AVL Search Tree is a self-balancing binary search tree named after its inventors, Adelson-Velsky and Landis. In data structure, a binary search tree is a tree-like data structure where each node has at most two children – a left child and a right child. The AVL Search Tree is an extension of the binary search tree with an additional balancing property.
What makes AVL Search Tree special?
The key feature of an AVL Search Tree is that it automatically maintains its balance, ensuring that the height of the left and right subtrees of any node differs by at most one. This balancing property provides efficient search, insertion, and deletion operations.
Why is balance important?
The balance factor of a node in an AVL Search Tree is the difference between the heights of its left and right subtrees. The balance factor can be either -1, 0, or 1. When the balance factor exceeds this range, rotations are performed to restore the balance.
Rotations:
Rotations are fundamental operations in AVL trees that maintain their balance. There are four types of rotations: left rotation, right rotation, left-right rotation (also known as RL rotation), and right-left rotation (also known as LR rotation). These rotations preserve the order of elements in the tree while adjusting its structure.
- Left Rotation: It involves moving a right child to become the new root while making the old root its left child.
- Right Rotation: It involves moving a left child to become the new root while making the old root its right child.
- Left-Right Rotation (RL Rotation): It combines a left rotation followed by a right rotation.
- Right-Left Rotation (LR Rotation): It combines a right rotation followed by a left rotation.
Insertion in AVL Search Tree:
When inserting a new element into an AVL Search Tree, the tree is first updated like a regular binary search tree. After the insertion, the balance factor of each node is checked. If any node violates the balance property, rotations are performed to restore it.
The insertion process can be summarized as follows:
- Perform a regular binary search tree insertion.
- Update the balance factor of each affected node.
- If any balance factor becomes -2 or +2, perform necessary rotations.
- Continue updating balance factors and performing rotations until the entire tree is balanced.
Deletion in AVL Search Tree:
Similar to insertion, deletion in an AVL Search Tree follows the process of a regular binary search tree deletion. After deleting the node, the balance property may be violated at certain nodes. In such cases, rotations are performed to restore balance.
The deletion process can be summarized as follows:
- Perform a regular binary search tree deletion.
Benefits of AVL Search Trees:
- Efficient searching: The AVL Search Tree has an average time complexity of O(log n) for searching operations due to its balanced structure.
- Faster than unbalanced trees: Compared to unbalanced binary search trees, AVL trees provide faster search, insertion, and deletion operations.
- Suitable for real-time applications: The self-balancing property of AVL trees makes them suitable for real-time systems where quick response times are crucial.
In conclusion, AVL Search Trees are self-balancing binary search trees that automatically maintain balance through rotations. Their balanced structure ensures efficient search, insertion, and deletion operations. With their benefits and ability to handle dynamic data efficiently, AVL trees are a valuable tool in various applications.