My first instinct was plain Dijkstra but then the stop constraint throws a wrench in it because you can't just track visited nodes the usual way.
Model the problem as a shortest path with a constraint on the number of edges (stops). Use BFS with a priority queue (Dijkstra) where the state includes the city and the number of stops used so far, or use Bellman-Ford with exactly k+1 iterations. Compare BFS and Bellman-Ford approaches, discussing time and space complexity.
Pro tip: Clarify whether the graph can have cycles and whether prices are positive; this affects algorithm choice. Mention that BFS with a queue works if all edge weights are equal, but since prices vary, Dijkstra or Bellman-Ford is needed.
Confirm details: directed graph, non-negative prices, at most k stops (i.e., at most k+1 edges), return -1 if no route. Ask about constraints (n, k) to choose the right algorithm.
Consider Bellman-Ford with k+1 iterations (O(k * E)) or Dijkstra with state (city, stops) (O(E log V) but with extra dimension). Discuss trade-offs.
For Bellman-Ford: initialize distances to infinity, set dist[src]=0, relax all edges k+1 times, but use a copy of distances to avoid using more than k stops. For Dijkstra: use a priority queue storing (cost, city, stops), and track best cost per (city, stops).
Check if source equals destination (0 stops, cost 0), if k=0 (only direct flights), and if no path exists (return -1). Also handle disconnected graphs.
State time and space complexity. Walk through a small example to verify correctness, and discuss potential optimizations (e.g., early termination).
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.