Problem Description

You are tasked with implementing a monitoring component designed to track numerous concurrent simulations. This component will process a continuous stream of events, identify simulations that have timed out, and report them.

Event Structure and Semantics

Each simulation produces event objects with the following structure:

• sim_id (string or integer): A unique identifier for the simulation.
• type (string): Indicates the event type, one of "start", "ping", or "end".
• timestamp (integer or long): The event time in seconds or milliseconds, guaranteed to be monotonically non-decreasing across all events.

The semantics for each event type are:

• start: The simulation sim_id has begun at this timestamp. Its last activity timestamp is set to this timestamp.
• ping: The simulation sim_id is still active. Its last activity timestamp is updated to this timestamp.
• end: The simulation sim_id has completed normally at this timestamp. It should no longer be considered active.

Timeout Condition

You are provided with a timeout limit T (e.g., 3 seconds). A simulation is considered timed out and automatically ended if its inactivity duration exceeds T. Specifically, a simulation sim_id times out if:

current_time - last_activity_timestamp(sim_id) > T

where current_time is the timestamp of the most recently processed event.

processEvent Function

Design a function, processEvent(event), that receives events one by one in chronological order. Upon receiving a new event with timestamp ts_current, it must perform the following actions:

1. Update State: Adjust the internal state based on the incoming event (start, ping, or end).
2. Identify Timeouts: Determine which simulations have just become timed out at or before ts_current. These are simulations that:
   • Are currently active (not previously ended by an end event or a prior timeout).
   • Satisfy the timeout condition: ts_current - last_activity_timestamp > T.
3. Mark as Ended: Mark these newly timed-out simulations as ended so they are not reported again.
4. Return Timed-Out IDs: Return a set or list of all sim_ids that have just been identified as timed out.

Performance and Implementation Constraints

• The function must be efficient for a large number of concurrent simulations and events.
• Aim for a time complexity close to O(log n) per event, where n is the number of active simulations.
• You are required to specify the data structures you would use and describe the key operations your implementation must support. Full code is not necessary.
• Assume the process is long-running and must handle many events over an extended period without requiring restarts.