Stared at this for a while before I even understood what 'two consecutive days' meant for scheduling.
First, clarify the problem constraints and edge cases, then model it as a scheduling problem where each center can process at most one city per day, with processing time 1 if center matches city else 2. The goal is to minimize makespan, which can be solved by greedy assignment or binary search on days with feasibility check.
Pro tip: Demonstrate Amazon's leadership principles by discussing trade-offs between optimality and simplicity, and by proactively considering scalability for large N and M.
Ask questions to confirm assumptions: Can a center work on multiple orders for the same city in one day? Are orders for the same city independent? Is preemption allowed? What are the constraints on N and M?
Represent each city's orders as a job with processing time 1 if assigned to its matching center, else 2. Each center is a machine that can process at most one job at a time. Minimize makespan.
The difficulty is assigning cities to centers to balance load and minimize the maximum completion time, considering that mismatched assignments take longer.
Use binary search on the answer D (days). For a given D, check feasibility: each center can handle at most D days of work, where a matching city takes 1 day and a non-matching takes 2. Greedily assign cities to centers, prioritizing matching centers.
Discuss time complexity (e.g., O((N+M) log M)) and handle edge cases like more cities than centers, or all orders for one city.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.