Compute rooms and verify tree completeness

Q: Compute rooms and verify tree completeness

This question evaluates understanding of interval overlap and resource allocation for meeting-room scheduling alongside recognition of binary tree structure and completeness properties.

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Question

Given a list of closed-open time intervals [start, end) representing meetings on a single calendar, compute the minimum number of rooms required so that no meetings in the same room overlap. Implement an algorithm, justify its time and space complexity, and discuss how you would handle very large inputs.
Given the root of a binary tree, determine whether it is a complete binary tree (all levels filled except possibly the last, which is filled from left to right). Provide an algorithm, analyze complexity, and describe edge cases and test cases.

Compute rooms and verify tree completeness

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