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[WIP] Add simple cycles algorithm #33

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51b97f7
Add Tarjan's strongly connected components algorithm
phyrwork Jul 25, 2017
3f712af
Add elementary cycles algorithm
phyrwork Oct 7, 2018
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106 changes: 106 additions & 0 deletions src/SimpleCycles.php
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<?php

namespace Graphp\Algorithms;

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

class SimpleCycles
{
/** @var Vertex[] */
protected $blockedSet;

/** @var Vertex[][] */
protected $blockedMap;

/** @var Vertex[] */
protected $stack;

/** @var Vertices[] */
protected $cycles;

/**
* Remove node from blocked set and recursively remove all dependent nodes from blocked set
* @param Vertex $v Node to unblock
*/
protected function unblock(Vertex $v)
{
unset($this->blockedSet[$v->getId()]);
if (isset($this->blockedMap[$v->getId()])) {
foreach ($this->blockedMap[$v->getId()] as $w) {
if (isset($this->blockedSet[$w->getId()])) {
$this->unblock($w);
}
}
unset($this->blockedMap[$v->getId()]);
}
}

/**
* Recursive node visit procedure
* @param Vertex $r Root node
* @param Vertex $v Visited node
* @return bool Found cycle
*/
protected function visit(Vertex $r, Vertex $v)
{
array_push($this->stack, $v);
$this->blockedSet[$v->getId()] = $v;
$found = false;
// Examine adjacent nodes
foreach ($v->getVerticesEdgeTo() as $w) {
if ($w->getId() === $r->getId()) {
// Adjacent node == start node .'. found a cycle
$found = true;
// Cycle is whatever is on the stack
$this->cycles[] = new Vertices($this->stack);
} else if (!isset($this->blockedSet[$w->getId()])) {
// Only visit adjacent node if not blocked
$found = $this->visit($r, $w) || $found;
}
}
if ($found) {
// If cycle found, block node and all nodes mapped to it
$this->unblock($v);
} else {
// Otherwise add node to all adjacent nodes' blocked map
foreach ($v->getVerticesEdgeTo() as $w) {
if (!isset($this->blockedMap[$w->getId()])) {
$this->blockedMap[$w->getId()] = array();
}
$this->blockedMap[$w->getId()][$v->getId()] = $v;
}
}
array_pop($this->stack);
return $found;
}

/**
* @param Graph $g
*/
protected function findCycles(Graph $g)
{
$this->blockedSet = array();
$this->blockedMap = array();
$this->stack = array();
foreach ($g->getVertices() as $v) {
$this->visit($v, $v);
$v->destroy();
}
}

/**
* @param Graph $graph
* @return array|Vertices[]
*/
public function getSimpleCycles(Graph $graph)
{
$this->cycles = array();
$components = new StronglyConnectedComponents();
foreach ($components->stronglyConnectedGraph($graph) as $component) {
$this->findCycles($component);
}
return $this->cycles;
}
}
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);
}
}
90 changes: 90 additions & 0 deletions tests/SimpleCyclesTest.php
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<?php

use Fhaculty\Graph\Graph;
use Fhaculty\Graph\Set\Vertices;
use Graphp\Algorithms\SimpleCycles;

class SimpleCyclesTest extends TestCase
{
public function providerGetSimpleCycles()
{
return array(
"simple cycle" => array(
"edges" => array(
array(8, 9),
array(9, 8),
),
"cycles" => array(
array(8, 9),
),
),
"strongly connected component (isolated)" => array(
"edges" => array(
array(1, 2),
array(1, 5),
array(2, 3),
array(3, 1),
array(3, 2),
array(3, 4),
array(3, 6),
array(4, 5),
array(5, 2),
array(6, 4),
),
"cycles" => array(
array(1, 2, 3),
array(1, 5, 2, 3),
array(2, 3),
array(2, 3, 4, 5),
array(2, 3, 6, 4, 5),
),
),
"strongly connected component (connected)" => array(
"edges" => array(
array(1, 2),
array(1, 5),
array(1, 8),
array(2, 3),
array(2, 7),
array(2, 9),
array(3, 1),
array(3, 2),
array(3, 4),
array(3, 6),
array(4, 5),
array(5, 2),
array(6, 4),
array(8, 9),
array(9, 8),
),
"cycles" => array(
array(8, 9),
array(1, 2, 3),
array(1, 5, 2, 3),
array(2, 3),
array(2, 3, 4, 5),
array(2, 3, 6, 4, 5),
),
),
);
}



/**
* @dataProvider providerGetSimpleCycles
*/
public function testGetSimpleCycles(array $edges, array $cycles)
{
$graph = new Graph();
foreach ($edges as $edge) {
$graph->createVertex($edge[0], true)->createEdgeTo($graph->createVertex($edge[1], true));
}
$alg = new SimpleCycles();
$actual = array();
foreach ($alg->getSimpleCycles($graph) as $cycle) {
$actual[] = $cycle->getIds();
}
$this->assertSame($cycles, $actual);
}
}
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