AVL Trees

AVL Trees are a type of self-balancing binary search tree, named after the inventors Adelson-Velsky and Landis. In an AVL tree, the heights of the left and right subtrees of any node differ by at most one.

The balancing property of AVL trees ensures that the tree remains balanced, providing efficient searching, insertion, and deletion operations with a time complexity of O(log n).

Balanced Tree

In an AVL tree, every node satisfies the AVL property, which states that the heights of the left and right subtrees of the node differ by at most one. If the difference exceeds one, the tree is considered unbalanced and requires balancing operations to maintain the AVL property.

Balancing Operations

There are four types of balancing operations: left rotation, right rotation, left-right rotation, and right-left rotation. These operations are performed to restore the balance of the tree when it becomes unbalanced due to insertions or deletions.

C++ Code Implementation

Here's an example of AVL tree implementation in C++:

1#include <iostream>
2using namespace std;
3
4struct Node {
5    int data;
6    Node* left;
7    Node* right;
8    int height;
9
10    Node(int value) {
11        data = value;
12        left = nullptr;
13        right = nullptr;
14        height = 1;
15    }
16};
17
18int main() {
19    // AVL tree code implementation
20
21    return 0;
22}