Model the flight network as a directed weighted graph where cities are nodes and tickets are edges with cost and stops (or time) as weights. Use a modified shortest path algorithm like Dijkstra with a Pareto frontier to handle two objectives, or transform the problem by combining cost and stops into a single weighted sum with a tunable parameter. Discuss how to present trade-offs, such as computing the Pareto-optimal set of itineraries and letting the user choose.
Pro tip: Mention that real-world systems often use multi-criteria shortest path with Pareto optimization, and that you can also precompute or cache results for frequent queries. Show awareness of scalability and practical constraints like flight schedules and availability.
Ask clarifying questions: Is 'best' a weighted sum of cost and stops? Are there constraints like maximum stops or budget? Should we return one itinerary or a set of trade-off options?
Represent cities as nodes and flights as directed edges with attributes: cost and stops (or duration). This forms a directed graph with two edge weights per edge.
For a single objective, use Dijkstra. For two objectives, use multi-objective Dijkstra maintaining a Pareto frontier per node, or scalarize the objectives with a parameter and run Dijkstra multiple times.
Explain Pareto optimality: an itinerary is Pareto-optimal if no other itinerary is better in both cost and stops. Maintain a set of non-dominated labels per node during search.
Discuss time and space complexity, potential exponential blow-up in worst case, and practical optimizations like pruning, A* with admissible heuristic, or limiting the Pareto set size.
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