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I knew the greedy angle pretty quickly: sort by start day, use a min-heap keyed by end day, iterate day by day and always pick the event expiring soonest.
Clarify the problem constraints and edge cases, then propose a greedy algorithm that sorts events by end day and selects the earliest-ending event for each available day. Explain how this maximizes the count and analyze the time complexity.
Pro tip: Mention that this is a classic interval scheduling problem and that the greedy choice of earliest end time is optimal; also discuss how to handle multiple events with the same end day by picking any.
Ask if events can span multiple days, if start and end are inclusive, and if there are constraints on the number of events or days. Confirm that you can attend at most one event per day and that events cannot be partially attended.
Recognize this as an interval scheduling maximization problem. The optimal strategy is to sort events by their end day and greedily select events that start after the last attended day.
Sort events by end day ascending. Initialize lastAttendedDay to -infinity and count to 0. Iterate through events: if event.start > lastAttendedDay, attend it, increment count, and set lastAttendedDay = event.end. Return count.
Time complexity is O(n log n) due to sorting, space O(1) or O(n) depending on sort. Discuss edge cases: no events, all events on same day, events with same end day, and events that start and end on the same day.
Walk through a small example to verify correctness, e.g., events = [[1,2],[2,3],[3,4]] yields 3, while [[1,2],[1,2],[1,2]] yields 1. Explain why greedy works by exchange argument.
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