Recursive node traversal go through whole graph?

Question

I'm trying to solve this work problem, but I'm having some difficuly, since I suck at recursion.

My question is: is there a way where I can pick a node in a graph and traverse the graph all the way through back to the same node where I started, but the nodes can only be visited once? And of course to save the resulting edges traversed.

The graph is unweighted, but it is coordinates in a 2D x and y coordinate system, so each coordinate has an x and y value, meaning the edges can weighted by calculating the distance between the coordinates. If that helps...

Loop through the children of the source node and BFS starting from each one, check if last node is source and all nodes visited — Mohd
– Mohd, Commented Apr 16, 2018 at 10:55
I'm not sure I understand that. Could you expand a bit on the details? But it sounds like you're onto something! Thanks! — Johan -
– Johan -, Commented Apr 16, 2018 at 11:02

Edward Doolittle · Accepted Answer · 2018-11-16 23:01:52Z

0

I'm not completely sure I understand, but here is a suggestion: pick a node n0, then an edge e=(n0,n1). Then remove that edge from the graph, and use a breadth-first search to find the shortest path from n1 back to n0 if it exists.

Another suggestion, which might help you to control the length of the resulting path better: Pick a starting node n0 and find a spanning tree T emanating from n0. Remove n0, and T will (hopefully) break into components. Find an edge e=(n1,n2) from one component to another. Then that edge, plus the edges in T connecting the n1 to n0, plus the edges in T connecting n2 to n0, is a cycle with the properties you desire.

answered Nov 16, 2018 at 23:01

Edward Doolittle

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