This was a lot to hold in your head at once.
Start by clarifying requirements and constraints, then outline a MapReduce pipeline that discretizes time into slots, maps each user's busy intervals to slot-level busy markers, and reduces to find slots where all users are free. Discuss partitioning, skew handling, and validation strategies to ensure scalability and correctness.
Pro tip: Mention that you would use a composite key (user group + time slot) to ensure all relevant data for a slot goes to the same reducer, and consider using a combiner to pre-aggregate busy counts per slot per user to reduce shuffle size.
Ask about data scale, time granularity, definition of 'free' (e.g., no busy intervals overlapping), and whether the group of users is fixed or dynamic. Confirm that duration d is in the same units as the time slots.
Discretize time into fixed-size slots (e.g., 15 minutes) and map each user's busy interval to all overlapping slots, emitting (slot, user_id) as key-value pairs. Alternatively, emit (user_id, slot) and use a secondary sort, but ensure all users for a slot are processed together.
Partition by time slot (or a composite key of group and slot) so that all busy markers for a slot go to the same reducer. In the reducer, count distinct users busy in that slot; if count < total users in group, the slot is free for all. Then, post-process to find contiguous free slots of length >= d.
Address skew from popular slots or users by using a combiner to pre-aggregate per user per slot, or by salting keys. Consider using a two-stage MapReduce: first compute per-user free slots, then intersect across users.
Validate correctness by comparing with a brute-force approach on small data, and use unit tests for edge cases (e.g., overlapping intervals, d=0). At scale, monitor reducer times, use sampling, and consider incremental updates if data changes frequently.
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