TheAlgorithms-PHP/DataStructures/AVLTree/AVLTree.php

<?php

namespace DataStructures\AVLTree;

/**
 * Class AVLTree
 * Implements an AVL Tree data structure with self-balancing capability.
 */
class AVLTree
{
    private ?AVLTreeNode $root;
    private int $counter;

    public function __construct()
    {
        $this->root = null;
        $this->counter = 0;
    }

    /**
     * Get the root node of the AVL Tree.
     */
    public function getRoot(): ?AVLTreeNode
    {
        return $this->root;
    }

    /**
     * Retrieve a node by its key.
     *
     * @param mixed $key The key of the node to retrieve.
     * @return ?AVLTreeNode The node with the specified key, or null if not found.
     */
    public function getNode($key): ?AVLTreeNode
    {
        return $this->searchNode($this->root, $key);
    }

    /**
     * Get the number of nodes in the AVL Tree.
     */
    public function size(): int
    {
        return $this->counter;
    }

    /**
     * Insert a key-value pair into the AVL Tree.
     *
     * @param mixed $key The key to insert.
     * @param mixed $value The value associated with the key.
     */
    public function insert($key, $value): void
    {
        $this->root = $this->insertNode($this->root, $key, $value);
        $this->counter++;
    }

    /**
     * Delete a node by its key from the AVL Tree.
     *
     * @param mixed $key The key of the node to delete.
     */
    public function delete($key): void
    {
        $this->root = $this->deleteNode($this->root, $key);
        $this->counter--;
    }

    /**
     * Search for a value by its key.
     *
     * @param mixed $key The key to search for.
     * @return mixed The value associated with the key, or null if not found.
     */
    public function search($key)
    {
        $node = $this->searchNode($this->root, $key);
        return $node ? $node->value : null;
    }

    /**
     * Perform an in-order traversal of the AVL Tree.
     * Initiates the traversal on the root node directly and returns the array of key-value pairs.
     */
    public function inOrderTraversal(): array
    {
        return TreeTraversal::inOrder($this->root);
    }

    /**
     * Perform a pre-order traversal of the AVL Tree.
     * Initiates the traversal on the root node directly and returns the array of key-value pairs.
     */
    public function preOrderTraversal(): array
    {
        return TreeTraversal::preOrder($this->root);
    }

    /**
     * Perform a post-order traversal of the AVL Tree.
     * Initiates the traversal on the root node directly and returns the array of key-value pairs.
     */
    public function postOrderTraversal(): array
    {
        return TreeTraversal::postOrder($this->root);
    }

    /**
     * Perform a breadth-first traversal of the AVL Tree.
     */
    public function breadthFirstTraversal(): array
    {
        return TreeTraversal::breadthFirst($this->root);
    }

    /**
     * Check if the AVL Tree is balanced.
     * This method check balance starting from the root node directly
     */
    public function isBalanced(): bool
    {
        return $this->isBalancedHelper($this->root);
    }

    /**
     * Insert a node into the AVL Tree and balance the tree.
     *
     * @param ?AVLTreeNode $node The current node.
     * @param mixed $key The key to insert.
     * @param mixed $value The value to insert.
     * @return AVLTreeNode The new root of the subtree.
     */
    private function insertNode(?AVLTreeNode $node, $key, $value): AVLTreeNode
    {
        if ($node === null) {
            return new AVLTreeNode($key, $value);
        }

        if ($key < $node->key) {
            $node->left = $this->insertNode($node->left, $key, $value);
        } elseif ($key > $node->key) {
            $node->right = $this->insertNode($node->right, $key, $value);
        } else {
            $node->value = $value; // Update existing value
        }

        $node->updateHeight();
        return $this->balance($node);
    }

    /**
     * Delete a node by its key and balance the tree.
     *
     * @param ?AVLTreeNode $node The current node.
     * @param mixed $key The key of the node to delete.
     * @return ?AVLTreeNode The new root of the subtree.
     */
    private function deleteNode(?AVLTreeNode $node, $key): ?AVLTreeNode
    {
        if ($node === null) {
            return null;
        }

        if ($key < $node->key) {
            $node->left = $this->deleteNode($node->left, $key);
        } elseif ($key > $node->key) {
            $node->right = $this->deleteNode($node->right, $key);
        } else {
            if (!$node->left) {
                return $node->right;
            }
            if (!$node->right) {
                return $node->left;
            }

            $minNode = $this->getMinNode($node->right);
            $node->key = $minNode->key;
            $node->value = $minNode->value;
            $node->right = $this->deleteNode($node->right, $minNode->key);
        }

        $node->updateHeight();
        return $this->balance($node);
    }

    /**
     * Search for a node by its key.
     *
     * @param ?AVLTreeNode $node The current node.
     * @param mixed $key The key to search for.
     * @return ?AVLTreeNode The node with the specified key, or null if not found.
     */
    private function searchNode(?AVLTreeNode $node, $key): ?AVLTreeNode
    {
        if ($node === null) {
            return null;
        }

        if ($key < $node->key) {
            return $this->searchNode($node->left, $key);
        } elseif ($key > $node->key) {
            return $this->searchNode($node->right, $key);
        } else {
            return $node;
        }
    }

    /**
     * Helper method to check if a subtree is balanced.
     *
     * @param ?AVLTreeNode $node The current node.
     * @return bool True if the subtree is balanced, false otherwise.
     */
    private function isBalancedHelper(?AVLTreeNode $node): bool
    {
        if ($node === null) {
            return true;
        }

        $leftHeight = $node->left ? $node->left->height : 0;
        $rightHeight = $node->right ? $node->right->height : 0;

        $balanceFactor = abs($leftHeight - $rightHeight);
        if ($balanceFactor > 1) {
            return false;
        }

        return $this->isBalancedHelper($node->left) && $this->isBalancedHelper($node->right);
    }

    /**
     * Balance the subtree rooted at the given node.
     *
     * @param ?AVLTreeNode $node The current node.
     * @return ?AVLTreeNode The new root of the subtree.
     */
    private function balance(?AVLTreeNode $node): ?AVLTreeNode
    {
        if ($node->balanceFactor() > 1) {
            if ($node->left && $node->left->balanceFactor() < 0) {
                $node->left = $this->rotateLeft($node->left);
            }
            return $this->rotateRight($node);
        }

        if ($node->balanceFactor() < -1) {
            if ($node->right && $node->right->balanceFactor() > 0) {
                $node->right = $this->rotateRight($node->right);
            }
            return $this->rotateLeft($node);
        }

        return $node;
    }

    /**
     * Perform a left rotation on the given node.
     *
     * @param AVLTreeNode $node The node to rotate.
     * @return AVLTreeNode The new root of the rotated subtree.
     */
    private function rotateLeft(AVLTreeNode $node): AVLTreeNode
    {
        $newRoot = $node->right;
        $node->right = $newRoot->left;
        $newRoot->left = $node;

        $node->updateHeight();
        $newRoot->updateHeight();

        return $newRoot;
    }

    /**
     * Perform a right rotation on the given node.
     *
     * @param AVLTreeNode $node The node to rotate.
     * @return AVLTreeNode The new root of the rotated subtree.
     */
    private function rotateRight(AVLTreeNode $node): AVLTreeNode
    {
        $newRoot = $node->left;
        $node->left = $newRoot->right;
        $newRoot->right = $node;

        $node->updateHeight();
        $newRoot->updateHeight();

        return $newRoot;
    }

    /**
     * Get the node with the minimum key in the given subtree.
     *
     * @param AVLTreeNode $node The root of the subtree.
     * @return AVLTreeNode The node with the minimum key.
     */
    private function getMinNode(AVLTreeNode $node): AVLTreeNode
    {
        while ($node->left) {
            $node = $node->left;
        }
        return $node;
    }
}