← Snowflake Interview Insights
I knew this problem but still second-guessed myself on the heap approach.
Clarify that intervals are half-open [start, end) to avoid false conflicts. Then present the sweep line algorithm: create events for starts (+1) and ends (-1), sort them, and track the running count to find the maximum. This gives O(n log n) time and O(n) space, which is optimal.
Pro tip: Mention that if the input is already sorted by start time, you can use a min-heap of end times to achieve O(n log n) without sorting all events, and that this approach naturally extends to finding the actual room assignments if needed.
Confirm that intervals are half-open [start, end) so that a meeting ending at time t does not conflict with one starting at t. Also ask if the input is sorted or if we can modify it.
Describe creating events: for each interval, add (start, +1) and (end, -1). Sort events by time, with ends before starts if times are equal (to handle half-open intervals). Then iterate, maintaining a running count and tracking the maximum.
State that sorting takes O(n log n) time and the sweep takes O(n), so overall O(n log n) time. Space is O(n) for the events array. This is optimal because we must at least read the input.
Mention the min-heap method: sort intervals by start time, then iterate; if the earliest ending meeting is done, reuse its room; otherwise allocate a new room. The heap size at the end is the answer. This also runs in O(n log n).
Cover empty input (return 0), single meeting (return 1), and all meetings overlapping (return n). If asked, explain how to output the actual room assignments by tracking room IDs.
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