The AVL tree is a balanced binary search tree that ensures fast and efficient data operations. To achieve balance, it performs left- and right-turn operations, adjusting subtrees that violate balance. AVL trees utilize height balancing to ensure that the height of the tree is always small relative to the number of nodes, enabling logarithmic time complexity (O(log n)) lookup operations and maintaining data structure efficiency even on large data sets.

PHP data structure: The balance of the AVL tree, maintaining an efficient and orderly data structure

AVL (Adelson-Velsky and Landis) tree is a binary search tree that is balanced to ensure fast and efficient search, insertion, and deletion operations. The key is height balancing, ensuring that the height of the tree (the distance from the root node to the deepest leaf node) is always small relative to the number of nodes in the tree.

To achieve the balance of the AVL tree, we need to perform two main operations:

1. Left rotation: Adjust the subtree that violates the balance and move it from the left subtree The tree is rotated to the right subtree.
2. Right rotation: Adjust the subtree that violates the balance and rotate it from the right subtree to the left subtree.

Implementing AVL tree

We start with a simple binary search tree class:

class BinarySearchTree {
    protected $root;

    // 插入節(jié)點(diǎn)
    public function insert($value) {
        // ...
    }

    // 查找節(jié)點(diǎn)
    public function search($value) {
        // ...
    }
}

In order to implement AVL tree, we need Add the following functionality:

class AVLTree extends BinarySearchTree {
    // 獲取節(jié)點(diǎn)的高度
    public function height(Node $node) {
        // ...
    }

    // 檢查節(jié)點(diǎn)是否平衡
    public function isBalanced(Node $node) {
        // ...
    }

    // 左旋節(jié)點(diǎn)
    public function leftRotate(Node $node) {
        // ...
    }

    // 右旋節(jié)點(diǎn)
    public function rightRotate(Node $node) {
        // ...
    }
}

Practical case

Let us use an AVL tree to store a set of integers and perform lookup operations:

$avlTree = new AVLTree();
$avlTree->insert(10);
$avlTree->insert(5);
$avlTree->insert(15);
$avlTree->insert(3);
$avlTree->insert(7);
$avlTree->insert(12);
$avlTree->insert(17);

// 查找值 12
$result = $avlTree->search(12);

if ($result) {
    echo "找到值 " . $result->value . PHP_EOL;
} else {
    echo "未找到值 12" . PHP_EOL;
}

In a well-balanced In an AVL tree, even if the amount of data is large, the search operation can be completed efficiently within logarithmic time complexity (O(log n)), keeping the data structure fast and efficient.

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