/**
* Kruskal's algorithm to find a minimum-cost spanning tree
* for the given edge-weighted, undirected graph.
* Uses a partition and a priority queue.
*
* @param object IGraph $g An edge-weighted, undirected graph.
* It is assumed that the edge weights are <code>Int</code>s
* @return object IGraph An unweighted, undirected graph that represents
* the minimum-cost spanning tree.
*/
public static function kruskalsAlgorithm(IGraph $g)
{
$n = $g->getNumberOfVertices();
$result = new GraphAsLists($n);
for ($v = 0; $v < $n; ++$v) {
$result->addVertex($v);
}
$queue = new BinaryHeap($g->getNumberOfEdges());
foreach ($g->getEdges() as $edge) {
$weight = $edge->getWeight();
$queue->enqueue(new Association($weight, $edge));
}
$partition = new PartitionAsForest($n);
while (!$queue->isEmpty() && $partition->getCount() > 1) {
$assoc = $queue->dequeueMin();
$edge = $assoc->getValue();
$n0 = $edge->getV0()->getNumber();
$n1 = $edge->getV1()->getNumber();
$s = $partition->findItem($n0);
$t = $partition->findItem($n1);
if ($s !== $t) {
$partition->join($s, $t);
$result->addEdge($n0, $n1);
}
}
return $result;
}