Question

I have implemented a union find algorithm that finds and joins an undirected graph with vertexes that are represented by integers. I want to know if someone has any psuedocode or an idea on how to see if components “connected” ie there is a path that goes from one node to another. For example, I have the following vertexes:

7 (source vertex), 9 (destination vertex) and 8 (source vertex), 7 (destination vertex) are all connected. However, something like 3 (source vertex), 5 (destination vertex) would not be connected to the previous set of components. Could anyone guide me in the right direction or give me an idea on how to test this? Thanks!

Answer 1

Yes, all you do is test whether the two nodes have the same root. If you use path compression when you build your graph, this turns out to be very fast.

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I think it is because I am trying to incorporate it into an
implementation of Kruskal’s algorithm with it. After I have found all
connected components, I want to sort output something that will denote
each disjoint set from each disjoint set. Sorry to bother you so much
but if possible might you have any psuedo code to explain what you
mean?

The sets are already identified by a common root node. After you have done all your unions, each unique set will have a single root. So you then run through each node and call Find on it. How about this:

typedef std::list< Node* > TNodeList;
typedef std::map< Node*, TNodeList > TSetMap;

TSetMap mysets;

// Assuming you have nodes stored in the list type I declared above...
for( TNodeList::iterator n = nodes.begin(); n != nodes.end(); n++ )
{
    Node *thisnode = *n;
    Node *rootnode = Find(thisnode);

    // Add to list for root.  Using the [] operator on map will create a new
    // list if none exists for that node.
    mysets[rootnode].push_back(thisnode);
}

Now you have a map containing all your sets as individual lists, and you can do what you like…

std::cout << "Number of disjoint sets: " << mysets.size() << std::endl;
int count = 0;

for( TSetMap::iterator s = mysets.begin(); s != mysets.end(); s++ )
{
    TNodeList & nl = s->second;
    std::cout << "Set " << ++count << " contains " << nl.size() << " nodes\n";
}

To make all these calls to Find efficient, you should implement path compression in your Union function.