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<?php |
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namespace App\Component\Math\Graph\Path; |
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/** |
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* Weighted graph path finder using Floydwarshall method. |
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* Constructor expects a weighted square matrix |
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* and a nodes name collection to indentify nodes by name if required. |
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* |
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* @author Pierre Fromager <[email protected]> |
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*/ |
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class Floydwarshall |
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{ |
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/** |
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* max nodes |
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*/ |
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const INFINITE = 66666; |
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/** |
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* Distances array |
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* @var array |
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*/ |
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protected $dist; |
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/** |
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* Precedence matrix |
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* @var array |
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*/ |
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protected $pred; |
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/** |
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* Weights array |
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* @var array |
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*/ |
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protected $weights; |
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/** |
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* Number of nodes |
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* @var integer |
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*/ |
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protected $nodeCount; |
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/** |
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* Node names list |
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* @var array |
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*/ |
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protected $nodenames; |
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/** |
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* path. |
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* @var array |
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*/ |
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protected $path; |
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/** |
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* instanciate |
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* @param array $weightedMatrix graph weighted square matrice. |
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* @param array $nodenames nodes names as array. |
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*/ |
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public function __construct(array $weightedMatrix, array $nodenames = []) |
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{ |
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$this->reset(); |
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$this->weights = $weightedMatrix; |
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$this->nodeCount = count($this->weights); |
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if (!empty($nodenames) && $this->nodeCount == count($nodenames)) { |
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$this->nodenames = $nodenames; |
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} |
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} |
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/** |
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* populate from square matrix then calculate distance and precedence |
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*/ |
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public function process(): Floydwarshall |
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{ |
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$this->reset(); |
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$this->populate(); |
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for ($k = 0; $k < $this->nodeCount; $k++) { |
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for ($i = 0; $i < $this->nodeCount; $i++) { |
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for ($j = 0; $j < $this->nodeCount; $j++) { |
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$nextDist = $this->dist[$i][$k] + $this->dist[$k][$j]; |
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if ($this->dist[$i][$j] > $nextDist) { |
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$this->dist[$i][$j] = $nextDist; |
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$this->pred[$i][$j] = $this->pred[$k][$j]; |
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} |
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} |
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} |
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} |
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return $this; |
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} |
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/** |
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* return path |
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* |
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* @param string $src |
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* @param string $dst |
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* @param boolean $withNames |
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* @return array |
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*/ |
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public function path(string $src, string $dst, bool $withNames = false): array |
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{ |
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$srcIdx = array_search($src, $this->nodenames); |
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$dstIdx = array_search($dst, $this->nodenames); |
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$this->path = []; |
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$this->searchPath($srcIdx, $dstIdx); |
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$path = ($withNames) |
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? array_map(function ($v) { |
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return $this->nodenames[$v]; |
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}, $this->path) |
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: $this->path; |
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return $path; |
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} |
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/** |
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* recursive search for node path |
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* |
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* @param integer $i |
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* @param integer $j |
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* @return Floydwarshall |
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*/ |
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protected function searchPath(int $i, int $j): Floydwarshall |
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{ |
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if ($i != $j) { |
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$pred = $this->pred[$i][$j]; |
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$this->searchPath($i, $pred); |
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} |
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$this->path[] = $j; |
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return $this; |
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} |
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/** |
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* return distance matrix |
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* |
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* @return array |
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*/ |
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public function getDistances(): array |
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{ |
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return $this->dist; |
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} |
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/** |
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* return distance between two nodes identified by row/col couple. |
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* if one member of couple is undefined infinite value is returned. |
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* |
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* @return float |
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*/ |
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public function getDistance(int $i, int $j): float |
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{ |
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return (isset($this->dist[$i][$j])) ? $this->dist[$i][$j] : self::INFINITE; |
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} |
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/** |
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* return precedence matrix |
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* |
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* @return array |
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*/ |
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public function getPrecedences(): array |
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{ |
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return $this->pred; |
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} |
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/** |
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* reset |
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* |
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* @return Floydwarshall |
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*/ |
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protected function reset(): Floydwarshall |
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{ |
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$this->path = []; |
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$this->dist = [[]]; |
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$this->pred = [[]]; |
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return $this; |
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} |
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/** |
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* populate graph nodes to |
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* set distances matrix from weights |
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* and set matrix precedences |
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* |
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* @return Floydwarshall |
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*/ |
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protected function populate(): Floydwarshall |
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{ |
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for ($i = 0; $i < $this->nodeCount; $i++) { |
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for ($j = 0; $j < $this->nodeCount; $j++) { |
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if ($i == $j) { |
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$this->dist[$i][$j] = 0; |
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} elseif (isset($this->weights[$i][$j]) && $this->weights[$i][$j] > 0) { |
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$this->dist[$i][$j] = $this->weights[$i][$j]; |
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} else { |
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$this->dist[$i][$j] = self::INFINITE; |
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} |
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$this->pred[$i][$j] = $i; |
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} |
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} |
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return $this; |
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} |
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} |
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pierre-fromager /
nymfonya
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