Time Taken to Cross the Door

Determine the minimum time for a set of people/tasks to all pass through a single constrained doorway (with per-person crossing times, ordering/arrival constraints and limited concurrency or door availability), where you must schedule crossings to respect overlaps and door state. This requires event-driven simulation or a feasibility check (often via greedy scheduling or binary search on time with priority queues) to handle timing conflicts and minimize total completion time.