Find minimal time to serve customers

Q: Find minimal time to serve customers

This question evaluates algorithm design and mathematical reasoning for rate-based scheduling, including aggregate capacity computation, integer arithmetic, correctness proof, and analysis of edge cases.

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Question

You manage a bank with k tellers; teller i takes serviceTimes[i] minutes to serve one customer and works continuously. Given an integer array serviceTimes and an integer m (customers to serve), return the minimum integer time T such that sum over i of floor(T / serviceTimes[i]) >= m. Describe your algorithm, prove correctness, analyze time/space complexity, and implement it. Discuss edge cases (very large m, slow tellers, identical rates).

Find minimal time to serve customers

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