Beacon Activity Window

Problem

Field beacons report observations with explicit timestamps. Design BeaconActivityWindow to retain those observations and answer which beacons were active during a configurable window ending at any requested time. Multiple threads may share one instance.

Requirements

Recorded history. The logical observation history contains exactly the valid (beaconId, observedAtSecond) pairs supplied to completed recordPulse calls.
Historical queries. Query timestamps may move forward or backward, and an earlier query must not alter the result of any later query.
Exact activity. isActive returns true exactly when the named beacon has an observation in the inclusive interval [asOfSecond - windowSeconds + 1, asOfSecond].
Distinct total. activeBeaconCount returns the number of distinct beacon IDs that satisfy Exact activity for its asOfSecond.
Atomic shared access. Every public call is linearizable when threads share one instance.

API

Signature	Returns	Behavior
`BeaconActivityWindow(windowSeconds: integer)`	New `BeaconActivityWindow`	Creates an empty history and fixes the window size.
`recordPulse(beaconId: string, observedAtSecond: integer)`	`void`	Adds the observation to the logical history.
`isActive(beaconId: string, asOfSecond: integer)`	`boolean`	Reports whether the beacon has an observation in the activity interval.
`activeBeaconCount(asOfSecond: integer)`	`integer`	Reports the number of distinct active beacons.

Examples

For a window size of 3:

Step	Operation	Result
1	`isActive("alpha", 5)`	`false`
2	`recordPulse("alpha", 5)`	No return value
3	`isActive("alpha", 7)`	`true`
4	`activeBeaconCount(7)`	`1`
5	`isActive("alpha", 8)`	`false`

Constraints

1 <= windowSeconds <= 120
beaconId matches [a-z][a-z0-9-]{0,19}
Each testcase uses at most 100 distinct beacon IDs.
0 <= observedAtSecond, asOfSecond <= 10_000
Each testcase has at most 200 public-method calls and 12 threads.
The same (beaconId, observedAtSecond) pair is not recorded twice.
All supplied inputs are valid and non-null.
Timestamps use signed 64-bit integer bindings in Java and C++, and Python integers. Counts fit signed 32-bit integers.

Notes

All testcase threads share one object. Calls retain their listed order within one thread. Calls from different threads may interleave in any order consistent with real-time precedence.

Linearizable means that each call takes effect at one instant between its invocation and response. A query that overlaps a recordPulse call may include or exclude that observation according to either valid ordering. A query invoked after that record returns must include it when its timestamp lies in the query interval.

Public operations have no domain waiting condition. Cancellation, shutdown, fairness, user-visible timeouts, and wait-free progress are outside the contract.