CareerCup

BFS algorithm should work for this.

shortest path with DP.

Easy using recursive methods but checking circle is tricky...
void FindPaths(const string& source, const string& dest, list<string>& path)
{
path.push_back(source);
if(source == dest)
{
PrintPath(path);
path.pop_back();
return;
}

list<string> destList = RetriveDestinations(source);
for(list<string>::const_iterator iter = destList.begin(); iter != destList.end(); ++iter)
{
if(find(path.begin(), path.end(), *iter) != path.end())
{
continue;
}
else
{
FindPaths(*iter, dest, path);
}
}

path.pop_back();
}

Very good solution using recursion.
wgfa.blogspot.com/2005/07/all-paths-between-two-nodes-in.html

This is a graph problem.
I think the finding the minimum spanning tree gives the best path and
finding all the spanning trees gives u the all the routes.