← Morgan Stanley Interview Insights
Classic interval scheduling problem and I knew it was greedy the second I saw it.
Recognize this as the classic interval scheduling maximization problem, which is solved optimally by a greedy algorithm: sort meetings by end time and iteratively select the next meeting that starts at or after the last selected meeting's end. Explain why this greedy choice works (earliest finish time leaves maximum room for remaining meetings) and analyze the time complexity.
Pro tip: In a data science context, connect the algorithm to real-world applications like scheduling computational jobs or resource allocation, and mention that the greedy approach is optimal for this problem—unlike many scheduling problems where greedy fails. This shows you understand both theory and practical implications.
Confirm that intervals are half-open (end == start is non-overlapping) and that the goal is to maximize the count, not total duration. Ask if the input is sorted or if we can modify it.
Sort meetings by end time ascending. Initialize a count and track the end time of the last selected meeting. Iterate through sorted meetings, selecting any whose start time is >= last end time.
Explain the exchange argument: choosing the meeting with the earliest finish time is always safe because it leaves at least as much room for subsequent meetings as any other choice.
State time complexity O(n log n) due to sorting, and space O(1) or O(n) depending on sorting implementation. Discuss edge cases: empty list, single meeting, all overlapping, all non-overlapping.
Mention applications like scheduling model training jobs, allocating analyst time, or optimizing trade execution windows. Highlight that this greedy algorithm is a fundamental building block in operations research.
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