Model the flight network as a weighted directed graph and use a modified BFS (level-order traversal) to explore paths with increasing number of stops, updating the minimum cost to each city. Alternatively, use Bellman-Ford with at most k+1 relaxations, or Dijkstra with state (city, stops).
Pro tip: Clarify edge cases upfront (e.g., k=0, no path, cycles) and discuss time/space complexity trade-offs between approaches. Mention that BFS with a priority queue (Dijkstra) can be adapted but requires careful state management to avoid revisiting cities with more stops and higher cost.
Confirm details: directed graph, non-negative prices, at most k stops (i.e., k intermediate cities), return -1 if no route. Ask about constraints (n, k, price range) to choose the optimal algorithm.
Compare BFS with level-order traversal (O(k * E)), Bellman-Ford (O(k * E)), and Dijkstra with state (O(E log V) but with stops dimension). Select the most suitable based on constraints and explain why.
Use an adjacency list for the graph, a distance array to track min cost to each city, and a queue (or priority queue) for BFS/Dijkstra. For Bellman-Ford, use a copy of distances per iteration.
Code the chosen algorithm, ensuring stops are limited to k. Handle cases: source equals destination (cost 0), no path (return -1), and unreachable cities. Test with small examples.
State time and space complexity. Discuss potential optimizations like early termination if destination reached, or using a priority queue to prune suboptimal paths.
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Start by clarifying the scale and requirements, then propose a high-level architecture that separates read and write paths, uses caching and asynchronous updates, and ensures consistency where needed. Discuss trade-offs between consistency, latency, and cost, and how to handle real-time price updates efficiently.
Pro tip: Emphasize the importance of idempotency and exactly-once processing for price updates to avoid inconsistencies, and mention how Stripe's infrastructure (e.g., Kafka, Redis) could be leveraged.
Ask about scale (number of flights, users, updates per second), latency requirements, consistency needs, and budget constraints.
Propose a microservices-based system with separate services for flight search, pricing, and booking. Use a message queue for asynchronous price updates and a cache for read-heavy operations.
Choose appropriate databases: a distributed SQL or NoSQL for flight data, and an in-memory data store for caching. Discuss consistency models (e.g., eventual consistency for price updates, strong consistency for bookings).
Implement caching strategies (TTL, write-through), sharding, read replicas, and CDN for static content. Use batch processing and debouncing for price updates.
Discuss trade-offs between consistency and availability, cost vs performance. Mention monitoring, alerting, and auto-scaling to handle load spikes.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the system architecture and what caches exist (e.g., search results, price calendars, recommendation feeds). Then, identify which cached results depend on the changed flight price and propose a targeted invalidation strategy using dependency tracking or versioning, avoiding full recomputation.
Pro tip: Mention that you would use a write-through or write-behind cache with a pub/sub invalidation mechanism, and highlight the trade-off between consistency and latency. Also, consider using a bloom filter or inverted index to quickly find affected caches.
Ask questions to understand what caches exist (e.g., search results, price calendars, recommendation feeds) and how they are keyed. This ensures you address the right components.
Determine which cached results depend on the changed flight price. For example, search results for routes including that flight, price history graphs, and deal alerts.
Propose a mechanism to invalidate only affected caches, such as maintaining a dependency graph or using versioned keys. Consider using a pub/sub system to notify cache nodes.
Discuss how to avoid recomputing everything: use incremental updates, lazy invalidation, or partial recomputation. Mention data structures like inverted indices to quickly find affected entries.
Talk about consistency vs. latency, handling cascading invalidations, and ensuring the solution scales with high write throughput.
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I knew the concept vaguely from road network routing papers but had never applied it to flight graphs.
Start by clarifying the problem: point-to-point shortest path on a large flight graph with time-dependent edge weights. Then explain how contraction hierarchies (CH) or hierarchical graph decomposition can preprocess the graph to create shortcuts and node orderings, enabling faster queries. Finally, discuss trade-offs like preprocessing cost, memory overhead, and handling dynamic updates (e.g., flight delays).
Pro tip: Emphasize that flight graphs are time-dependent and often have a natural hierarchy (e.g., hubs vs. regional airports), so you can combine CH with time-dependent routing or use hub labeling for even faster queries. Also mention that Stripe cares about scalability and real-time performance, so highlight how you'd handle frequent schedule changes.
Ask about graph size, query latency requirements, update frequency, and whether edge weights are time-dependent (e.g., flight schedules). This shows you understand the problem context.
Describe how CH preprocesses the graph by iteratively contracting nodes based on importance, adding shortcuts to preserve shortest paths. Queries then run bidirectional Dijkstra on the contracted graph.
Discuss how to handle time-dependent edges (e.g., using time-expanded graphs or time-dependent CH) and leverage the natural hierarchy of airports (hubs vs. regional).
Compare CH with other hierarchical methods (e.g., highway hierarchies, hub labeling) and discuss preprocessing time, memory, and update handling. Mention that CH may need periodic rebuilds or dynamic updates.
Summarize why CH or a variant is suitable for this use case, and suggest a hybrid approach if needed (e.g., CH for static parts, caching for frequent queries).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.