design an efficient algorithm for finding the next available slot, likely using interval trees or sorted lists. For rescheduling, outline the steps to validate the new slot, update the booking, and handle conflicts, emphasizing trade-offs between time and space complexity.
Pro tip: Discuss how you would handle edge cases like back-to-back bookings, buffer times, and concurrent rescheduling requests, showing you think about real-world robustness. Also, mention how you might extend the solution to support multiple courts or varying slot lengths, demonstrating scalability.
Ask about the granularity of time slots, maximum booking duration, whether courts have operating hours, and if there are buffer times between bookings. Confirm if rescheduling must preserve the original duration and if the new slot must be on the same court.
Propose using a balanced interval tree or a sorted list of bookings per court to quickly find gaps. Consider a segment tree or bitset for discrete time slots if the granularity is fixed (e.g., 15-minute increments).
Outline an algorithm that iterates through existing bookings to find the earliest contiguous free interval of the required length. If using an interval tree, perform a range query to find gaps; if using a sorted list, scan and merge intervals.
Describe the steps: validate the new slot is available and meets constraints, remove the old booking, insert the new booking, and update any indexes. Handle atomicity to avoid race conditions in concurrent environments.
Compare time complexities: interval tree O(log n + k) for queries vs. sorted list O(n) for scanning. Discuss space overhead and whether to precompute availability. Mention potential caching or lazy evaluation for performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.