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<?php |
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/** |
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* Box packing (3D bin packing, knapsack problem). |
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* |
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* @author Doug Wright |
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*/ |
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declare(strict_types=1); |
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namespace DVDoug\BoxPacker; |
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use Psr\Log\LoggerAwareInterface; |
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use Psr\Log\LoggerInterface; |
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use Psr\Log\LogLevel; |
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use Psr\Log\NullLogger; |
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use WeakMap; |
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use function array_filter; |
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use function array_map; |
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use function array_merge; |
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use function array_sum; |
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use function assert; |
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use function count; |
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use function iterator_to_array; |
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use function usort; |
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/** |
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* Actual packer. |
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* @internal |
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*/ |
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class WeightRedistributor implements LoggerAwareInterface |
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{ |
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private LoggerInterface $logger; |
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/** |
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* @param WeakMap<Box, int> $boxQuantitiesAvailable |
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*/ |
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public function __construct( |
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private readonly BoxList $boxes, |
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private readonly PackedBoxSorter $packedBoxSorter, |
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private WeakMap $boxQuantitiesAvailable |
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) { |
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$this->logger = new NullLogger(); |
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} |
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public function setLogger(LoggerInterface $logger): void |
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{ |
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$this->logger = $logger; |
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} |
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/** |
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* Given a solution set of packed boxes, repack them to achieve optimum weight distribution. |
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*/ |
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public function redistributeWeight(PackedBoxList $originalBoxes): PackedBoxList |
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{ |
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$targetWeight = $originalBoxes->getMeanItemWeight(); |
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$this->logger->log(LogLevel::DEBUG, "repacking for weight distribution, weight variance {$originalBoxes->getWeightVariance()}, target weight {$targetWeight}"); |
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$boxes = iterator_to_array($originalBoxes); |
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usort($boxes, static fn (PackedBox $boxA, PackedBox $boxB) => $boxB->getWeight() <=> $boxA->getWeight()); |
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do { |
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$iterationSuccessful = false; |
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foreach ($boxes as $a => &$boxA) { |
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foreach ($boxes as $b => &$boxB) { |
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if ($b <= $a || $boxA->getWeight() === $boxB->getWeight()) { |
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continue; // no need to evaluate |
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} |
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$iterationSuccessful = $this->equaliseWeight($boxA, $boxB, $targetWeight); |
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if ($iterationSuccessful) { |
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$boxes = array_filter($boxes, static fn (?PackedBox $box) => $box instanceof PackedBox); // remove any now-empty boxes from the list |
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break 2; |
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} |
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} |
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} |
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} while ($iterationSuccessful); |
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// Combine back into a single list |
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$packedBoxes = new PackedBoxList($this->packedBoxSorter); |
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$packedBoxes->insertFromArray($boxes); |
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return $packedBoxes; |
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} |
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/** |
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* Attempt to equalise weight distribution between 2 boxes. |
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* |
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* @return bool was the weight rebalanced? |
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*/ |
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private function equaliseWeight(PackedBox &$boxA, PackedBox &$boxB, float $targetWeight): bool |
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{ |
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$anyIterationSuccessful = false; |
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if ($boxA->getWeight() > $boxB->getWeight()) { |
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$overWeightBox = $boxA; |
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$underWeightBox = $boxB; |
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} else { |
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$overWeightBox = $boxB; |
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$underWeightBox = $boxA; |
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} |
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$overWeightBoxItems = $overWeightBox->items->asItemArray(); |
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$underWeightBoxItems = $underWeightBox->items->asItemArray(); |
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foreach ($overWeightBoxItems as $key => $overWeightItem) { |
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if (!self::wouldRepackActuallyHelp($overWeightBoxItems, $overWeightItem, $underWeightBoxItems, $targetWeight)) { |
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continue; // moving this item would harm more than help |
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} |
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$newLighterBoxes = $this->doVolumeRepack(array_merge($underWeightBoxItems, [$overWeightItem]), $underWeightBox->box); |
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if ($newLighterBoxes->count() !== 1) { |
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continue; // only want to move this item if it still fits in a single box |
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} |
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$underWeightBoxItems[] = $overWeightItem; |
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if (count($overWeightBoxItems) === 1) { // sometimes a repack can be efficient enough to eliminate a box |
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$boxB = $newLighterBoxes->top(); |
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$boxA = null; |
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--$this->boxQuantitiesAvailable[$underWeightBox->box]; |
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++$this->boxQuantitiesAvailable[$overWeightBox->box]; |
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return true; |
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} |
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unset($overWeightBoxItems[$key]); |
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$newHeavierBoxes = $this->doVolumeRepack($overWeightBoxItems, $overWeightBox->box); |
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if (count($newHeavierBoxes) !== 1) { |
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assert(true, 'Could not pack n-1 items into box, even though n were previously in it'); |
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continue; |
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} |
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++$this->boxQuantitiesAvailable[$overWeightBox->box]; |
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++$this->boxQuantitiesAvailable[$underWeightBox->box]; |
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--$this->boxQuantitiesAvailable[$newHeavierBoxes->top()->box]; |
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--$this->boxQuantitiesAvailable[$newLighterBoxes->top()->box]; |
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$underWeightBox = $boxB = $newLighterBoxes->top(); |
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$overWeightBox = $boxA = $newHeavierBoxes->top(); |
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$anyIterationSuccessful = true; |
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} |
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return $anyIterationSuccessful; |
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} |
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/** |
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* Do a volume repack of a set of items. |
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* @param iterable<Item> $items |
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*/ |
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private function doVolumeRepack(iterable $items, Box $currentBox): PackedBoxList |
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{ |
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$packer = new Packer(); |
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$packer->throwOnUnpackableItem(false); |
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$packer->setLogger($this->logger); |
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$packer->setBoxes($this->boxes); // use the full set of boxes to allow smaller/larger for full efficiency |
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foreach ($this->boxes as $box) { |
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$packer->setBoxQuantity($box, $this->boxQuantitiesAvailable[$box]); |
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} |
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$packer->setBoxQuantity($currentBox, $this->boxQuantitiesAvailable[$currentBox] + 1); |
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$packer->setItems($items); |
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return $packer->doBasicPacking(true); |
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} |
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/** |
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* Not every attempted repack is actually helpful - sometimes moving an item between two otherwise identical |
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* boxes, or sometimes the box used for the now lighter set of items actually weighs more when empty causing |
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* an increase in total weight. |
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* @param array<Item> $overWeightBoxItems |
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* @param array<Item> $underWeightBoxItems |
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*/ |
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private static function wouldRepackActuallyHelp(array $overWeightBoxItems, Item $overWeightItem, array $underWeightBoxItems, float $targetWeight): bool |
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{ |
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$overWeightItemsWeight = array_sum(array_map(static fn (Item $item) => $item->getWeight(), $overWeightBoxItems)); |
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$underWeightItemsWeight = array_sum(array_map(static fn (Item $item) => $item->getWeight(), $underWeightBoxItems)); |
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if ($overWeightItem->getWeight() + $underWeightItemsWeight > $targetWeight) { |
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return false; |
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} |
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$oldVariance = self::calculateVariance($overWeightItemsWeight, $underWeightItemsWeight); |
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$newVariance = self::calculateVariance($overWeightItemsWeight - $overWeightItem->getWeight(), $underWeightItemsWeight + $overWeightItem->getWeight()); |
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return $newVariance < $oldVariance; |
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} |
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private static function calculateVariance(int $boxAWeight, int $boxBWeight): float |
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{ |
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return ($boxAWeight - (($boxAWeight + $boxBWeight) / 2)) ** 2; // don't need to calculate B and ÷ 2, for a 2-item population the difference from mean is the same for each box |
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} |
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} |
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dvdoug /
BoxPacker
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