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<?php
namespace Graphp\Algorithms\MinimumSpanningTree;
use Fhaculty\Graph\Edge\Base as Edge;
use Fhaculty\Graph\Graph;
use Fhaculty\Graph\Set\Edges;
use Graphp\Algorithms\Base as AlgorithmBase;
use SplPriorityQueue;
/**
* Abstract base class for minimum spanning tree (MST) algorithms
*
* A minimum spanning tree of a graph is a subgraph that is a tree and connects
* all the vertices together while minimizing the total sum of all edges'
* weights.
*
* A spanning tree thus requires a connected graph (single connected component),
* otherwise we can span multiple trees (spanning forest) within each component.
* Because a null graph (a Graph with no vertices) is not considered connected,
* it also can not contain a spanning tree.
*
* Most authors demand that the input graph has to be undirected, whereas this
* library supports also directed and mixed graphs. The actual direction of the
* edge will be ignored, only its incident vertices will be checked. This is
* done in order to be consistent to how ConnectedComponents are checked.
*
* @link http://en.wikipedia.org/wiki/Minimum_Spanning_Tree
* @link http://en.wikipedia.org/wiki/Spanning_Tree
* @link http://mathoverflow.net/questions/120536/is-the-empty-graph-a-tree
*/
abstract class Base extends AlgorithmBase
{
/**
* create new resulting graph with only edges on minimum spanning tree
*
* @return Graph
* @uses self::getGraph()
* @uses self::getEdges()
* @uses Graph::createGraphCloneEdges()
*/
public function createGraph()
{
return $this->getGraph()->createGraphCloneEdges($this->getEdges());
}
/**
* get all edges on minimum spanning tree
*
* @return Edges
*/
abstract public function getEdges();
/**
* return reference to current Graph
*
* @return Graph
*/
abstract protected function getGraph();
/**
* get total weight of minimum spanning tree
*
* @return float
*/
public function getWeight()
{
return $this->getEdges()->getSumCallback(function (Edge $edge) {
return $edge->getWeight();
});
}
/**
* helper method to add a set of Edges to the given set of sorted edges
*
* @param Edges $edges
* @param SplPriorityQueue $sortedEdges
*/
protected function addEdgesSorted(Edges $edges, SplPriorityQueue $sortedEdges)
{
// For all edges
foreach ($edges as $edge) {
assert($edge instanceof Edge);
// ignore loops (a->a)
if (!$edge->isLoop()) {
// Add edges with negative weight because of order in stl
$sortedEdges->insert($edge, -$edge->getWeight());
}
}
}
}
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