Find the Minimum Meeting Rooms and Discuss Dynamic Constraints

Given meeting intervals, return the minimum number of conference rooms needed so that overlapping meetings use different rooms. ### Constraints and Clarifications For the baseline, use half-open intervals [start,end) with start<end, so a room is reusable at its previous meeting's end time. These endpoint conventions are explicit practice clarification. Empty input needs zero rooms; no numerical bounds are supplied. Follow-ups introduce a stream of new meetings and rooms with different capacities, which require additional policy choices beyond the baseline count. ### Part 1 — Static Meetings Find the minimum room count for a fixed collection of intervals and explain why the greedy algorithm works. #### What This Part Should Cover Sort by start time and track room end times in a min-heap, or use an equivalent sweep line. ### Part 2 — Dynamic Arrivals How would you check whether a new interval fits a fixed room limit when meetings can arrive in arbitrary order? #### What This Part Should Cover Clarify admission versus reassignment and discuss interval or segment-tree state rather than pretending start-time sorting is already available. ### Part 3 — Capacity Constraints What changes when each room has a capacity and each meeting has an attendee count? #### What This Part Should Cover Separate temporal availability from suitability, define the assignment objective, and avoid claiming the homogeneous-room lower bound alone proves feasibility. ### What a Strong Answer Covers A proven static solution with complexity and concrete, scoped designs for the two extensions. The baseline count is the deterministic coding contract; follow-up policies must be specified before implementation. ### Follow-up Questions - Why is an available but undersized room not a valid reuse candidate? - What guarantees are lost if previously assigned meetings cannot be moved?