Implemented AVL Tree Data Structure (#163)

* Added Disjoint Sets Data structure * Moved DisjointSetTest.php to tests/DataStructures * Update DataStructures/DisjointSets/DisjointSet.php Co-authored-by: Brandon Johnson <[email protected]> * Update DataStructures/DisjointSets/DisjointSetNode.php Co-authored-by: Brandon Johnson <[email protected]> * Update DataStructures/DisjointSets/DisjointSetNode.php Co-authored-by: Brandon Johnson <[email protected]> * Update tests/DataStructures/DisjointSetTest.php Co-authored-by: Brandon Johnson <[email protected]> * Update tests/DataStructures/DisjointSetTest.php Co-authored-by: Brandon Johnson <[email protected]> * Update tests/DataStructures/DisjointSetTest.php Co-authored-by: Brandon Johnson <[email protected]> * Considered PHPCS remarks. Unit Testing is now working. * Remove data type mixed. Considered annotations for php7.4. * Remove data type mixed. Considered annotations for php7.4. * updating DIRECTORY.md * Implemented AVLTree DataStructure * Implemented AVLTree DataStructure --------- Co-authored-by: Brandon Johnson <[email protected]> Co-authored-by: Ramy-Badr-Ahmed <[email protected]>
TheAlgorithms · Sep 18, 2024 · e43b4bf · e43b4bf
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diff --git a/DIRECTORY.md b/DIRECTORY.md
@@ -17,6 +17,9 @@
   * [Speedconversion](./Conversions/SpeedConversion.php)
 
 ## Datastructures
+  * AVLTree
+    * [AVLTree](./DataStructures/AVLTree/AVLTree.php)
+    * [AVLTreeNode](./DataStructures/AVLTree/AVLTreeNode.php)
   * Disjointsets
     * [Disjointset](./DataStructures/DisjointSets/DisjointSet.php)
     * [Disjointsetnode](./DataStructures/DisjointSets/DisjointSetNode.php)
@@ -117,6 +120,7 @@
   * Conversions
     * [Conversionstest](./tests/Conversions/ConversionsTest.php)
   * Datastructures
+    * [AVLTreeTest](./tests/DataStructures/AVLTreeTest.php)
     * [Disjointsettest](./tests/DataStructures/DisjointSetTest.php)
     * [Doublylinkedlisttest](./tests/DataStructures/DoublyLinkedListTest.php)
     * [Queuetest](./tests/DataStructures/QueueTest.php)

diff --git a/DataStructures/AVLTree/AVLTree.php b/DataStructures/AVLTree/AVLTree.php
@@ -0,0 +1,306 @@
+<?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;
+    }
+}
diff --git a/DataStructures/AVLTree/AVLTreeNode.php b/DataStructures/AVLTree/AVLTreeNode.php
@@ -0,0 +1,41 @@
+<?php
+
+namespace DataStructures\AVLTree;
+
+class AVLTreeNode
+{
+    /**
+     * @var int|string
+     */
+    public $key;
+    /**
+     * @var mixed
+     */
+    public $value;
+    public ?AVLTreeNode $left;
+    public ?AVLTreeNode $right;
+    public int $height;
+
+    public function __construct($key, $value, ?AVLTreeNode $left = null, ?AVLTreeNode $right = null)
+    {
+        $this->key = $key;
+        $this->value = $value;
+        $this->left = $left;
+        $this->right = $right;
+        $this->height = 1; // New node is initially at height 1
+    }
+
+    public function updateHeight(): void
+    {
+        $leftHeight = $this->left ? $this->left->height : 0;
+        $rightHeight = $this->right ? $this->right->height : 0;
+        $this->height = max($leftHeight, $rightHeight) + 1;
+    }
+
+    public function balanceFactor(): int
+    {
+        $leftHeight = $this->left ? $this->left->height : 0;
+        $rightHeight = $this->right ? $this->right->height : 0;
+        return $leftHeight - $rightHeight;
+    }
+}