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The event-sweep approach clicked pretty fast: emit a +1 at each start and -1 at each end, sort everything, then walk through tracking how many tasks are active.
Clarify that we need intervals where no GPU task is running on any node, then merge all task intervals across all nodes into a single timeline and compute the gaps between them. Handle edge cases like overlapping tasks, zero-duration tasks, and tasks that touch at endpoints.
Pro tip: Mention that this is essentially the 'merge intervals' problem and that you would sort by start time and sweep through, which is O(n log n) and scales well. Also note that if the input is already sorted or streaming, you can adapt the approach.
Ask whether intervals are inclusive/exclusive, whether zero-duration tasks count, and whether the output should be sorted. Confirm that 'no task running on any GPU' means the union of all tasks across all nodes.
Decide to merge all intervals: sort by start time, then iterate to merge overlapping or adjacent intervals. The gaps between merged intervals are the idle periods.
Sort intervals, initialize current merged interval, and for each interval, if it overlaps/adjacent to current, extend; else, record gap and start new merged interval. After loop, record final gap if needed.
Test with no tasks (entire timeline idle), all tasks overlapping (no idle), tasks that touch at endpoints, and unsorted input. Ensure output intervals are correct and sorted.
State time complexity O(n log n) due to sorting, space O(n) for merged intervals. Mention that if input is already sorted, O(n) is possible, and discuss streaming or distributed scenarios.
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