Satellite Message Propagation

A graph-simulation OA: model a satellite network where a message floods from Earth, each satellite forwards to its lower-id-first neighbors with a 10s-per-forward cost, then reports back to Earth after a 30s processing delay. Output the order in which satellites report back, with timing tie-breaks. Requirements Process a stream of N instructions and implement the SatelliteNetwork class: SatelliteConnected(satelliteId) — a satellite joins the network. Calling ErrDuplicateSatellite(id) if it connects more than once. RelationshipEstablished(satelliteId1, satelliteId2) — a two-way link. Reference to a non-existent satellite triggers ErrInvalidSatellite(id) and the whole instruction is skipped. MessageReceived(M, id_1, …, id_M) — M satellites simultaneously receive a message from Earth. Protocol: A satellite that receives the message forwards it to each direct connection that hasn't received it yet, in increasing SatelliteId order. Forwarding to one connection is synchronous and atomic and takes exactly 10 seconds; a sender forwards to only one connection at a time. While a forward to some satellite is in progress, other satellites may also attempt to forward to it (also spending 10s), but a satellite never re-notifies one already known to be notified, and never notifies the satellite that notified it. Once all of a satellite's direct connections have been notified, it spends 30 seconds processing, then reports back to Earth by calling OnSatelliteReportedBack(satelliteId). If two satellites report back at the same time, the one with the smaller SatelliteId is first. Notes This is a timed graph traversal: maintain each satellite's notified set and a per-sender serial forwarding timeline, then compute each satellite's report time as (time all its neighbors are notified) + 30s. The subtle parts are the per-sender atomic 10s queue (a satellite with many neighbors forwards sequentially) and the simultaneous-report tie-break by id. Output is the report order keyed by report timestamp, emitted via OnSatelliteReportedBack in order. Preparation Model the event timeline explicitly (priority queue of forward-completion events) rather than a plain BFS, since edge traversal has duration and per-sender serialization. Test simultaneous notifications (multiple seeds in one MessageReceived) and the id tie-break on equal report times.