what could be a problem when traveling with a resource constraint?

Shortest path problems with side constraints often can be turned into unconstrained shortest path problems on a derived graph. One possibility is to expand the idea of location from junction to (junction, fuel level), but the requested time bound doesn’t allow dependence on the size of the fuel tank. What does work here is to find shortest paths in a graph on junctions with fuel stations (including s) and d, with an edge between each pair of junctions such that the shortest path has length at most the range of the bike. The weight of each edge is the length of this shortest path.

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