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Sorted by arrival time first, then simulated a current-time pointer to track when the chef finishes each order.
Sort orders by arrival time, then simulate the chef's schedule using a min-heap keyed by arrival time to select the earliest-arrived waiting order. Track the current time and accumulate waiting times (finish - arrival) for each order, then compute the average.
Pro tip: Clarify the waiting time definition upfront—it's finish time minus arrival time, not just time in queue—and mention that this is essentially a single-server queue with FCFS scheduling, which helps frame the problem.
Confirm that orders are non-preemptive, the chef processes one at a time, and waiting time includes preparation time. Ask about ties in arrival times and whether arrival times are unique.
Sort the list of orders by their arrival time to ensure you process them in the order they arrive. This is crucial for the FCFS rule when the chef is idle.
Use a min-heap (priority queue) keyed by arrival time to store waiting orders. Iterate through sorted orders, adding them to the heap when they arrive, and when the chef is free, pop the earliest-arrived order, process it, and update the current time.
For each processed order, calculate waiting time as finish time minus arrival time. Sum these waiting times and divide by n to get the average.
State that sorting takes O(n log n) and heap operations take O(n log n) total, so overall O(n log n) time and O(n) space. Walk through a small example to verify correctness.
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Recognize this as the classic Shortest Job First (SJF) scheduling problem and explain that processing orders in ascending order of processing time minimizes average waiting time. Prove it with an exchange argument, then discuss practical trade-offs like starvation and the need for prediction in real systems.
Pro tip: Acknowledge that while SJF is theoretically optimal, real-world systems often use approximations like aging or priority queues to balance fairness and efficiency. Mentioning this shows you understand both theory and production constraints.
State that this is a scheduling problem where the goal is to minimize average waiting time, and the optimal strategy is Shortest Job First (SJF).
Use an exchange argument: if a longer job is scheduled before a shorter one, swapping them reduces the waiting time of the shorter job without increasing the longer job's waiting time, thus reducing the average.
Explain that in real systems, job processing times are unknown and must be predicted, and strict SJF can cause starvation of long jobs.
Suggest using historical data to estimate processing times, and implementing aging or priority adjustments to prevent starvation.
Connect to Instacart's context: predicting order fulfillment times based on factors like store, items, and shopper availability, and balancing efficiency with fairness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Went with a min-heap of size k tracking when each chef becomes free.
First, clarify the scheduling problem: likely assigning tasks to k chefs to minimize makespan. Then, propose an algorithm such as binary search on the answer combined with a greedy feasibility check, or a priority queue based approach. Finally, analyze the time complexity in terms of number of tasks n and chefs k.
Pro tip: Mention that for k=1, the problem reduces to the classic single-machine scheduling, and for large k, the problem becomes trivial; this shows you understand the problem's boundaries.
Ask clarifying questions to define the scheduling problem: are tasks independent? Can they be split? What is the objective (minimize makespan, maximize throughput)? Assume each chef can work on one task at a time and tasks have fixed durations.
For minimizing makespan with k identical chefs, use binary search on the makespan T, and check feasibility by greedily assigning tasks to chefs if total time ≤ k*T. Alternatively, use a priority queue to simulate scheduling: assign each task to the chef with the earliest available time.
For binary search + greedy: O(n log(sum of task times)) time, O(1) extra space. For priority queue: O(n log k) time, O(k) space. State which is more efficient depending on constraints.
Compare approaches: binary search is simpler but may be slower if task times are large; priority queue is efficient for large n. Handle edge cases: k=1, k≥n, zero-duration tasks.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.