## Problem Simulate a supermarket with `k` checkout lanes. Customers arrive at given times with a number of items. Each item takes 1 unit of time to scan; no setup time between customers. Each customer joins the lane with the fewest customers currently in it (ties broken by lane index). Return the time each customer finishes checking out. ```python def simulate_queues( customers: list[tuple[int, int]], # (arrival_time, num_items) k: int # number of lanes ) -> list[int]: # finish time per customer (same order) pass ``` ## Example ``` Input: customers=[(0,3),(0,4),(2,2),(4,1)], k=2 Customer 0: arrives 0, joins lane 0 (both empty), finishes at 3 Customer 1: arrives 0, joins lane 1, finishes at 4 Customer 2: arrives 2, joins lane 0 (1 customer remaining), finishes at max(3,2)+2=5 Customer 3: arrives 4, joins lane 0 (done at 5) or lane 1 (done at 4) -> lane 1, finishes at max(4,4)+1=5 Output: [3, 4, 5, 5] ``` ## Follow-ups 1. What is the time complexity of your solution? How does it change with `k` and `n`? 2. How would you extend this to model express lanes (items < 10) and self-checkout lanes? 3. If customers can observe queue lengths and switch lanes, how does that change the simulation?

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Supermarket Queue: Simulate and Optimize a Multi-Checkout Queue System

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Problem Simulate a supermarket with k checkout lanes. Customers arrive at given times with a number of items. Each item takes 1 unit of time to scan; no setup time between customers. Each customer joins the lane with the fewest customers currently in it (ties broken by lane index). Return the time each customer finishes checking out. Example Follow-ups What is the time complexity of your solution? How does it change with k and n? How would you extend this to model express lanes (items < 10) and…

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This is a reported interview question from a jane street interview during the phone round.

It covers the following topics: Coding, Phone, Queue .

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Supermarket Queue: Simulate and Optimize a Multi-Checkout Queue System

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