AVL Tree: Full Form and Overview
AVL Tree stands for Adelson-Velsky and Landis Tree, named after its inventors, Georgy Adelson-Velsky and Evgenii Landis, who introduced it in 1962.
Key Features of AVL Trees:
- Self-Balancing:
AVL trees maintain their height balance through rotations, ensuring that the difference in heights between the left and right subtrees is at most 1.
Height-Balancing Property:
The balance factor for any node is defined as:
- Balance Factor (BF) = Height of Left Subtree – Height of Right Subtree
- A node is considered balanced if the balance factor is in the range of -1, 0, 1.
Operations:
- Insertion: Requires rebalancing using rotations if the tree becomes unbalanced after adding a node.
- Deletion: Similar to insertion, may require rebalancing.
- Searching: Like binary search trees, AVL trees allow for efficient searching, with a time complexity of O(log n).
Advantages of AVL Trees:
- Faster Lookups:
Due to their balanced nature, AVL trees provide quicker search operations compared to unbalanced binary search trees.
Guaranteed Logarithmic Height:
- AVL trees maintain a height of O(log n), ensuring efficiency in operations.
Disadvantages of AVL Trees:
- Complex Rotations:
The need for rebalancing through rotations can make insertion and deletion operations more complex than in other tree structures.
Higher Memory Usage:
- Each node requires extra memory for storing balance factors, which can be a drawback in memory-constrained environments.
Summary
In summary, the AVL Tree is a highly efficient self-balancing binary search tree that provides excellent search performance while maintaining balance through a series of rotations. Its name reflects the contributions of its creators, Adelson-Velsky and Landis, and serves as a foundational concept in computer science for data structure optimization.