I went straight for the min-heap approach because I'd seen something like it before.
Clarify the problem constraints and edge cases, then propose an efficient solution using a sweep line or priority queue approach. Explain the algorithm step-by-step, analyze time and space complexity, and discuss potential trade-offs.
Pro tip: Mention that sorting by start times and using a min-heap of end times is a common pattern for interval problems, and highlight that the number of rooms equals the maximum number of overlapping meetings at any point.
Ask about input format, whether intervals are inclusive/exclusive, if meetings can be back-to-back, and expected constraints (e.g., number of meetings).
Compare brute-force (check all pairs) with optimized methods like sweep line or min-heap. Explain why the optimized approach is better.
Describe sorting intervals by start time, then using a min-heap to track end times. For each meeting, if the earliest end time is <= current start, reuse a room; otherwise allocate a new one.
State that sorting takes O(n log n) and heap operations take O(n log n), resulting in O(n log n) time and O(n) space.
Walk through a small example to verify correctness and edge cases like empty input or all meetings overlapping.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying requirements: stream is unbounded, K is fixed, need top K by score with tie-breaking by smaller itemId. Then propose a min-heap of size K where the heap ordering is by (score, -itemId) so the root is the worst among the top K, allowing O(log K) updates per item. Discuss trade-offs with alternative approaches like balanced BST or sorted list, and handle edge cases like duplicate itemIds and K=0.
Pro tip: Mention that you can optimize for the common case where the new item's score is less than the heap root's score by doing an O(1) comparison before any heap operation, and discuss how to handle updates to existing items if the stream allows duplicates.
Ask about stream characteristics (unbounded, online), K size, whether itemIds can repeat, and if updates to existing items are allowed. Confirm tie-breaking rule: higher score first, then smaller itemId.
Propose a min-heap of size K. Define the heap comparator: items with lower score are 'smaller'; for equal scores, the item with larger itemId is 'smaller' (so the root is the worst among top K).
For each new (itemId, score): if heap size < K, push; else if (score, -itemId) > (root.score, -root.itemId), pop root and push new item. Otherwise, ignore. This maintains top K.
Time: O(log K) per item worst-case, O(1) for rejected items. Space: O(K). Compare with alternatives: balanced BST (O(log K) but higher constants), sorted array (O(K) insertion), or keeping all items (O(N) space).
Discuss K=0, duplicate itemIds (if updates allowed, need a map from itemId to heap node for O(log K) update), and potential concurrency if stream is parallel. Mention that if K is large, consider a more advanced structure like a Fibonacci heap or a skip list.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.