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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\Interfaces\TreeInterface; |
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use DataStructures\Trees\Interfaces\BinaryNodeInterface; |
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/** |
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* BinaryTreeAbstract |
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* |
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* BinaryTreeAbstract class is an abstract class that implements |
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* common binary trees methods. |
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* |
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* @author Siro Diaz Palazon <[email protected]> |
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*/ |
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abstract class BinaryTreeAbstract implements TreeInterface { |
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protected $root; |
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protected $size; |
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public abstract function createNode($key, $data, $parent = null, $left = null, $right = null); |
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/** |
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* Checks if the tree is empty. |
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* |
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* @return boolean true if is empty, else false. |
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*/ |
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public function empty() { |
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return $this->root === null; |
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} |
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/** |
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* Returns the tree size. |
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* |
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* @return int the length |
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*/ |
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public function size() { |
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return $this->size; |
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} |
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/** |
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* Inserts data in the correct position. |
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* |
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* @param integer|string $key the key used to store. |
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* @param mixed $data the data to store. |
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* @param bool $update if false the node isn't updated |
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* else if the key matches is updated. |
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*/ |
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public function put($key, $data, $update = false) { |
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$newNode = $this->createNode($key, $data); |
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if($this->root === null) { |
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$this->root = &$newNode; |
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$this->size++; |
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return; |
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} |
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$parentNode = null; |
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$current = &$this->root; |
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while($current !== null) { |
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$parentNode = &$current; |
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if($key < $current->key) { |
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$current = &$current->left; |
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View Code Duplication |
} else if($key > $current->key) { |
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$current = &$current->right; |
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} else { |
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if($update) { |
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$current->data = $data; |
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} |
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return; |
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} |
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} |
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$newNode->parent = &$parentNode; |
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if($key < $parentNode->key) { |
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$parentNode->left = &$newNode; |
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} else { |
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$parentNode->right = &$newNode; |
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} |
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$this->size++; |
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} |
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/** |
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* Creates a new node or updates it if already exists. |
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* |
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* @param int|string $key the key. |
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* @param mixed $data the data to be stored. |
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*/ |
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public function putOrUpdate($key, $data) { |
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$this->put($key, $data, true); |
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} |
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/** |
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* Retrieve the data stored in the tree. |
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* |
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* @param int|string $key the key to identify the data. |
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* @return mixed |
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*/ |
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public function get($key){ |
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if($this->root === null) { |
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return null; |
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} |
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$node = $this->root; |
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while($node !== null) { |
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if($key < $node->key) { |
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$node = $node->left; |
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} else if($key > $node->key) { |
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$node = $node->right; |
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} else { |
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return $node->data; |
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} |
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} |
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return null; |
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} |
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/** |
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* Returns the root node. |
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* |
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* @return DataStructures\Trees\Nodes\BSTNode|null the root node. |
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*/ |
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public function getRoot(){ |
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return $this->root; |
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} |
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/** |
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* Looks for the node with the given key. |
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* |
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* @param int|string $key the key used to look for. |
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* @return bool true if was found. |
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*/ |
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public function exists($key){ |
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// $this->_exists($this->root, $key); for recursive search |
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if($this->root === null) { |
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return false; |
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} |
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if($this->root->key === $key) { |
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return true; |
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} else { |
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$node = $this->root; |
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while($node !== null) { |
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View Code Duplication |
if($key < $node->key) { |
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$node = $node->left; |
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} else if($key > $node->key) { |
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$node = $node->right; |
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} else { |
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return true; |
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} |
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} |
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} |
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return false; |
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} |
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/** |
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* Method that retrieves true if found a node with the specified key. |
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* It's the recursive version of exists method and it's used internally |
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* for traverse through a root node. |
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* |
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* @param DataStructures\Trees\Nodes\BSTNode|null $node the root node. |
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* @param int|string $key the key used to look for. |
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* @return bool true if exists a node with that key. |
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*/ |
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private function _exists($node, $key) : bool { |
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if($node === null) { |
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return false; |
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} |
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if($node->key === $key) { |
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return true; |
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} else if($key < $node->key) { |
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return $this->_exists($node->left, $key); |
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} else if($key > $node->key) { |
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return $this->_exists($node->right, $key); |
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} |
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} |
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public function floor($key){} |
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public function ceil($key){} |
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/** |
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* Gets the node with the minimum key. The most left and more bottom. |
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* |
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* @return DataStructures\Trees\Nodes\BSTNode|null the minum node or |
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* null if the tree is empty. |
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*/ |
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public function min() { |
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if($this->root === null) { |
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return null; |
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} |
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if($this->root->left === null) { |
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return $this->root; |
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} |
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$current = $this->root; |
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while($current->left !== null) { |
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$current = $current->left; |
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} |
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return $current; |
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} |
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/** |
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* Gets the node with the maximum key. The most right and more bottom. |
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* |
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* @return DataStructures\Trees\Nodes\BSTNode|null the maximum node or |
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* null if the tree is empty. |
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*/ |
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public function max() { |
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if($this->root === null) { |
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return null; |
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} |
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if($this->root->right === null) { |
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return $this->root; |
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} |
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$node = $this->root; |
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while($node->right !== null) { |
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$node = $node->right; |
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} |
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return $node; |
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} |
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/** |
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* Returns the minimum node from a given node in position X. |
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* |
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* @param DataStructures\Trees\Nodes\BSTNode $node the start point. |
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* @return DataStructures\Trees\Nodes\BSTNode|null the minimum node. |
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*/ |
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View Code Duplication |
private function getMinNode(BinaryNodeInterface $node = null) { |
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if($node === null) { |
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return null; |
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} |
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while($node->left !== null) { |
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$node = $node->left; |
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} |
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return $node; |
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} |
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/** |
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* Returns the maximum node from a given node in position X. |
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* |
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* @param DataStructures\Trees\Nodes\BSTNode $node the start point. |
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* @return DataStructures\Trees\Nodes\BSTNode|null the maximum node. |
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*/ |
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private function getMaxNode(BinaryNodeInterface $node = null) { |
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if($node === null) { |
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return null; |
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} |
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while($node->right !== null) { |
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$node = $node->right; |
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} |
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return $node; |
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} |
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/** |
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* Deletes the node with the minimum key and returns it. The most left and more bottom. |
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* |
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* @param DataStructures\Trees\Nodes\BSTNode|null if null takes the root. |
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* @return DataStructures\Trees\Nodes\BSTNode|null the minimum node or |
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* null if the tree is empty. |
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*/ |
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View Code Duplication |
public function deleteMin(BinaryNodeInterface $node = null) { |
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$node = $this->getMinNode($node ?? $this->root); |
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if($node !== null) { |
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$this->_delete($node); |
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} |
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return $node; |
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} |
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/** |
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* Deletes the node with the maximum key and returns it. The most right and more bottom. |
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* |
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* @param DataStructures\Trees\Nodes\BSTNode|null if null takes the root. |
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* @return DataStructures\Trees\Nodes\BSTNode|null the maximum node or |
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* null if the tree is empty. |
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*/ |
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View Code Duplication |
public function deleteMax(BinaryNodeInterface $node = null) { |
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$node = $this->getMaxNode($node ?? $this->root); |
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if($node !== null) { |
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$this->_delete($node); |
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} |
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return $node; |
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} |
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/** |
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* Deletes the node with the maximum key and returns it. The most right and more bottom. |
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* |
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* @param DataStructures\Trees\Nodes\BSTNode|null if null takes the root. |
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* @return DataStructures\Trees\Nodes\BSTNode|null the maximum node or |
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* null if the tree is empty. |
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*/ |
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public function delete($key) { |
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$deleteNode = $this->search($key); |
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if($deleteNode !== null) { |
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$this->_delete($deleteNode); |
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return $deleteNode; |
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} |
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return null; |
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} |
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/** |
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* Deletes the selected node if is not null and returns the node |
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* that replaces the deleted node. Also decrease the size of tree. |
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* |
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* @param DataStructures\Trees\Nodes\BSTNode|null The node to be deleted. |
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* @return the node that replaces the deleted. |
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*/ |
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protected function _delete(BinaryNodeInterface &$node) { |
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if($node !== null) { |
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$nodeToReturn = null; |
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if($node->left === null) { |
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$nodeToReturn = $this->replace($node, $node->right); |
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} else if($node->right === null) { |
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$nodeToReturn = $this->replace($node, $node->left); |
|
|
|
|
|
|
333
|
|
|
} else { |
|
334
|
|
|
$successorNode = $this->getMinNode($node->right); |
|
|
|
|
|
|
335
|
|
|
if($successorNode->parent !== $node) { |
|
336
|
|
|
$this->replace($successorNode, $successorNode->right); |
|
337
|
|
|
$successorNode->right = &$node->right; |
|
|
|
|
|
|
338
|
|
|
$successorNode->right->parent = &$successorNode; |
|
339
|
|
|
} |
|
340
|
|
|
|
|
341
|
|
|
$this->replace($node, $successorNode); |
|
342
|
|
|
$successorNode->left = &$node->left; |
|
343
|
|
|
$successorNode->left->parent = &$successorNode; |
|
344
|
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|
$nodeToReturn = &$successorNode; |
|
345
|
|
|
} |
|
346
|
|
|
|
|
347
|
|
|
$this->size--; |
|
348
|
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|
return $nodeToReturn; |
|
349
|
|
|
} |
|
350
|
|
|
|
|
351
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return null; |
|
352
|
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} |
|
353
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|
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354
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/** |
|
355
|
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|
* Replaces the node n to remove a new one k and links k with the parent |
|
356
|
|
|
* of n. |
|
357
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* |
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358
|
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|
* @param DataStructures\Trees\Nodes\BSTNode $nodeToReplace the node to remove. |
|
359
|
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|
* @param DataStructures\Trees\Nodes\BSTNode|null $newNode the newNode |
|
360
|
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|
* to link with the $nodeToReplace parent. |
|
361
|
|
|
* @return DataStructures\Trees\Nodes\BSTNode the new linked node. |
|
362
|
|
|
*/ |
|
363
|
|
|
protected function replace(&$nodeToReplace, &$newNode) { |
|
364
|
|
|
if($nodeToReplace->parent === null) { |
|
365
|
|
|
$this->root = &$newNode; |
|
366
|
|
|
} else if($nodeToReplace === $nodeToReplace->parent->left) { |
|
367
|
|
|
$nodeToReplace->parent->left = &$newNode; |
|
368
|
|
|
} else if($nodeToReplace === $nodeToReplace->parent->right) { |
|
369
|
|
|
$nodeToReplace->parent->right = &$newNode; |
|
370
|
|
|
} |
|
371
|
|
|
|
|
372
|
|
|
if($newNode !== null) { |
|
373
|
|
|
$newNode->parent = &$nodeToReplace->parent; |
|
374
|
|
|
} |
|
375
|
|
|
|
|
376
|
|
|
return $newNode; |
|
377
|
|
|
} |
|
378
|
|
|
|
|
379
|
|
|
/** |
|
380
|
|
|
* Retrieves the node with the specified key. |
|
381
|
|
|
* |
|
382
|
|
|
* @param int|string $key the key used to store. |
|
383
|
|
|
* @return DataStructures\Trees\Nodes\BSTNode|null the node or null. |
|
384
|
|
|
*/ |
|
385
|
|
|
public function search($key) { |
|
386
|
|
|
if($this->root === null) { |
|
387
|
|
|
return null; |
|
388
|
|
|
} |
|
389
|
|
|
|
|
390
|
|
|
if($this->root->key === $key) { |
|
391
|
|
|
return $this->root; |
|
392
|
|
|
} else { |
|
393
|
|
|
$node = $this->root; |
|
394
|
|
|
while($node !== null) { |
|
395
|
|
View Code Duplication |
if($key < $node->key) { |
|
|
|
|
|
|
396
|
|
|
$node = $node->left; |
|
397
|
|
|
} else if($key > $node->key) { |
|
398
|
|
|
$node = $node->right; |
|
399
|
|
|
} else { |
|
400
|
|
|
return $node; |
|
401
|
|
|
} |
|
402
|
|
|
} |
|
403
|
|
|
} |
|
404
|
|
|
|
|
405
|
|
|
return null; |
|
406
|
|
|
} |
|
407
|
|
|
|
|
408
|
|
|
/** |
|
409
|
|
|
* Returns true if is leaf the node. |
|
410
|
|
|
* |
|
411
|
|
|
* @param DataStructures\Trees\Nodes\BSTNode|null $node default to null. |
|
412
|
|
|
* @return true if is leaf the node, is not null and their subtrees has no |
|
413
|
|
|
* pointers to successors. |
|
414
|
|
|
*/ |
|
415
|
|
|
public function isLeaf($node) { // BinaryTreeNode |
|
416
|
|
|
return ($node !== null && $node->left === null && $node->right === null); |
|
417
|
|
|
} |
|
418
|
|
|
|
|
419
|
|
|
/** |
|
420
|
|
|
* Checks if a node is root. New nodes that does not point to any other node |
|
421
|
|
|
* also are called a root node. |
|
422
|
|
|
* |
|
423
|
|
|
* @param DataStructures\Trees\Nodes\BSTNode|null $node default to null. |
|
424
|
|
|
* @return true if is root the node, is not null and their subtrees has no |
|
425
|
|
|
* pointers to successors. |
|
426
|
|
|
*/ |
|
427
|
|
|
public function isRoot($node) { |
|
428
|
|
|
return $node !== null && $node->parent === null; |
|
429
|
|
|
} |
|
430
|
|
|
|
|
431
|
|
|
/** |
|
432
|
|
|
* Traverse in preorder. This is: first visit the root, then |
|
433
|
|
|
* the left subtree and finally the right subtree. |
|
434
|
|
|
* |
|
435
|
|
|
* @param Callable|null $callback the callback function to apply to each |
|
436
|
|
|
* node. |
|
437
|
|
|
*/ |
|
438
|
|
|
public function preorder(Callable $callback = null) { |
|
439
|
|
|
$this->_preorder($this->root, $callback); |
|
440
|
|
|
} |
|
441
|
|
|
|
|
442
|
|
|
/** |
|
443
|
|
|
* Private preorder traverse method that is recursive and is called by |
|
444
|
|
|
* the public preorder method. |
|
445
|
|
|
* |
|
446
|
|
|
* @param DataStructures\Trees\Nodes\BSTNode|null $node. |
|
|
|
|
|
|
447
|
|
|
* @param Callable|null $callback the callback function to apply to each |
|
448
|
|
|
* node. |
|
449
|
|
|
*/ |
|
450
|
|
View Code Duplication |
private function _preorder($node, Callable $callback = null) { |
|
|
|
|
|
|
451
|
|
|
if($node === null) { |
|
452
|
|
|
return; |
|
453
|
|
|
} |
|
454
|
|
|
if($callback !== null) { |
|
455
|
|
|
call_user_func($callback, $node); |
|
456
|
|
|
} |
|
457
|
|
|
$this->_preorder($node->left, $callback); |
|
458
|
|
|
$this->_preorder($node->right, $callback); |
|
459
|
|
|
} |
|
460
|
|
|
|
|
461
|
|
|
/** |
|
462
|
|
|
* Traverse in inorder. This is: first visit the left subtree, |
|
463
|
|
|
* then the root and finally the right subtree. |
|
464
|
|
|
* |
|
465
|
|
|
* @param Callable|null $callback the callback function to apply to each |
|
466
|
|
|
* node. |
|
467
|
|
|
*/ |
|
468
|
|
|
public function inorder(Callable $callback = null) { |
|
|
|
|
|
|
469
|
|
|
$this->_inorder($this->root); |
|
470
|
|
|
} |
|
471
|
|
|
|
|
472
|
|
|
/** |
|
473
|
|
|
* Private inorder traverse method that is recursive and is called by |
|
474
|
|
|
* the public inorder method. |
|
475
|
|
|
* |
|
476
|
|
|
* @param DataStructures\Trees\Nodes\BSTNode|null $node. |
|
|
|
|
|
|
477
|
|
|
* @param Callable|null $callback the callback function to apply to each |
|
478
|
|
|
* node. |
|
479
|
|
|
*/ |
|
480
|
|
View Code Duplication |
private function _inorder($node, Callable $callback = null) { |
|
|
|
|
|
|
481
|
|
|
if($node === null) { |
|
482
|
|
|
return; |
|
483
|
|
|
} |
|
484
|
|
|
|
|
485
|
|
|
$this->_inorder($node->left, $callback); |
|
486
|
|
|
if($callback !== null) { |
|
487
|
|
|
call_user_func($callback, $node); |
|
488
|
|
|
} |
|
489
|
|
|
$this->_inorder($node->right, $callback); |
|
490
|
|
|
} |
|
491
|
|
|
|
|
492
|
|
|
/** |
|
493
|
|
|
* Traverse in postorder. This is: first visit the left subtree, |
|
494
|
|
|
* then the right subtree and finally the root. |
|
495
|
|
|
* |
|
496
|
|
|
* @param Callable|null $callback the callback function to apply to each |
|
497
|
|
|
* node. |
|
498
|
|
|
*/ |
|
499
|
|
|
public function postorder(Callable $callback = null) { |
|
500
|
|
|
$this->_postorder($this->root, $callback); |
|
501
|
|
|
} |
|
502
|
|
|
|
|
503
|
|
|
/** |
|
504
|
|
|
* Private postorder traverse method that is recursive and is called by |
|
505
|
|
|
* the public postorder method. |
|
506
|
|
|
* |
|
507
|
|
|
* @param DataStructures\Trees\Nodes\BSTNode|null $node. |
|
|
|
|
|
|
508
|
|
|
* @param Callable|null $callback the callback function to apply to each |
|
509
|
|
|
* node. |
|
510
|
|
|
*/ |
|
511
|
|
View Code Duplication |
private function _postorder($node, Callable $callback = null) { |
|
|
|
|
|
|
512
|
|
|
if($node === null) { |
|
513
|
|
|
return; |
|
514
|
|
|
} |
|
515
|
|
|
$this->_postorder($node->left, $callback); |
|
516
|
|
|
$this->_postorder($node->right, $callback); |
|
517
|
|
|
if($callback !== null) { |
|
518
|
|
|
call_user_func($callback, $node); |
|
519
|
|
|
} |
|
520
|
|
|
} |
|
521
|
|
|
|
|
522
|
|
|
/** |
|
523
|
|
|
* Binds to count() method. This is equal to make $this->tree->size(). |
|
524
|
|
|
* |
|
525
|
|
|
* @return integer the tree size. 0 if it is empty. |
|
526
|
|
|
*/ |
|
527
|
|
|
public function count() { |
|
528
|
|
|
return $this->size; |
|
529
|
|
|
} |
|
530
|
|
|
} |