I went straight for modified Dijkstra because I'd seen something similar before, but I fumbled explaining why I needed to track stop count separately in the priority queue.
Model the flights as a weighted directed graph and use a modified BFS (level-by-level relaxation) or Bellman-Ford to find the cheapest path with at most k stops. Prioritize clarity by first explaining the graph representation, then the algorithm choice, and finally analyzing time/space complexity.
Pro tip: Mention that while Dijkstra's algorithm finds the shortest path, it doesn't directly handle the stop constraint; instead, use BFS with dynamic programming or Bellman-Ford with a stop limit. Also, discuss how you would handle edge cases like no route or cycles.
Ask clarifying questions: Are there multiple flights between same cities? Can there be negative prices? Is k inclusive of destination? Confirm input format and expected output.
Explain that BFS with level-order traversal (up to k+1 levels) or Bellman-Ford with k+1 iterations works. Justify why Dijkstra's is not ideal due to the stop constraint.
Describe the data structures: adjacency list for graph, a distance array to track min cost to each city, and a queue for BFS. Outline the relaxation process step by step.
State time complexity O(k * E) for Bellman-Ford or O(V + E) per level for BFS, and space O(V + E). Discuss trade-offs between BFS and Bellman-Ford in terms of simplicity and performance.
Mention edge cases: no route, source equals destination, k=0, cycles. Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the scale and real-time requirements, then propose a layered solution that separates static graph structure from dynamic pricing. Focus on algorithmic optimizations (e.g., A*, bidirectional search, contraction hierarchies) for large graphs and a streaming architecture with incremental updates for real-time prices. Emphasize trade-offs between latency, consistency, and cost, and tie choices to Stripe's reliability and scalability needs.
Pro tip: Show you understand that real-time price updates often require a trade-off between consistency and availability; propose a hybrid approach where critical paths use strong consistency while less critical queries can tolerate eventual consistency. This demonstrates maturity in distributed systems design.
Ask about graph size (nodes/edges), update frequency, latency SLAs, consistency needs, and query patterns. This ensures your optimizations target the actual bottlenecks.
Propose algorithmic improvements like A* with admissible heuristics, bidirectional search, or contraction hierarchies. Consider partitioning the graph geographically or by airline to parallelize computation.
Design a streaming pipeline (e.g., Kafka) to ingest price changes and update an in-memory cache or graph index incrementally. Use change data capture and avoid full recomputation.
Discuss caching strategies (TTL, write-through) and consistency models (strong vs. eventual). For critical queries, use a primary store; for others, serve slightly stale data from replicas.
Summarize trade-offs (latency vs. consistency, cost vs. performance) and suggest monitoring key metrics like p99 latency, update lag, and cache hit rate to validate the solution.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.