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<?php |
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namespace Bmichotte\Dijkstra; |
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class Dijkstra |
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{ |
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private $positions; |
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private $from; |
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private $to; |
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private $weights; |
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private $predecessors; |
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public function __construct(array $positions, Point $from, Point $to) |
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{ |
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$this->positions = $positions; |
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$this->from = $from; |
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$this->to = $to; |
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} |
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public function findShortestPath(): array |
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{ |
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$this->weights = []; |
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$this->predecessors = []; |
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foreach ($this->positions as $position) { |
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$weight = -1; |
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$passed = false; |
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if ($position->equals($this->from)) { |
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$weight = 0; |
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$passed = true; |
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} |
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// init weights array |
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$this->weights[$position->ref] = [ |
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'position' => $position, |
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'weight' => $weight, |
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'passed' => $passed, |
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]; |
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// init predecessors array |
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$this->predecessors[$position->ref] = [ |
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'position' => $position, |
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'previous' => null, |
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]; |
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} |
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return $this->run($this->from)->getPath(); |
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} |
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protected function run(Point $parent): self |
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{ |
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// we reached the final point ! |
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if ($parent->equals($this->to)) { |
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return $this; |
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} |
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// we can set this node has been passed by |
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$this->weights[$parent->ref]['passed'] = true; |
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// search for weight between $parent and its children |
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foreach ($parent->points as $child) { |
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$this->calculateWeight($parent, $child); |
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} |
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return $this->findNextParent(); |
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} |
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protected function findNextParent(): self |
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{ |
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// search for the next parent (smallest weight) |
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// we have to find the smallest weight for a node we didn't passed by atm |
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$smallest = INF; |
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$nextParent = null; |
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foreach ($this->weights as $weight) { |
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if ($weight['weight'] < $smallest && $weight['weight'] !== -1 && ! $weight['passed']) { |
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$smallest = $weight['weight']; |
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$nextParent = $weight['position']; |
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} |
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} |
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if ($nextParent !== null) { |
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return $this->run($nextParent); |
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} |
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return $this; |
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} |
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protected function getPath(): array |
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{ |
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$path = [$this->to]; |
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$point = $this->to; |
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while (true) { |
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foreach ($this->predecessors as $predecessor) { |
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if ($predecessor['position']->equals($point)) { |
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$point = $predecessor['previous']; |
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$path[] = $point; |
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break; |
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} |
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} |
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// $point is null -> path impossible |
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if (is_null($point)) { |
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unset($path[count($path) - 1]); |
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break; |
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} |
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if ($point->equals($this->from)) { |
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break; |
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} |
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} |
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$path = array_reverse($path); |
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return $path; |
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} |
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protected function calculateWeight(Point $parent, Point $child): void |
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{ |
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/* |
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* Dijkstra algo says : |
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* |
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* IF (child-node is not traversed yet) AND |
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* (WEIGHT(parent-node) + WEIGHT(DISTANCE(parent-node, child-node) < WEIGHT(child-node) OR WEIGHT(child-node) = -1) |
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* THEN |
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* WEIGHT(child-node) = WEIGHT(parent-node) + WEIGHT(DISTANCE(parent-node, child-node) |
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* PREDECESSOR(child-node) = parent-node |
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* ENDIF |
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*/ |
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if (! $this->weights[$child->ref]['passed'] |
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&& ($this->weights[$parent->ref]['weight'] + self::distance($parent, $child) < $this->weights[$child->ref]['weight'] |
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|| $this->weights[$child->ref]['weight'] === -1)) { |
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$this->weights[$child->ref]['weight'] = $this->weights[$parent->ref]['weight'] + self::distance($parent, $child); |
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$this->predecessors[$child->ref]['previous'] = $parent; |
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} |
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} |
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public static function distance(Point $p1, Point $p2): float |
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{ |
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// distance = square root of ((x2 - x1)^2 + (y2 - y1)^2) |
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return sqrt(bcpow($p2->x - $p1->x, 2) + bcpow($p2->y - $p1->y, 2)); |
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} |
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} |
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bmichotte /
dijkstra
