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<?php
namespace Graphp\Algorithms\Tree;
use Fhaculty\Graph\Graph;
use Fhaculty\Graph\Set\Vertices;
use Fhaculty\Graph\Vertex;
use Graphp\Algorithms\BaseGraph;
use Graphp\Algorithms\Degree;
/**
* Abstract base class for tree algorithms
*
* This abstract base class provides the base interface for working with
* graphs that represent a tree.
*
* A tree is a connected Graph (single component) with no cycles. Every Tree is
* a Graph, but not every Graph is a Tree. A null Graph (a Graph with no Vertices
* and thus no Edges) is *NOT* considered a valid Tree, as it is not considered
* connected (@see ConnectedComponents and @link)
*
* A
* / \
* B C
* / \
* D E
*
* Special cases are undirected trees (like the one pictured above), handled via
* Tree\Undirected and directed, rooted trees (InTree and OutTree), handled via
* Tree\BaseDirected.
*
* @link http://en.wikipedia.org/wiki/Tree_%28graph_theory%29
* @link http://en.wikipedia.org/wiki/Tree_%28data_structure%29
* @link http://mathoverflow.net/questions/120536/is-the-empty-graph-a-tree
* @see Undirected for an implementation of these algorithms on (undirected) trees
* @see BaseDirected for an abstract implementation of these algorithms on directed, rooted trees
*/
abstract class Base extends BaseGraph
{
/**
* @var Degree
*/
protected $degree;
public function __construct(Graph $graph)
{
parent::__construct($graph);
$this->degree = new Degree($graph);
}
/**
* checks whether the given graph is actually a tree
*
* @return bool
*/
abstract public function isTree();
/**
* checks if the given $vertex is a leaf (outermost vertext)
*
* leaf vertex is also known as leaf node, external node or terminal node
*
* @param Vertex $vertex
* @return bool
*/
abstract public function isVertexLeaf(Vertex $vertex);
/**
* checks if the given $vertex is an internal vertex (somewhere in the "middle" of the tree)
*
* internal vertex is also known as inner node (inode) or branch node
*
* @param Vertex $vertex
* @return bool
*/
abstract public function isVertexInternal(Vertex $vertex);
/**
* get array of leaf vertices (outermost vertices with no children)
*
* @return Vertices
* @uses Graph::getVertices()
* @uses self::isVertexLeaf()
*/
public function getVerticesLeaf()
{
return $this->graph->getVertices()->getVerticesMatch(array($this, 'isVertexLeaf'));
}
/**
* get array of internal vertices
*
* @return Vertices
* @uses Graph::getVertices()
* @uses self::isVertexInternal()
*/
public function getVerticesInternal()
{
return $this->graph->getVertices()->getVerticesMatch(array($this, 'isVertexInternal'));
}
}
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