The union-of-intervals part is standard sweep-line stuff, sort by start and merge when the next interval overlaps or touches the current one.
First, clarify the data model: the region table defines a town-city-state hierarchy, and attendance intervals are given per town for a single day. Then, for each town, sort its intervals by start time and merge overlapping or adjacent intervals to compute the union, summing the durations to get total party hours.
Pro tip: Mention that you would handle edge cases like intervals that touch at endpoints (e.g., [1,2] and [2,3]) and ensure the solution scales by processing towns independently, which allows for parallelization if needed.
Confirm the schema: region table with town-city-state hierarchy, and attendance intervals as [start, end] per town. Assume intervals are within a single day and times are in a consistent unit (e.g., hours or minutes).
Use the region table to map each town to its intervals, ensuring you only consider towns that have attendance data. This may involve a join or grouping operation.
For each town, sort intervals by start time. Iterate through them, merging overlapping or adjacent intervals into a single interval representing the union.
Sum the lengths of the merged intervals for each town to get the total party hours. Ensure the unit matches the expected output (e.g., hours).
Consider empty intervals, intervals that touch at endpoints, and intervals that span the entire day. Validate with small examples to ensure correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Once you have the merged party intervals per town, the idle segments are just the gaps between them plus the leading and trailing gaps against the day boundaries.
First, clarify the schema and assumptions: party intervals are per town, and the full day window is from 00:00 to 24:00. For each town, compute the complement of the union of party intervals within the day window to get idle segments, then join with the city mapping and group by city, ordering by city_id, town_id, and idle_start.
Pro tip: Mention handling edge cases like overlapping party intervals, intervals that extend beyond the day window, and towns with no parties (idle all day). Also, discuss efficient algorithms (e.g., sorting and merging) and the importance of deterministic ordering in the output.
Confirm the schema: tables for towns (with city_id), party intervals (town_id, start, end). Define the full day window (e.g., 00:00 to 24:00) and whether intervals are inclusive/exclusive. Ask about expected output ordering and handling of edge cases.
For each town, collect all party intervals, clip them to the day window, and merge overlapping or adjacent intervals to get a set of disjoint busy periods.
Given the merged busy periods, compute the complement within the day window: idle segments are the gaps between busy periods, including before the first and after the last. Handle the case of no busy periods (idle all day).
Join the idle segments with the town-to-city mapping, then group by city_id. Within each city, order by town_id and idle_start. Return city_id, town_id, idle_start, idle_end.
Check edge cases (e.g., town with no parties, intervals spanning midnight). Analyze time complexity: O(N log N) due to sorting intervals per town, where N is total intervals. Discuss potential optimizations if needed.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.