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Add Tree algorithms (skeleton)
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‎src/Tree/Base.php

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<?php
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namespace Fhaculty\Graph\Algorithm\Tree;
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use Fhaculty\Graph\Algorithm\BaseGraph;
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use Fhaculty\Graph\Graph;
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use Fhaculty\Graph\Vertex;
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use Fhaculty\Graph\Exception\UnderflowException;
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use Fhaculty\Graph\Exception\UnexpectedValueException;
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use Fhaculty\Graph\Algorithm\Search\StrictDepthFirst;
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/**
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*
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* @link http://en.wikipedia.org/wiki/Tree_%28graph_theory%29
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* @see OutTree
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* @see InTree
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*/
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abstract class Base extends BaseGraph
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{
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/**
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* checks whether the given graph is actually a tree
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*
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* @return boolean
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*/
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abstract public function isTree();
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/**
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* checks if the given $vertex is a leaf (outermost vertex / leaf node / external node / terminal node)
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*
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* @param Vertex $vertex
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* @return boolean
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*/
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abstract public function isVertexLeaf(Vertex $vertex);
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/**
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* checks if the given $vertex is an internal vertex (inner node / inode / branch node / somewhere in the "middle" of the tree)
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*
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* @param Vertex $vertex
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* @return boolean
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*/
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abstract public function isVertexInternal(Vertex $vertex);
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/**
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* get array of leaf vertices (outermost vertices with no children)
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*
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* @return Vertex[]
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* @uses Graph::getVertices()
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* @uses self::isVertexLeaf()
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*/
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public function getVerticesLeaf()
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{
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return array_filter($this->graph->getVertices(), array($this, 'isVertexLeaf'));
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}
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/**
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* get array of internal vertices
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*
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* @return Vertex[]
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* @uses Graph::getVertices()
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* @uses self::isVertexInternal()
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*/
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public function getVerticesInternal()
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{
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return array_filter($this->graph->getVertices(), array($this, 'isVertexInternal'));
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}
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}

‎src/Tree/BaseDirected.php

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<?php
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namespace Fhaculty\Graph\Algorithm\Tree;
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use Fhaculty\Graph\Algorithm\Tree\Base as Tree;
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use Fhaculty\Graph\Exception\UnderflowException;
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use Fhaculty\Graph\Exception\UnexpectedValueException;
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use Fhaculty\Graph\Algorithm\Search\Base as Search;
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use Fhaculty\Graph\Algorithm\Search\StrictDepthFirst;
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use Fhaculty\Graph\Vertex;
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/**
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*
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* @link http://en.wikipedia.org/wiki/Spaghetti_stack
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* @see OutTree
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*/
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abstract class BaseDirected extends Tree
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{
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const DIRECTION_CHILDREN = -1;
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/**
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* get root vertex for this in-tree
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*
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* @return Vertex
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* @throws UnderflowException if given graph is empty
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* @throws UnexpectedValueException if given graph is not a tree
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*/
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public function getVertexRoot()
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{
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$root = $this->getVertexPossibleRoot();
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$search = new StrictDepthFirst($root);
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$search->setDirection(static::DIRECTION_CHILDREN);
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$num = $search->getNumberOfVertices();
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if ($num !== $this->graph->getNumberOfVertices()) {
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throw new UnexpectedValueException();
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}
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return $root;
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}
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/**
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* checks if this is a tree
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*
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* @return boolean
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* @uses Graph::isEmpty()
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* @uses self::getVertexRoot() to actually check tree
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*/
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public function isTree()
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{
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if (!$this->graph->isEmpty()) {
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try {
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$this->getVertexRoot();
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}
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catch (UnexpectedValueException $e) {
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return false;
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}
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}
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return true;
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}
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/**
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* get parent vertex for given $vertex
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*
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* @param Vertex $vertex
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* @throws UnderflowException if vertex has no parent (is a root vertex)
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* @throws UnexpectedValueException if vertex has more than one possible parent (check isTree()!)
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* @return Vertex
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*/
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public function getVertexParent(Vertex $vertex)
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{
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$parents = $this->getVerticesParent($vertex);
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if (count($parents) !== 1) {
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if (!$parents) {
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throw new UnderflowException('No parents for given vertex found');
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} else {
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throw new UnexpectedValueException('More than one parent');
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}
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}
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return current($parents);
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}
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/**
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* get array of child vertices for given $vertex
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*
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* @param Vertex $vertex
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* @return Vertex[]
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*/
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abstract public function getVerticesChildren(Vertex $vertex);
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abstract protected function getVerticesParent(Vertex $vertex);
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protected function isVertexPossibleRoot(Vertex $vertex)
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{
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return (count($this->getVerticesParent($vertex)) === 0);
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}
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protected function getVertexPossibleRoot()
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{
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foreach ($this->graph->getVertices() as $vertex) {
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if ($this->isVertexPossibleRoot($vertex)) {
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return $vertex;
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}
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}
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throw new UnderflowException('No possible root found. Either empty graph or no Vertex with proper degree found.');
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}
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/**
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* checks if the given $vertex is a leaf (outermost vertex with no children)
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*
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* @param Vertex $vertex
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* @return boolean
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* @uses self::getVerticesChildren()
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*/
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public function isVertexLeaf(Vertex $vertex)
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{
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return (count($this->getVerticesChildren($vertex)) === 0);
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}
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public function isVertexInternal(Vertex $vertex)
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{
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return ($this->getVerticesParent($vertex) && $this->getVerticesChildren($vertex));
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}
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/**
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* get degree of tree (maximum number of children)
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*
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* @return int
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* @throws UnderflowException for empty graphs
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* @uses Graph::getVertices()
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* @uses self::getVerticesChildren()
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*/
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public function getDegree()
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{
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$max = null;
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foreach ($this->graph->getVertices() as $vertex) {
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$num = count($this->getVerticesChildren($vertex));
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if ($max === null || $num > $max) {
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$max = $num;
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}
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}
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if ($max === null) {
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throw new UnderflowException('No vertices found');
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}
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return $max;
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}
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/**
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* get depth of given $vertex (number of edges between root vertex)
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*
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* root has depth zero
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*
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* @param Vertex $vertex
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* @return int
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* @throws UnderflowException for empty graphs
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* @throws UnexpectedValueException if there's no path to root node (check isTree()!)
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* @uses self::getVertexRoot()
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* @uses self::getVertexParent() for each step
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*/
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public function getDepthVertex(Vertex $vertex)
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{
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$root = $this->getVertexRoot();
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$depth = 0;
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while ($vertex !== $root) {
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$vertex = $this->getVertexParent($vertex);
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++$depth;
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}
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return $depth;
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}
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/**
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* get height of this tree (longest downward path to a leaf)
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*
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* a single vertex graph has height zero
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*
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* @return int
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* @throws UnderflowException for empty graph
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* @uses self::getVertexRoot()
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* @uses self::getHeightVertex()
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*/
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public function getHeight()
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{
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return $this->getHeightVertex($this->getVertexRoot());
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}
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/**
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* get height of given vertex (longest downward path to a leaf)
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*
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* leafs has height zero
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*
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* @param Vertex $vertex
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* @return int
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* @uses self::getVerticesChildren() to get children of given vertex
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* @uses self::getHeightVertex() to recurse into sub-children
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*/
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public function getHeightVertex(Vertex $vertex)
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{
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$max = 0;
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foreach ($this->getVerticesChildren($vertex) as $vertex) {
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$height = $this->getHeightVertex($vertex) + 1;
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if ($height > $max) {
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$max = $height;
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}
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}
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return $max;
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}
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}

‎src/Tree/InTree.php

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<?php
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namespace Fhaculty\Graph\Algorithm\Tree;
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use Fhaculty\Graph\Algorithm\Tree\BaseDirected as DirectedTree;
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use Fhaculty\Graph\Exception\UnexpectedValueException;
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use Fhaculty\Graph\Algorithm\Search\Base as Search;
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use Fhaculty\Graph\Vertex;
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/**
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*
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* @link http://en.wikipedia.org/wiki/Spaghetti_stack
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* @see OutTree
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*/
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class InTree extends DirectedTree
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{
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const DIRECTION_CHILDREN = Search::DIRECTION_REVERSE;
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public function getVerticesChildren(Vertex $vertex)
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{
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return $vertex->getVerticesEdgeFrom();
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}
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protected function getVerticesParent(Vertex $vertex)
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{
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return $vertex->getVerticesEdgeTo();
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}
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}

‎src/Tree/OutTree.php

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<?php
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namespace Fhaculty\Graph\Algorithm\Tree;
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use Fhaculty\Graph\Algorithm\Tree\BaseDirected as DirectedTree;
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use Fhaculty\Graph\Exception\UnexpectedValueException;
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use Fhaculty\Graph\Algorithm\Search\StrictDepthFirst;
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use Fhaculty\Graph\Vertex;
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/**
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* A rooted tree with the "away from root" direction (a more narrow term is an "arborescence"), meaning:
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*
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* @link http://en.wikipedia.org/wiki/Arborescence_%28graph_theory%29
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* @see InTree
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*/
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class OutTree extends DirectedTree
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{
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const DIRECTION_CHILDREN = StrictDepthFirst::DIRECTION_FORWARD;
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public function getVerticesChildren(Vertex $vertex)
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{
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return $vertex->getVerticesEdgeTo();
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}
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protected function getVerticesParent(Vertex $vertex)
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{
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return $vertex->getVerticesEdgeFrom();
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}
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}

‎src/Tree/Undirected.php

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<?php
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namespace Fhaculty\Graph\Algorithm\Tree;
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use Fhaculty\Graph\Algorithm\Tree\Base as Tree;
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use Fhaculty\Graph\Exception\UnderflowException;
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use Fhaculty\Graph\Exception\UnexpectedValueException;
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use Fhaculty\Graph\Algorithm\Search\Base as Search;
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use Fhaculty\Graph\Algorithm\Search\StrictDepthFirst;
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use Fhaculty\Graph\Vertex;
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/**
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*
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*/
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class Undirected extends Tree
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{
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public function isTree()
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{
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if ($this->graph->isEmpty()) {
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return true;
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}
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// every vertex can represent a root vertex, so just pick one
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$root = $this->graph->getVertexFirst();
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// TODO: recurse $root to get sub-vertices
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$vertices = array();
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return (count($vertices) === $this->graph->getNumberOfVertices());
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}
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/**
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* checks if the given $vertex is a leaf (outermost vertex with exactly one edge)
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*
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* @param Vertex $vertex
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* @return boolean
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* @uses Vertex::getDegree()
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*/
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public function isVertexLeaf(Vertex $vertex)
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{
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return ($vertex->getDegree() === 1);
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}
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public function isVertexInternal(Vertex $vertex)
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{
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return ($vertex->getDegree() >= 2);
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}
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}

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