Let's say we have a fully connected directed graph G. The vertices are [a,b,c]. There are edges in both directions between each vertex.
Given a starting vertex a, I would like to traverse the graph in all directions and save the path only when I hit a vertex which is already in the path.
So, the function full_paths(a,G) should return:
- [{a,b}, {b,c}, {c,d}]
- [{a,b}, {b,d}, {d,c}]
- [{a,c}, {c,b}, {b,d}]
- [{a,c}, {c,d}, {d,b}]
- [{a,d}, {d,c}, {c,b}]
- [{a,d}, {d,b}, {b,c}]
I do not need 'incomplete' results like [{a,b}] or [{a,b}, {b,c}], because it is contained in the first result already.
Is there any other way to do it except of generating a powerset of G and filtering out results of certain size?
How can I calculate this?
Edit: As Ethan pointed out, this could be solved with depth-first search method, but unfortunately I do not understand how to modify it, making it store a path before it backtracks (I use Ruby Gratr to implement my algorithm)
Have you looked into depth first search or some variation? A depth first search traverses as far as possible and then backtracks. You can record the path each time you need to backtrack.