An AVL tree, also known as Adelson-Velsky and Landis tree, is a self-balancing binary search tree. In computer science, it is a data structure that maintains a balanced tree by automatically performing rotations whenever necessary. The full form of AVL is not very commonly used or referred to, and most people simply recognize it by its acronym.
What Is a Binary Search Tree?
To understand AVL trees, we first need to understand binary search trees (BST). A binary search tree is a data structure in which each node has at most two children: a left child and a right child. The left child contains values less than the node’s value, while the right child contains values greater than the node’s value.
Binary search trees are efficient for searching and inserting elements because they allow for fast lookup operations. However, in certain scenarios where the tree becomes unbalanced, the efficiency can degrade significantly.
Why Do We Need Balanced Trees?
When we insert or delete nodes from a binary search tree, there can be situations where the tree becomes skewed or imbalanced. In an imbalanced tree, one subtree can have significantly more nodes than the other subtree.
This imbalance affects the time complexity of various operations such as searching, insertion, and deletion. In an unbalanced tree, these operations can take longer to execute compared to balanced trees.
The Idea behind AVL Trees
The AVL tree was invented by Georgy Adelson-Velsky and Evgenii Landis in 1962 as a way to automatically balance binary search trees. Their goal was to maintain an efficient data structure that would provide faster lookup times while keeping the height of the tree relatively small.
In an AVL tree, each node stores an additional value called balance factor or height difference. The balance factor indicates the difference in height between the left and right subtrees of a node.
If the balance factor of a node is greater than 1 or less than -1, it means that the tree is unbalanced. To restore balance, AVL trees perform rotations that modify the structure of the tree.
How AVL Trees Maintain Balance
AVL trees maintain balance by performing rotations when necessary. A rotation is an operation that changes the structure of a tree while preserving its search order.
There are four types of rotations performed in AVL trees:
- Left rotation: This rotation is used to restore balance when a node’s right subtree is taller than its left subtree.
- Right rotation: This rotation is used to restore balance when a node’s left subtree is taller than its right subtree.
- Left-Right rotation: This rotation combines a left rotation followed by a right rotation. It restores balance when a node’s left child’s right subtree is taller than its left subtree.
- Right-Left rotation: This rotation combines a right rotation followed by a left rotation. It restores balance when a node’s right child’s left subtree is taller than its right subtree.
The Benefits of Using AVL Trees
The primary benefit of using AVL trees is their ability to maintain balance automatically. By ensuring that the tree remains balanced, we can achieve efficient search, insertion, and deletion operations with time complexity of O(log n).
AVL trees are particularly useful in scenarios where we need fast access to data and want to avoid performance degradation caused by unbalanced trees.
An AVL tree is a self-balancing binary search tree that automatically maintains balance by performing rotations. By keeping the height difference between left and right subtrees small, AVL trees ensure efficient search, insertion, and deletion operations.
Understanding AVL trees is crucial for anyone working with data structures and algorithms. They provide an excellent example of how balancing techniques can improve the performance of a data structure.