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<?php |
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declare(strict_types = 1); |
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namespace drupol\phpartition; |
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use drupol\phpartition\Partition\Partition; |
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use drupol\phpartition\Partitions\Partitions; |
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/** |
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* Class Linear. |
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*/ |
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class Linear extends Partitioner |
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{ |
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/** |
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* @var \ArrayObject |
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*/ |
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protected $dataset; |
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/** |
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* Linear constructor. |
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*/ |
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public function __construct() |
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{ |
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$this->dataset = new \ArrayObject(); |
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} |
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/** |
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* {@inheritdoc} |
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*/ |
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public function add(...$values) |
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{ |
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foreach ($values as $value) { |
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$this->dataset->append($value); |
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} |
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return $this; |
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} |
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/** |
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* @param \drupol\phpartition\Partitions\Partitions $partitions |
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* @param array $dataset |
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* @param int $chunks |
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*/ |
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protected function fillPartitions(Partitions $partitions, array $dataset, int $chunks): void |
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{ |
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// An array S of non-negative numbers {s1, ... ,sn} |
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$s = \array_merge([null], \array_values($dataset)); // adapt indices here: [0..n-1] => [1..n] |
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// Integer K - number of ranges to split items into |
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$k = $chunks; |
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$n = \count($dataset); |
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// Let M[n,k] be the minimum possible cost over all partitionings of N elements to K ranges |
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$m = []; |
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// Let D[n,k] be the position of K-th divider |
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// which produces the minimum possible cost partitioning of N elements to K ranges |
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$d = []; |
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// Note: For code simplicity we don't use zero indices for `m` and `d` |
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// to make code match math formulas |
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// Let pi be the sum of first i elements (cost calculation optimization) |
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$p = []; |
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// 1) Init prefix sums array |
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// pi = sum of {s1, ..., si} |
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$p[0] = $this->getPartitionItemFactory()::create(0); |
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for ($i = 1; $i <= $n; ++$i) { |
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$p[$i] = $this->getPartitionItemFactory()::create($p[$i - 1]->getWeight() + $s[$i]->getWeight()); |
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} |
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// 2) Init boundaries |
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for ($i = 1; $i <= $n; ++$i) { |
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// The only possible partitioning of i elements to 1 range is a single all-elements range |
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// The cost of that partitioning is the sum of those i elements |
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$m[$i][1] = $p[$i]; // sum of {s1, ..., si} -- optimized using pi |
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} |
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for ($j = 1; $j <= $k; ++$j) { |
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// The only possible partitioning of 1 element into j ranges is a single one-element range |
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// The cost of that partitioning is the value of first element |
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$m[1][$j] = $s[1]; |
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} |
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// 3) Main recurrence (fill the rest of values in table M) |
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for ($i = 2; $i <= $n; ++$i) { |
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for ($j = 2; $j <= $k; ++$j) { |
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$solutions = []; |
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for ($x = 1; ($i - 1) >= $x; ++$x) { |
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$solutions[] = [ |
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0 => $this->getPartitionItemFactory()::create( |
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\max( |
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$m[$x][$j - 1]->getWeight(), |
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$p[$i]->getWeight() - $p[$x]->getWeight() |
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) |
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), |
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1 => $x, |
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]; |
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} |
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\usort( |
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$solutions, |
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static function (array $x, array $y) { |
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return $x[0] <=> $y[0]; |
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} |
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); |
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$best_solution = $solutions[0]; |
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$m[$i][$j] = $best_solution[0]; |
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$d[$i][$j] = $best_solution[1]; |
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} |
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} |
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// 4) Reconstruct partitioning |
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$i = $n; |
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$j = $k; |
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$partition = []; |
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while (0 < $j) { |
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// delimiter position |
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$dp = $d[$i][$j] ?? 0; |
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// Add elements after delimiter {sdp, ..., si} to resulting $partition. |
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$partition[] = \array_slice($s, $dp + 1, $i - $dp); |
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// Step forward: look for delimiter position for partitioning M[$dp, $j-1] |
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$i = $dp; |
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--$j; |
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} |
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// Fix order as we reconstructed the partitioning from end to start |
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$partition = \array_reverse($partition); |
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foreach ($partition as $i => $p) { |
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$partitions->partition($i)->exchangeArray($p); |
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} |
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} |
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} |
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drupol /
phpartition
