My first instinct was to just do a brute-force overlap check and I started going down that path before realizing it gets messy fast with more than two people.
Clarify the input format (e.g., list of busy intervals per person) and the definition of a valid time slot. Then propose an algorithm that merges all busy intervals and finds gaps where everyone is free, or uses a sweep line to count overlapping busy intervals.
Pro tip: Discuss trade-offs between different approaches (e.g., merging vs. sweep line) and mention how to handle edge cases like zero-length intervals or time zones. Also, consider scalability for large inputs.
Ask about input format (e.g., list of busy intervals per person), output format (e.g., list of free intervals), and constraints (e.g., time granularity, number of people).
Decide between merging intervals or using a sweep line. Merging is simpler for few people; sweep line is efficient for many people or large data.
For merging: combine all busy intervals, sort by start time, merge overlapping, then find gaps between merged intervals. For sweep line: create events for start/end of busy times, sort, and track count of busy people.
Discuss time and space complexity (e.g., O(N log N) for sorting). Mention edge cases: no common free time, all free, intervals touching at endpoints, etc.
Suggest optimizations (e.g., using a heap for sweep line) or extensions (e.g., finding slots of minimum duration, handling recurring events).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.