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<?php |
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namespace BingoSoft\Heap\Tree; |
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use Exception; |
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use InvalidArgumentException; |
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use BingoSoft\Heap\exception\NoSuchElementException; |
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use BingoSoft\Heap\MergeableAddressableHeapInterface; |
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use BingoSoft\Heap\AddressableHeapHandleInterface; |
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/** |
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* Class PairingHeap |
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* |
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* @package BingoSoft\Heap\Tree |
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*/ |
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class PairingHeap implements MergeableAddressableHeapInterface |
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{ |
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/** |
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* The heap unique hash |
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* |
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* @var string |
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*/ |
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private $hash; |
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/** |
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* The heap root node |
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* |
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* @var PairingHeapNode |
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*/ |
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private $root = null; |
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/** |
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* Size of the heap |
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* |
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* @var int |
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*/ |
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private $size = 0; |
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/** |
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* Reference to current or some other heap in case of melding |
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* |
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* @var PairingHeap |
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*/ |
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private $other; |
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/** |
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* Construct a new Pairing heap |
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*/ |
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public function __construct() |
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{ |
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$this->root = null; |
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$this->size = 0; |
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$this->other = $this; |
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$this->hash = uniqid('', true); |
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} |
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/** |
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* Insert a new node to the heap |
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* |
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* @param int $key - node key |
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* @param null|mixed $value - node value |
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* |
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* @return AddressableHeapHandleInterface |
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* |
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* @throws Exception |
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*/ |
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public function insert(int $key, $value = null): AddressableHeapHandleInterface |
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{ |
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if ($this->other != $this) { |
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throw new Exception("A heap cannot be used after a meld"); |
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} |
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$node = new PairingHeapNode($this, $key, $value); |
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$this->root = $this->link($this->root, $node); |
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$this->size += 1; |
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return $node; |
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} |
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/** |
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* Find heap node with the minimal key |
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* |
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* @return AddressableHeapHandleInterface |
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* |
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* @throws NoSuchElementException |
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*/ |
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public function findMin(): AddressableHeapHandleInterface |
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{ |
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if ($this->size == 0) { |
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throw new NoSuchElementException("No such element!"); |
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} |
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return $this->root; |
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} |
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/* |
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* Delete a node |
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* |
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* @param PairingHeapNode $node - the node to delete |
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*/ |
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public function delete(PairingHeapNode $node): void |
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{ |
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if ($this->root == $node) { |
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$this->deleteMin(); |
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$node->o_c = null; |
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$node->y_s = null; |
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$node->o_s = null; |
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return; |
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} |
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if (is_null($node->o_s)) { |
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throw new InvalidArgumentException("Invalid handle!"); |
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} |
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// unlink from parent |
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if (!is_null($node->y_s)) { |
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$node->y_s->o_s = $node->o_s; |
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} |
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if ($node->o_s->o_c == $node) { |
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$node->o_s->o_c = $node->y_s; |
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} else { |
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$node->o_s->y_s = $node->y_s; |
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} |
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$node->y_s = null; |
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$node->o_s = null; |
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// perform delete-min at tree rooted at this |
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$t = $this->combine($this->cutChildren($node)); |
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// and merge with other cut tree |
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$this->root = $this->link($this->root, $t); |
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$this->size -= 1; |
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} |
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/** |
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* Delete an element with the minimal key. |
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* |
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* @return AddressableHeapHandleInterface |
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* |
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* @throws NoSuchElementException |
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*/ |
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public function deleteMin(): AddressableHeapHandleInterface |
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{ |
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if ($this->size == 0) { |
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throw new NoSuchElementException("No such element!"); |
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} |
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$oldRoot = $this->root; |
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$this->root = $this->combine($this->cutChildren($this->root)); |
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$this->size -= 1; |
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return $oldRoot; |
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} |
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/** |
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* Check if the heap is empty. |
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* |
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* @return bool |
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*/ |
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public function isEmpty(): bool |
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{ |
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return $this->size == 0; |
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} |
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/** |
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* Get the number of elements in the heap. |
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* |
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* @return int |
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*/ |
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public function size(): int |
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{ |
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return $this->size; |
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} |
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/** |
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* Get the other heap referenced in the current heap |
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* |
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* @return MergeableAddressableHeapInterface |
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*/ |
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public function getOther(): MergeableAddressableHeapInterface |
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{ |
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return $this->other; |
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} |
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/** |
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* Reference the other heap in the current heap |
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* |
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* @param MergeableAddressableHeapInterface $other - the other heap |
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*/ |
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public function setOther(MergeableAddressableHeapInterface $other): void |
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{ |
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if (!($other instanceof PairingHeap)) { |
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throw new InvalidArgumentException("The heap must be of type Pairing."); |
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} |
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$this->other = $other; |
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} |
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/** |
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* Clear all the elements in the heap |
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*/ |
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public function clear(): void |
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{ |
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$this->root = null; |
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$this->size = 0; |
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$this->other = $this; |
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} |
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/** |
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* Meld other heap to the current heap |
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* |
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* @param MergeableAddressableHeapInterface $other - the heap to be melded |
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* |
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* @throws Exception |
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*/ |
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public function meld(MergeableAddressableHeapInterface $other): void |
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{ |
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if (!($other instanceof PairingHeap)) { |
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throw new InvalidArgumentException("The heap to be melded must be of type Pairing."); |
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} |
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if ($other->other != $other) { |
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throw new Exception("A heap cannot be used after a meld."); |
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} |
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$this->size += $other->size; |
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$this->root = $this->link($this->root, $other->root); |
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// clear other |
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$other->size = 0; |
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$other->root = null; |
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// take ownership |
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$other->other = $this; |
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} |
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/** |
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* Decrease the node key |
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* |
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* @param PairingHeapNode $node - the node |
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* @param int $newKey - the node new key |
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* |
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* @throws Exception |
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*/ |
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public function decreaseKey(PairingHeapNode $node, int $newKey): void |
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{ |
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if ($newKey > $node->key) { |
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throw new InvalidArgumentException("Keys can only be decreased!"); |
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} elseif ($node->key != $newKey) { |
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if (is_null($node->o_s)) { |
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throw new InvalidArgumentException("Invalid handle!"); |
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} |
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$node->key = $newKey; |
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// unlink from parent |
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if (!is_null($node->y_s)) { |
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$node->y_s->o_s = $node->o_s; |
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} |
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if ($node->o_s->o_c == $node) { |
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$node->o_s->o_c = $node->y_s; |
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} else { |
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$node->o_s->y_s = $node->y_s; |
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} |
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$node->y_s = null; |
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$node->o_s = null; |
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// merge with root |
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$this->root = $this->link($this->root, $node); |
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} |
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} |
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/* |
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* Link two nodes |
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* |
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* @param PairingHeapNode $first - first node |
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* @param PairingHeapNode $second - second node |
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* |
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* @return null|PairingHeapNode |
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*/ |
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private function link(?PairingHeapNode $first = null, ?PairingHeapNode $second = null): ?PairingHeapNode |
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{ |
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if (is_null($second)) { |
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return $first; |
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} elseif (is_null($first)) { |
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return $second; |
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} elseif ($first->key < $second->key) { |
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$second->y_s = $first->o_c; |
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$second->o_s = $first; |
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if ($first->o_c != null) { |
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$first->o_c->o_s = $second; |
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} |
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$first->o_c = $second; |
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return $first; |
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} |
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return $this->link($second, $first); |
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} |
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/** |
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* Cut the children of a node and return the list. |
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* |
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* @param PairingHeapNode $node - the root node |
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* |
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* @return PairingHeapNode |
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*/ |
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private function cutChildren(PairingHeapNode $node): ?PairingHeapNode |
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{ |
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$child = $node->o_c; |
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$node->o_c = null; |
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if (!is_null($child)) { |
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$child->o_s = null; |
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} |
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return $child; |
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} |
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/* |
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* Two pass pair and compute root. |
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* |
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* @param PairingHeapNode $node - the node |
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* |
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* @return null|PairingHeapNode |
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*/ |
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private function combine(?PairingHeapNode $node = null): ?PairingHeapNode |
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{ |
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if (is_null($node)) { |
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return null; |
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} |
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if (!is_null($node->o_s)) { |
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throw new InvalidArgumentException("Invalid handle!"); |
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} |
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// left-right pass |
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$pairs = null; |
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$it = $node; |
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while (!is_null($it)) { |
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$p_it = $it; |
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$it = $it->y_s; |
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if (is_null($it)) { |
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// append last node to pair list |
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$p_it->y_s = $pairs; |
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$p_it->o_s = null; |
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$pairs = $p_it; |
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} else { |
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$n_it = $it->y_s; |
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// disconnect both |
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$p_it->y_s = null; |
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$p_it->o_s = null; |
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$it->y_s = null; |
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$it->o_s = null; |
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// link trees |
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$p_it = $this->link($p_it, $it); |
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// append to pair list |
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$p_it->y_s = $pairs; |
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$pairs = $p_it; |
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// advance |
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$it = $n_it; |
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} |
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} |
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// second pass (reverse order - due to add first) |
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$it = $pairs; |
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$f = null; |
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while (!is_null($it)) { |
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$nextIt = $it->y_s; |
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$it->y_s = null; |
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$f = $this->link($f, $it); |
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$it = $nextIt; |
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} |
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return $f; |
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} |
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} |
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