The overlap part is what trips you up if you're not careful.
First, clarify the problem statement and input/output formats with the interviewer, including edge cases like zero-duration orders and overlapping intervals. Then, propose a sweep-line algorithm that processes start and end events in sorted order, tracking the number of active orders to compute earnings per segment. Finally, analyze time and space complexity, and discuss test cases covering various overlap scenarios.
Pro tip: Explicitly discuss how you would handle large inputs and whether the rate is per-minute or per-second, showing attention to real-world constraints and scalability.
Ask the interviewer to confirm the input format (e.g., list of [start, end] pairs, time units) and output format (e.g., total earnings as a number). Discuss edge cases like zero-length orders, negative times, and whether orders can start and end at the same time.
Propose a sweep-line approach: create events for each order's start (+1) and end (-1), sort them by time, and iterate while maintaining the active order count. For each interval between consecutive events, add (time difference) * rate * active_count to total earnings.
State that sorting takes O(n log n) time, and the sweep takes O(n) time, so overall O(n log n) time. Space complexity is O(n) for storing events.
Cover cases: no orders, single order, non-overlapping orders, fully overlapping orders, partially overlapping orders, and orders with same start/end times. Also test with zero-duration orders and large inputs.
Mention alternative approaches like sorting intervals and using a priority queue, but highlight that sweep-line is optimal. Discuss handling of large inputs and potential integer overflow.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.