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Asked: 2026-05-15T04:39:18+00:00

Here is my problem : I have an array of points, the points have

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Here is my problem : I have an array of points, the points have three properties : the “x” and “y” coordinates, and a sequence number “n”. The “x” and “y” are defined for all the points, the “n” are not.
You can access and write them calling points[i]->x, points[i]->y, points[i]->n. i.e. :

points[i]->n = var
var = points[i]->n

So the title maybe ruined the surprise, but I’m looking for a possible implementation of a solution to the Hamiltonian path problem : I need to set the “n” number of each point, so that the sequence is the shortest path (not cycle, the edges have to be disjoint) that goes exactly once through each point. I looked for a solution and I found The Bellman Ford Algorithm but I think it doesn’t work since the problem doesn’t specify that it has to go through all of the points is it correct ?

If it is, does somebody has another algorithm and the implementation ?
If the Bellman Ford Algorithm works, how would I implement it ?

Thanks a lot,

Julien

Edit : the problem is that I have to recreate a list of geographic points which represent bus stops, and I have to figure out a realistic sequence. Performance is not important at all since the goal is only to populate a database.

Edit : Here is a picture :My Hamiltonian Path Problem http://www.stoeffler.cc/hpp.png

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1 Answer

  1. Editorial Team

    This is called Euclidean Travelling Salesman (in 2-dimensions) and is also NP-Complete like TSP.

    The other answers are inaccurate as they are doing the opposite: reducing your problem to Hamiltonian Path, while it should be the other way round, to show NP-Completeness. Sorry to say this, but it seems to be a pretty common problem on this site.

    We can say that this fundamentally differs from the normal TSP in the following sense:

    If P != NP,

    There are other algorithms which guarantee 2-approximation (using Minimum Spanning Trees) and 3/2-approximation and might be simpler. Arora’s paper mentions those and you should be able to track down using the references in Arora’s paper.

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