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Add Tarjan's strongly connected components algorithm #26

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121 changes: 121 additions & 0 deletions src/StronglyConnectedComponents.php
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<?php

namespace Graphp\Algorithms;

use Fhaculty\Graph\Set\Vertices;
use Fhaculty\Graph\Graph;
use Fhaculty\Graph\Vertex;
use SplObjectStorage;

/**
* Tarjan's strongly connected components algorithm
*
* @link https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm
*/
class StronglyConnectedComponents
{
/** @var int */
public $minSize = 1;

/**
* Get vertices adjacent to vertex
*
* @param Vertex $v
* @return Vertex[]
*/
protected function vertexAdjacent(Vertex $v)
{
return $v->getVerticesEdgeTo()->getVector();
}

/**
* Find the strongly connected components of the given graph and return a set of Vertices which
* refer to the original Vertexes
*
* @param Graph $graph
* @return Vertices[]
*/
public function stronglyConnectedVertices(Graph $graph)
{
/** @var SplObjectStorage $preorder int[] */
$preorder = new SplObjectStorage();
/** @var SplObjectStorage $lowlink int[] */
$lowlink = new SplObjectStorage();
/** @var SplObjectStorage $scc_found bool[] */
$scc_found = new SplObjectStorage();
/** @var Vertex[] $scc_queue */
$scc_queue = array();
/** @var int $i */
$i = 0; // preorder counter
/** @var Vertices[] $sccs */
$sccs = array();

foreach ($graph->getVertices() as $source) {
if (!$scc_found->contains($source)) {
$queue = array($source);
while ($queue) {
/** @var Vertex $v */
$v = end($queue);
if (!$preorder->contains($v)) {
$i++;
$preorder[$v] = $i;
}
/** @var bool $done */
$done = true;
$v_nbrs = $this->vertexAdjacent($v);
foreach ($v_nbrs as $w) {
if (!$preorder->contains($w)) {
array_push($queue, $w);
$done = false;
break;
}
}
if ($done) {
$lowlink[$v] = $preorder[$v];
foreach ($v_nbrs as $w) {
if (!$scc_found->contains($w)) {
if ($preorder[$w] > $preorder[$v]) {
$lowlink[$v] = min($lowlink[$v], $lowlink[$w]);
} else {
$lowlink[$v] = min($lowlink[$v], $preorder[$w]);
}
}
}
array_pop($queue);
if ($lowlink[$v] === $preorder[$v]) {
$scc_found->attach($v);
/** @var Vertex[] $scc (Dictionary) */
$scc = array($v);
while ($scc_queue && $preorder[end($scc_queue)] > $preorder[$v]) {
/** @var Vertex $k */
$k = array_pop($scc_queue);
$scc_found->attach($k);
array_push($scc, $k);
}
array_push($sccs, new Vertices($scc));
} else {
array_push($scc_queue, $v);
}
}
}
}
}

$minSize = $this->minSize; // PHP < 5.4
return array_filter($sccs, function (Vertices $vertices) use ($minSize) { return $vertices->count() >= $minSize; });
}

/**
* Return a set of new Graphs each representing a discovered strongly connected connected component
*
* @param Graph $graph
* @return Graph[]
*/
public function stronglyConnectedGraph(Graph $graph)
{
$sccs = $this->stronglyConnectedVertices($graph);
return array_map(function(Vertices $vertices) use ($graph) {
return $graph->createGraphCloneVertices($vertices);
}, $sccs);
}
}
93 changes: 93 additions & 0 deletions tests/StronglyConnectedComponentsTest.php
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<?php

use Graphp\Algorithms\StronglyConnectedComponents;
use Fhaculty\Graph\Edge\Directed;
use Fhaculty\Graph\Graph;
use Fhaculty\Graph\Set\Vertices;

class StronglyConnectedComponentsTest extends TestCase
{
/**
* @link https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm
* @link https://en.wikipedia.org/wiki/Strongly_connected_component#Algorithms
*
* @return array
*/
public function providerCyclicDigraphs()
{
return array(
/** @link https://en.wikipedia.org/wiki/Strongly_connected_component#/media/File:Scc.png */
'1' => array(
'edges' => array(
array(1,2),
array(2,3), array(2,5), array(2,6),
array(3,4), array(3,7),
array(4,3), array(4,8),
array(5,1), array(5,6),
array(6,7),
array(7,6),
array(8,4), array(8,7),
),
'sets' => array(
array(1,2,5),
array(3,4,8),
array(6,7),
),
),
/** @link https://en.wikipedia.org/wiki/File:Tarjan%27s_Algorithm_Animation.gif */
'2' => array(
'edges' => array(
array(1,2),
array(2,3),
array(3,1),
array(4,2), array(4,3), array(4,5),
array(5,4), array(5,6),
array(6,3), array(6,7),
array(7,6),
array(8,5), array(8,7),
// array(8,8), /* @link https://github.com/clue/graph/issues/154 */
),
'sets' => array(
array(1,2,3),
array(4,5),
array(6,7),
array(8),
),
),
);
}

/**
* @param Graph $graph
* @param array $edge
* @return Directed
*/
public function addEdgeToGraph(Graph $graph, array $edge)
{
$from = $graph->createVertex($edge[0], true);
$to = $graph->createVertex($edge[1], true);
return $from->createEdgeTo($to);
}

/**
* @dataProvider providerCyclicDigraphs
* @param array $edges
* @param array $expected
*/
public function testStronglyConnectedSets(array $edges, array $expected)
{
$graph = new Graph();

foreach ($edges as $edge) {
$this->addEdgeToGraph($graph, $edge);
}

$alg = new StronglyConnectedComponents();
$sets = array_map(function (Vertices $vertices) {
return $vertices->getIds();
}, $alg->stronglyConnectedVertices($graph));

// Assert unordered array equals
$this->assertEquals($expected, $sets, "\$canonicalize = true", 0.0, 2, true);
}
}