The per-user structure is what saves you here.
First, clarify the problem constraints and edge cases, then propose an efficient algorithm that leverages the sorted order of both lists. A common approach is to group events by user and then use a two-pointer technique to find the closest pair for each user, achieving O(n + m) time after grouping.
Pro tip: Mention that if the lists are too large to fit in memory, you can process them in a streaming fashion by reading both lists in parallel and maintaining the last seen event per user, which shows awareness of scalability.
Ask about input size, memory limits, whether timestamps are integers, and if multiple events per user are possible. Confirm the output format (e.g., return the pair or just the time difference).
Explain that you will group events by user, then for each user find the closest pair using a two-pointer technique on the sorted timestamps. Alternatively, if memory is a concern, describe a streaming merge approach.
For each user, maintain two pointers (one for orders, one for impressions) and advance the pointer with the smaller timestamp, updating the minimum difference. This works because both lists are sorted by timestamp within each user.
State time complexity: O(n + m) after grouping, where n and m are the number of events. Discuss edge cases: users with only one event type, empty lists, duplicate timestamps, and ties.
Walk through a small example to verify correctness, such as orders: [(1,10), (1,20)], impressions: [(1,15), (1,25)] -> closest pair (20,15) with diff 5.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.