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<?php |
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namespace TemplesOfCode\NodesAndEdges\BFS; |
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use TemplesOfCode\NodesAndEdges\Graph; |
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/** |
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* Class BreadthFirstPaths |
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* @package TemplesOfCode\NodesAndEdges\BFS |
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*/ |
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class BreadthFirstPaths |
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{ |
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/** |
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* @var int |
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*/ |
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private const INFINITY = PHP_INT_MAX; |
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/** |
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* @var bool[] |
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*/ |
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private $marked; |
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/** |
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* edgeTo[v] = previous edge on shortest s-v path |
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* |
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* @var int[] |
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*/ |
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private $edgeTo; |
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/** |
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* distTo[v] = number of edges shortest s-v path |
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* |
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* @var int[] |
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*/ |
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private $distTo; |
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/** |
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* @var mixed |
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*/ |
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private $sourceV; |
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/** |
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* @var Graph |
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*/ |
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private $graph; |
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/** |
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* @param Graph $graph |
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* @param mixed $sourceV |
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*/ |
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public function __construct(Graph $graph, $sourceV) |
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{ |
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// set |
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$vertices = $graph->getVertices(); |
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// init |
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$this->distTo = array_fill(0, $vertices, static::INFINITY); |
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// check for data type |
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if (is_array($sourceV)) { |
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// handle multiple source vertices |
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$sourceVertices = $sourceV; |
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// iterate over the set of vertices |
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foreach ($sourceVertices as $vertex) { |
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// validate this vertex in the context of the given graph |
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Graph::validateVertex($vertex, $vertices); |
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} |
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} else { |
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// handle single vertex |
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$sourceVertex = $sourceV; |
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// validate this vertex in the context of the given graph |
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Graph::validateVertex($sourceVertex, $vertices); |
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// the distance to our source vertex is always zero |
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$this->distTo[$sourceVertex] = 0; |
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} |
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// set |
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$this->sourceV = $sourceV; |
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// init |
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$this->marked = array_fill(0, $vertices, false); |
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// init |
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$this->edgeTo = []; |
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// set |
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$this->graph = $graph; |
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// invoke bfs |
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$this->bfs(); |
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// check for data type |
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if (!is_array($sourceV)) { |
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// assert correct build |
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assert($this->check($this->graph, $sourceV)); |
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} |
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} |
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/** |
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* |
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*/ |
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private function bfs() |
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{ |
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// init |
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$queue = []; |
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// check for data type |
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if (is_array($this->sourceV)) { |
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// iterate over the set of source vertices |
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foreach ($this->sourceV as $vertex) { |
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// consider this vertex visited |
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$this->marked[$vertex] = true; |
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// set the distance |
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$this->distTo[$vertex] = 0; |
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// add to the queue |
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$queue[] = $vertex; |
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} |
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} else { |
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// init |
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$this->marked[$this->sourceV] = true; |
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// add beginning of queue |
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$queue = [$this->sourceV]; |
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} |
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// begin loop over the queue |
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while (!empty($queue)) { |
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// get the next vertex |
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$vertex = array_shift($queue); |
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// get the neighbors |
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$neighbors = $this->graph->adjacent($vertex); |
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// iterate over the adjacent vertices |
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foreach ($neighbors as $w) { |
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// process only if this vertex has been visited |
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if (!$this->marked[$w]) { |
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// $w can be reached via $vertex |
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$this->edgeTo[$w] = $vertex; |
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// add to the distance |
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$this->distTo[$w] = $this->distTo[$vertex] + 1; |
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// consider this vertex visited |
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$this->marked[$w] = true; |
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// add to the queue |
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$queue[] = $w; |
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} |
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} |
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} |
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} |
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/** |
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* @param int $vertex |
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* @return bool |
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*/ |
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public function hasPathTo(int $vertex) |
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{ |
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// validate this vertex in the context of the given graph |
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Graph::validateVertex($vertex, $this->graph->getVertices()); |
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// return the flag |
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return $this->marked[$vertex]; |
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} |
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/** |
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* @param int $vertex |
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* @return int |
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*/ |
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public function distTo(int $vertex) |
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{ |
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// validate this vertex in the context of the given graph |
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Graph::validateVertex($vertex, $this->graph->getVertices()); |
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// return the value |
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return $this->distTo[$vertex]; |
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} |
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/** |
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* @param int $vertex |
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* @return array|null |
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*/ |
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public function pathTo(int $vertex) |
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{ |
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// validate this vertex in the context of the given graph |
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Graph::validateVertex($vertex, $this->graph->getVertices()); |
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// check if there is a path |
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if (!$this->hasPathTo($vertex)) { |
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// there is no path |
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return null; |
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} |
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// init |
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$path = []; |
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// iterate over the path |
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for ($x = $vertex; $this->distTo[$x] != 0; $x = $this->edgeTo[$x]) { |
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// add this vertex |
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array_unshift($path, $x); |
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} |
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// add final vertex |
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array_unshift($path, $x); |
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// return the path |
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return $path; |
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} |
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/** |
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* @param Graph $graph |
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* @param int $sourceVertex |
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* @return bool |
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*/ |
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private function check(Graph $graph, int $sourceVertex) |
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{ |
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// check that the distance of s = 0 |
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if ($this->distTo[$sourceVertex] != 0) { |
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// check failed |
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return false; |
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} |
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// init |
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$vertices = $graph->getVertices(); |
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// check that for each edge v-w dist[w] <= dist[v] + 1 |
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// provided v is reachable from s |
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for ($vertex = 0; $vertex < $vertices; $vertex++) { |
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// get neighbors |
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$neighbors = $graph->adjacent($vertex); |
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// iterate over the neighbors |
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foreach ($neighbors as $w) { |
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// check paths |
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if ($this->hasPathTo($vertex) != $this->hasPathTo($w)) { |
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// check failed |
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return false; |
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} |
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// check distances |
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if ($this->hasPathTo($vertex) && ($this->distTo[$w] > $this->distTo[$vertex] + 1)) { |
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// check failed |
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return false; |
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} |
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} |
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} |
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// check that v = edgeTo[w] satisfies distTo[w] = distTo[v] + 1 |
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// provided v is reachable from s |
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for ($w = 0; $w < $vertices; $w++) { |
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if (!$this->hasPathTo($w) || $w == $sourceVertex) { |
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// good to go |
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continue; |
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} |
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// set |
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$v = $this->edgeTo[$w]; |
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// check distances |
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if ($this->distTo[$w] != $this->distTo[$v] + 1) { |
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// check failed |
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return false; |
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} |
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} |
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// check passed |
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return true; |
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} |
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} |
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templesofcode /
nodes-and-edges
