My first instinct was classic interval merging, which got me partway there.
First, clarify the problem constraints and edge cases, such as whether jobs are given in sorted order and how truncation and resumption affect scheduling. Then, model the problem as merging overlapping intervals and checking if the total merged duration per day exceeds the available time, considering carry-over from previous days. Finally, design an algorithm that efficiently simulates the server's daily processing, possibly using a sweep line or interval merging approach.
Pro tip: Demonstrate awareness of real-world scheduling by discussing how to handle jobs that span multiple days and the importance of choosing data structures that allow efficient merging and querying. Also, mention that you would validate your solution with edge cases like zero-duration jobs or jobs exactly at day boundaries.
Ask questions to understand the input format, job ordering, definition of a day, and whether jobs can be split or must run contiguously. Confirm if the server can process jobs in any order or must follow a specific sequence.
Represent jobs as intervals and define the daily capacity. Consider how overlapping jobs merge and how truncation at day's end creates a remaining portion to be scheduled next day.
Choose an approach: either simulate day by day, merging intervals and tracking carry-over, or use a sweep line to compute total busy time per day. Ensure the algorithm handles jobs that span multiple days.
Discuss time and space complexity of your approach. Compare alternatives like sorting-based merging versus priority queues, and justify your choice based on expected input size and constraints.
Walk through examples including no jobs, jobs exactly filling a day, jobs that overlap and truncate, and jobs that resume across multiple days. Verify correctness and efficiency.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.