Sorting the intervals first was the obvious move but I second-guessed myself for a minute on how to handle overlapping ones before merging.
First, clarify the problem constraints: whether intervals are sorted, if they can overlap, and the definition of free time (e.g., between end of one and start of next). Then, sort intervals by start time if needed, merge overlapping intervals, and iterate through to collect gaps between consecutive merged intervals.
Pro tip: Mention that handling edge cases like empty input, single interval, or intervals that cover the entire timeline is crucial, and discuss how to handle them gracefully. Also, note that if intervals are already sorted, you can avoid the sort step, but always confirm with the interviewer.
Ask if intervals are sorted, if they can overlap, and what constitutes free time (e.g., gaps between intervals, before first, after last). Confirm output format (list of intervals).
If not sorted, sort intervals by start time. Then merge overlapping intervals to simplify gap detection.
Iterate through merged intervals and collect the time between the end of the current interval and the start of the next interval.
Consider empty input, single interval, intervals that touch (no gap), and intervals that extend beyond the typical day boundaries if applicable.
State time complexity (O(n log n) due to sorting) and space complexity (O(n) for output). Walk through a few test cases to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the scheduling objective and constraints, then identify the optimal algorithm (e.g., shortest processing time first for minimizing total completion time). Explain the greedy strategy, prove its optimality via exchange argument, and analyze time complexity. Discuss trade-offs with other metrics like fairness or deadlines.
Pro tip: Always state the objective precisely—minimizing total completion time (sum of completion times) is different from minimizing makespan or average waiting time. Mention that SPT is optimal for the former on a single machine, and note that if queries have priorities or deadlines, the problem changes.
Ask whether it's a single machine or multiple machines, whether preemption is allowed, and whether the goal is to minimize total completion time, average waiting time, or makespan. Confirm if all queries are available at time zero.
For single-machine, non-preemptive scheduling to minimize total completion time, the optimal policy is Shortest Processing Time first (SPT). Explain that sorting by processing time ascending yields the minimum sum of completion times.
Use an exchange argument: if two adjacent jobs are out of order (longer before shorter), swapping them reduces the total completion time. This shows SPT is optimal.
Sorting takes O(n log n) time, which is optimal for comparison-based sorting. Implementation is straightforward: sort the list by processing time and compute the cumulative sum.
Mention that SPT minimizes average waiting time but can starve long jobs. If queries have deadlines or weights, other algorithms (e.g., weighted SPT, EDD) may be needed. For multiple machines, the problem becomes NP-hard (e.g., P||Cmax).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.