如何找到最长的路线？

Question

Following problem:

An engine (for instance a car) starts its journey on a straight road. Its consumption is directly proportional to the distance (for instance 480 km uses one unit of fuel and thus 48km uses a tenth unit of fuel). This engine can transport at most one unit of fuel.

At the start point is a supply of n0 fuel units. At different points on the route, are fuel depots (for instance n1 @ d1, n2 @ d2 etc.) and the driver can unload fuel anywhere on the route. For instance, with the values 480 km for one unit, the driver could drive for 160km create a depot with 1/3 units of fuel and drive back to the starting point to refuel his engine.

I'm looking for an algorithm (or some ideas to find one) to find the maximum distance that can be achieved depending on the starting fuel and the depots on the route.

Answer 1

By intuition a greedy algorithm should be optimal, ie by maximizing the amount of fuel available at each depot, you are maximizing the possible route. This is just my opinion, and I assume that "anywhere on the route" is "actually at any depot".

How will a greedy algorithm work? At each point of time, you have only two decision to take : "move forward" or "go back to the previous depot to refill". The greedy will always move back as long as it will increase the current depot reserve.

Answer 2

I think that you could also "invert" the "<=" comparison used in your a*, dijkstra method.

Or add a logic parameter (best, worst) path.

So you can keep the same path search without repeated code.