SPX2 wrote:
> And what you have to do after you have found path a1...an with a1 input
> and an output
> is to try to remember the cost of the path in a vector.
> that is all i think
> Depth path will assure different pathways.
> If you want the fastest path you can use dijkstra/royfloyd.

I think you are not understanding my algorithm. There is no need for
finding a shortest path at all.  It works incrementally.

It would proceed in this manner.

Visit 1.  Do nothing.
Visit 2.  See that this a node with 1 in-edge and 1 out-edge.
Therefore delete edges 1-2 and 2-3.  Replace with edge 1-3 having sum
of weights.  Restart search at 3.
Visit 3.  See that this a node with 1 in-edge and 1 out-edge.
Therefore delete edges 1-3 and 3-6.  Replace with edge 1-6 having sum
of weights.  Restart search at 6.
Visit 6.  Do nothing.
DFS backtracks to 1.
Visit 4.  See that this a node with 1 in-edge and 1 out-edge.
Therefore delete edges 1-4 and 4-5.  Replace with edge 1-5 having sum
of weights.  Restart search at 5.
Visit 5.  See that this a node with 1 in-edge and 1 out-edge.
Therefore delete edges 1-5 and 5-6.  Replace with new edge 1-6 having
sum of weights. 
Done.


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