Took me a minute to realize this was just interval union under a different costume.
Start by clarifying the problem: intervals are per courier, pay is per minute of active time, and overlaps within a courier's intervals should be merged. Then propose an algorithm: for each courier, sort intervals by start time and merge overlapping ones, summing the merged durations. Finally, multiply the total active minutes by the flat rate to get the salary.
Pro tip: Mention that you would handle edge cases like zero-length intervals, intervals that touch at endpoints (e.g., [1,2] and [2,3] should be merged if they are contiguous), and large inputs by using efficient sorting (O(n log n)). Also, discuss whether to process couriers independently or in parallel for scalability.
Confirm that intervals are half-open [start, end) or inclusive, and that overlapping or contiguous intervals should be merged. Ask about input format, constraints, and expected output.
For each courier, collect all intervals, sort them by start time, and iterate through to merge overlapping intervals. Keep track of the merged intervals or directly accumulate total active minutes.
Sum the lengths of the merged intervals to get total active minutes. Multiply by the flat rate per minute to compute the courier's salary.
Discuss time complexity: O(n log n) per courier due to sorting, where n is the number of intervals for that courier. Space complexity O(n) for storing intervals. Consider if intervals can be processed in a streaming fashion or if couriers can be processed in parallel.
Walk through examples: no overlaps, full overlap, contiguous intervals, zero-length intervals, and large numbers of intervals. Verify that the algorithm handles them correctly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.