Use Dijkstra's algorithm to find the shortest path from city 0 to every other city, since the graph is undirected and edge weights are non-negative.

Construct a new graph where nodes are cities and edges are the shortest path costs between them. Then, model this as a maximum node coverage problem under budget constraints, which can be approached using a priority queue to explore paths in order of increasing cost.

Apply a modified Dijkstra's algorithm where you track the maximum number of cities visited for each remaining budget, prioritizing paths that visit more cities within the budget. Use a priority queue to explore states (current city, remaining budget, visited cities) in order of maximum cities visited.