Spent the first few minutes just trying to nail down what 'simultaneously active' even meant since a driver can have multiple intervals.
Clarify the problem constraints and define inclusivity rules (e.g., intervals are half-open [start, end) and the query window is (T-24h, T]). Then propose an efficient solution using a sweep-line algorithm or interval tree to count distinct active drivers, and analyze time and space complexity.
Pro tip: Explicitly state your assumptions about inclusivity and edge cases (e.g., intervals touching boundaries) before diving into the algorithm; this shows attention to detail and prevents misunderstandings.
Ask about data characteristics (e.g., interval frequency, driver count), define inclusivity rules for interval overlap and the query window, and confirm whether the stream is static or dynamic.
Select an approach such as sweep-line with events (start/end) and a hash set for active drivers, or an interval tree for efficient overlap queries. Consider preprocessing if multiple queries are expected.
Ensure each driver is counted only once even if multiple intervals overlap the query moment. Use a set to track distinct active drivers during the sweep.
Derive time and space complexity for the chosen approach (e.g., O(N log N) time, O(N) space for sweep-line). Discuss trade-offs between preprocessing and query time.
Walk through examples including intervals exactly at boundaries, multiple intervals per driver, and no active drivers. Verify inclusivity rules are correctly applied.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.