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My first instinct was to just scan all pings on every query and that obviously wasn't the point.
Start by clarifying the problem: define the 5-slot window, what constitutes an inactive slot, and the threshold for instability. Then propose a solution that preprocesses the log to enable fast queries, such as sorting pings per sensor and using binary search to check slot activity, or precomputing a timeline of active slots. Discuss trade-offs between preprocessing time and query time, and consider edge cases like multiple pings in a slot and queries outside the log range.
Pro tip: Mention that you would preprocess the log by grouping pings by sensor and sorting timestamps, then for each query, use binary search to determine active slots in O(log n) per slot, or precompute a bitmask of active slots per sensor for O(1) queries. This shows you optimize for repeated queries.
Ask about the expected number of sensors, pings, and queries, and whether the log is static or streaming. Confirm the definition of a slot (60 seconds starting at T) and that a ping at exactly T+60k falls into slot k.
Group pings by sensor ID and sort timestamps. For each sensor, store a sorted list of ping times. Optionally, precompute a boolean array or bitmask indicating which 60-second slots (relative to a global epoch) have at least one ping.
For a query (sensor, T), check each of the 5 slots: slot i covers [T+60i, T+60(i+1)). Use binary search on the sensor's ping times to see if any ping falls in that interval. Count consecutive inactive slots and return UNSTABLE if count >= 3, else STABLE.
If queries are frequent, precompute for each sensor a list of active slot indices (e.g., slot index = floor(timestamp/60)). Then for a query, determine the 5 slot indices and check membership in a hash set or use a bitset. This reduces query time to O(5) = O(1).
Discuss time/space trade-offs: preprocessing O(N log N) to sort, O(N) space for slot sets. Handle edge cases: no pings for sensor, pings exactly on slot boundaries, queries before first ping or after last ping, and multiple pings in same slot.
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