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<?php |
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/** |
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* DataStructures for PHP |
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* |
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* @link https://github.com/SiroDiaz/DataStructures |
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* @copyright Copyright (c) 2017 Siro Díaz Palazón |
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* @license https://github.com/SiroDiaz/DataStructures/blob/master/README.md (MIT License) |
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*/ |
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namespace DataStructures\Trees; |
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use DataStructures\Trees\BinaryTreeAbstract; |
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use DataStructures\Trees\Nodes\AVLNode; |
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/** |
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* AVLTree |
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* |
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* This class is an implementation of a AVL tree. It has as main feature that access, |
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* insertion and deletion is O(log n). This is like a BST but it has a slightly difference |
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* in nodes: contains a height attribute, used to detect when is needed to rebalance the |
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* tree to keep the O(log n). |
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* |
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* @author Siro Diaz Palazon <[email protected]> |
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*/ |
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class AVLTree extends BinaryTreeAbstract { |
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/** |
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* Creates a AVLNode. |
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* |
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* @param int|string $key the key used to store. |
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* @param mixed $data the data. |
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* @param DataStructures\Trees\Nodes\AVLNode|null $parent the parent node. |
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* @param DataStructures\Trees\Nodes\AVLNode|null $left the left child node. |
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* @param DataStructures\Trees\Nodes\AVLNode|null $right the right child node. |
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* |
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* @return DataStructures\Trees\Nodes\AVLNode the new node created. |
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*/ |
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public function createNode($key, $data, $parent = null, $left = null, $right = null) { |
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return new AVLNode($key, $data, $parent, $left, $right); |
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} |
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/** |
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* Does a right rotation. |
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* Example, rotate Y |
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* k2 k1 |
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* / \ / \ |
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* k1 Z ==> X k2 |
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* / \ / \ |
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*X Y Y Z |
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* |
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*/ |
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private function rightRotation(AVLNode $node) { |
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$aux = $node->right; |
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$node->right = &$aux->left; |
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$aux->left = $node; |
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$node->height = 1 + max($node->left->height, $node->right->height); |
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$aux->height = 1 + max($aux->right->height, $node->height); |
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$node = &$aux; |
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} |
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/* Does a right rotation. |
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* k2 k1 |
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* / \ / \ |
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* X k1 ==> k2 Z |
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* / \ / \ |
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* Y Z X Y |
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*/ |
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private function leftRotation(AVLNode $node) { |
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$aux = $node->left; |
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$node->left = &$aux->right; |
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$aux->right = $node; |
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$node->height = 1 + max($node->left->height, $node->right->height); |
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$aux->height = 1 + max($node->height, $aux->left->height); |
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$node = &$aux; |
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} |
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/** |
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* Double right rotation does first a left rotation of right child node |
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* that detects the imbalance and finally does a right rotation |
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* in the subtree root that detects the imbalance. |
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*/ |
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private function doubleRightRotation(AVLNode $node) { |
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$this->leftRotation($node->right); |
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$this->rightRotation($node); |
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} |
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/** |
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* Double left rotation does first a right rotation of left child node |
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* that detects the imbalance and finally does a left rotation |
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* in the subtree root that detects the imbalance. |
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*/ |
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private function doubleLeftRotation(AVLNode $node) { |
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$this->rightRotation($node->left); |
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$this->leftRotation($node); |
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} |
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} |
SiroDiaz /
DataStructures
