I got the basic interval-sweep approach pretty quickly: sort events, track active order count, multiply duration by count by rate.
Clarify the input format and edge cases, then propose a sweep-line algorithm that processes events in chronological order, grouping events with the same timestamp and handling all accepts before fulfills. Maintain a running count of active orders and accumulate pay based on the time intervals between consecutive timestamps.
Pro tip: Explicitly state the assumption that pay accrues only during intervals when at least one order is active, and that the active order count changes at event timestamps. This shows you understand the discrete nature of the problem and avoids off-by-one errors.
Ask about input format (e.g., list of events with timestamp, type, order ID), whether timestamps are sorted, and how to handle simultaneous events. Confirm that pay is calculated per minute and that partial minutes are prorated.
Sort events by timestamp if not already sorted. Use a sweep-line approach: iterate through timestamps, and for each timestamp, process all accepts before fulfills. Track the number of active orders and the last processed timestamp.
For each timestamp, before updating active orders, calculate the duration since the last timestamp and multiply by the current active order count and the rate ($0.30/min). Add to total pay. Then update active orders based on events at this timestamp.
Consider cases with no events, all events at the same timestamp, overlapping orders, and orders that start and end at the same timestamp. Walk through a small example to verify correctness.
State time complexity O(n log n) due to sorting (or O(n) if already sorted) and space complexity O(1) extra. Discuss alternative approaches like event-driven simulation and their trade-offs.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.