A vertex (B) is a successor to another vertex (A) if an arc points from
A to B. In such an arc, A is considered the 'tail', B is considered the
'head', as it would be visually represented with an arrow:
A -> B
Note that, in set terms,
g.adjacentTo(x) == g.successorsOf(x) ∪ g.predecessorsOf(x)
| public successorsOf ( object $vertex ) : Generator | ||
| $vertex | object | The vertex whose successor vertices should be enumerated. |
| return | Generator | A generator that yields successor vertices as values. |
/**
* Finds connected components in the provided directed graph.
*
* @param Digraph $graph
* The Digraph to search for connected components.
* @param TarjanSCCVisitor $visitor
* The visitor that will collect and store the connected components. One
* will be created if not provided.
*
* @return TarjanSCCVisitor
* The finalized visitor.
*/
public static function tarjan_scc(Digraph $graph, TarjanSCCVisitor $visitor = NULL)
{
$visitor = $visitor ?: new TarjanSCCVisitor();
$counter = 0;
$stack = array();
$indices = new \SplObjectStorage();
$lowlimits = new \SplObjectStorage();
$visit = function ($vertex) use(&$visit, &$counter, $graph, &$stack, $indices, $lowlimits, $visitor) {
$indices->attach($vertex, $counter);
$lowlimits->attach($vertex, $counter);
$stack[] = $vertex;
$counter++;
foreach ($graph->successorsOf($vertex) as $head) {
if (!$indices->contains($head)) {
$visit($head);
$lowlimits[$vertex] = min($lowlimits[$vertex], $lowlimits[$head]);
} else {
if (in_array($head, $stack, TRUE)) {
$lowlimits[$vertex] = min($lowlimits[$vertex], $indices[$head]);
}
}
}
if ($lowlimits[$vertex] === $indices[$vertex]) {
$visitor->newComponent();
do {
$other = array_pop($stack);
$visitor->addToCurrentComponent($other);
} while ($other != $vertex);
}
};
foreach ($graph->vertices() as $v) {
if (!$indices->contains($v)) {
$visit($v);
}
}
return $visitor;
}
public static function isLiveVar(Variable $var, Vertex $vtx, Digraph $graph)
{
static $seen = [];
if (in_array($vtx, $seen, true)) {
return false;
} elseif (in_array($var, $vtx->getVariables(), true)) {
return true;
}
$seen[] = $vtx;
foreach ($graph->successorsOf($vtx) as $sub) {
if (self::isLiveVar($var, $sub, $graph)) {
array_pop($seen);
return true;
}
}
array_pop($seen);
return false;
}