Check carpool trip feasibility
Overview
This question evaluates understanding of sweep-line algorithms, interval/event aggregation, and complexity analysis for capacity-constrained scheduling on a one-dimensional route, including handling simultaneous events and edge cases in event ordering.
You are given a list of trips where each trip i is (passengers_i, start_i, end_i) with start_i < end_i on a one-dimensional route. A single vehicle with capacity C moves in the increasing direction only; passengers board at start_i and alight at end_i. Implement can_complete_carpool(trips, C) that returns True iff all trips can be completed without exceeding capacity at any point. Use a sweep-line approach with +passengers at start_i and -passengers at end_i; target time/position complexity O(n log n). Discuss edge cases when multiple events share the same coordinate.