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2023-07-11T11:13:36
VIJAYA VITTALA INSTITUTE OF TECHNOLOGY
A splay tree is a type of self-adjusting binary search tree. The idea is to bring the recently accessed item t
A splay tree is a type of self-adjusting binary search tree. The idea is to bring the recently accessed item to the root of the tree through a series of tree rotations, which are called "splay" operations. This adjustment makes future accesses to the same element more efficient. Splay trees are beneficial when the tree is accessed non-uniformly, and certain elements are accessed more frequently than others. They also provide good performance for sequences of operations that access a small subset of elements repeatedly. Here's a brief overview of how a splay operation works: If the node to be splayed is the root, no splay operation is performed. If the node is a child of the root (i.e., it is one level away from the root), a single rotation operation is performed to make it the new root. This operation is called a "zig" operation. If the node is not a child of the root (i.e., it is more than one level away from the root), we look at the path from the root to the node. If the node and its parent are either both right children or both left children, a "zig-zig" operation is performed. This involves a rotation on the parent of the node, followed by a rotation on the node itself. If the node and its parent are not the same (one is a right child and the other is a left child), a "zig-zag" operation is performed. This involves a rotation on the node twice. The process continues until the node to be splayed is the root of the tree. Every operation involves at most a constant number of pointer changes and does not depend on the size of the tree, making them efficient. A splay tree does not need to keep explicit balance information like AVL or Red-Black trees, and all tree operations, like insert, delete, and find, cause a splay operation to occur, helping to ensure that frequently accessed elements are near the top of the tree. However, while operations on a splay tree have an average case complexity of O(log n), they can degrade to O(n) in the worst case, unlike AVL and Red-Black trees, which guarantee an O(log n) complexity in all cases. Still, for certain types of access patterns, splay trees can outperform other types of trees.
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