This is basically an online knapsack problem and it's nastier than it looks.
Start by clarifying the problem constraints and expected update patterns, then propose a class design that separates data storage from optimization logic. For incremental updates, suggest maintaining a priority queue or dynamic programming table that can be updated in O(log n) or O(1) per event, and discuss trade-offs between exact and approximate solutions.
Pro tip: Emphasize the importance of defining clear interfaces and invariants early, and mention how you would test the incremental updates for correctness and performance under high-throughput streaming scenarios.
Ask about the scale of flights and cargo, update frequency, and whether exact optimality is required or approximations are acceptable. Confirm the interface: methods for adding flights, adding cargo, and getting the current best assignment.
Decide on a representation for flights (e.g., list with capacities) and cargo (e.g., priority queue by value/weight ratio). For incremental optimization, consider maintaining a max-heap of cargo per flight or a dynamic programming table that updates only affected states.
For each new flight or cargo, update the current assignment without recomputing from scratch. For example, when adding cargo, try to insert it into the best flight if capacity allows, possibly displacing lower-value items; when adding a flight, redistribute cargo if beneficial.
Discuss time and space complexity of each operation. Compare exact vs. greedy approaches, and explain how you would handle worst-case scenarios (e.g., many small updates causing cascading reassignments).
Mention handling of zero-capacity flights, overweight cargo, duplicate items, and concurrent updates. Propose unit tests for incremental correctness and stress tests for performance.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Knew the cancellation question was coming and still didn't have a clean answer.
Start by clearly stating the per-event time complexity of your incremental approach, justifying it with the data structures used. Then, discuss how you would extend the design to handle flight cancellations and mid-stream capacity changes, focusing on maintaining efficiency and correctness.
Pro tip: Emphasize the trade-offs between different data structures and the importance of amortized analysis. Mention that handling cancellations and capacity changes often requires lazy deletion or dynamic updates, which can affect complexity.
Clearly specify the time complexity for processing a single event (e.g., O(log n) or O(1)) and briefly explain why, referencing the data structures and algorithms used.
Explain how the chosen data structures (e.g., heaps, balanced BSTs, hash maps) enable the stated complexity, and discuss any invariants maintained.
Describe how to handle flight cancellations, such as using lazy deletion with tombstones or updating the data structure directly, and analyze the impact on per-event complexity.
Discuss mid-stream capacity changes, e.g., adjusting the capacity of a resource, and how to update the data structures efficiently, possibly using dynamic resizing or rebalancing.
Conclude by summarizing the trade-offs between different approaches, emphasizing correctness, efficiency, and scalability.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.