# What Is Splay Tree in Data Structure?

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Scott Campbell

What Is Splay Tree in Data Structure?

Splay tree is a self-adjusting binary search tree that provides efficient access to recently accessed elements. It is a form of binary search tree that reorganizes itself after each search operation, making frequently accessed elements more accessible by bringing them closer to the root. This self-adjusting property makes splay trees an excellent choice for applications where certain elements are accessed more frequently than others.

## How Does a Splay Tree Work?

A splay tree operates by performing a sequence of splaying operations. A splay operation moves the accessed element to the root of the tree by repeatedly performing rotations. The rotation is determined based on the position of the node with respect to its parent and grandparent.

Splaying consists of three main types of operations:

### 1. Zig-Zig:

• If both the node and its parent are left children or both are right children, perform a zig-zig rotation.
• This rotation involves two consecutive rotations: first around the parent node and then around the grandparent node.

### 2. Zig-Zag:

• If one node is a left child and the other is a right child, perform a zig-zag rotation.

### 3. Zig:

• If the accessed node has no grandparent, perform a single rotation around its parent.

The splaying process continues until the accessed element becomes the root of the tree or there are no more splaying operations possible.

• Efficient Access: Splay trees adapt to the access patterns of elements, making frequently accessed elements quicker to access by moving them closer to the root.
• Self-Adjusting: The self-adjusting property ensures that the tree is always reorganized and optimized based on recent access patterns.
• Simple Implementation: The implementation of splay trees is relatively straightforward compared to other complex data structures like AVL trees or red-black trees.

Splay trees also have some limitations:

• Lack of Balance: Unlike balanced search trees such as AVL or red-black trees, splay trees do not guarantee strict balance. In certain scenarios, splaying operations may result in an imbalanced tree.
• Potential Performance Degradation: Although splay trees generally provide efficient access, in worst-case scenarios, their performance can degrade to O(n), where n is the number of elements in the tree. However, these cases are rare and unlikely to occur in practice.

## Applications of Splay Trees

Splay trees find applications in various fields, including but not limited to:

• Caches: Splay trees are commonly used for implementing cache eviction policies due to their ability to quickly adapt to frequently accessed elements.
• Data Compression Algorithms: Splay trees are used in certain data compression algorithms where efficient access to recently accessed elements is crucial.
• Dynamic Optimality: Splay trees have been used to study and analyze the dynamic optimality conjecture, which relates to the efficiency of search algorithms in various scenarios.

## Conclusion

Splay trees are self-adjusting binary search trees that provide efficient access to frequently accessed elements. By reorganizing themselves after each search operation, splay trees optimize access patterns and make frequently accessed elements closer to the root. While they have some limitations, their advantages make them a popular choice for applications where certain elements are accessed more frequently than others.

Understanding splay trees can be beneficial for developers and computer science enthusiasts as they offer unique insights into self-adjusting data structures.