I got the brute force pretty fast, keep a list, scan everything.
Start by clarifying requirements and constraints, then propose a data structure like a balanced BST or sorted list to store bookings, enabling efficient insertion and lookup. For finding the earliest available slot, consider using a tree to find the first booking after the given time and check gaps, or maintain a separate structure for free slots. Discuss time complexity trade-offs and potential optimizations like interval trees or segment trees.
Pro tip: Mention that real-world systems often use a combination of data structures (e.g., a balanced BST for bookings and a min-heap for free slots) and that concurrency control is crucial for correctness in multi-user scenarios.
Ask about expected number of bookings, frequency of operations, concurrency needs, and whether bookings can be modified or cancelled. This guides data structure choice.
Propose using a balanced binary search tree (e.g., Red-Black Tree) or a sorted list (if insertions are infrequent) to store intervals, allowing O(log n) insertion and efficient overlap checks.
Given a start time and duration, traverse the tree to find the first booking that ends after the start time, then check if the gap before it fits the duration. If not, move to the next booking and repeat.
Consider maintaining a separate structure for free slots (e.g., a min-heap of gaps) or using an interval tree to quickly query overlapping bookings. Discuss trade-offs in update complexity.
Compare time complexities: O(log n) for insertion and O(k log n) for lookup where k is number of overlapping bookings. Discuss space-time trade-offs and scalability.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.