Splay trees, a form of self-adjusting binary tree, were introduced by Sleator and Tarjan in the early 1980s. Their main use is to store ordered lists. The idea is to keep the trees reasonably well balanced through a ‘splay heuristic.’ Sleator and Tarjan showed that if amortised rather than worst-case times are considered, splay trees are optimal. Splay trees have the advantage of simplicity: th...

In this paper we derive a linear-time, constant-space algorithm to construct a binary heap whose inorder traversal equals a given sequence. We do so in two steps. First, we invert a program that computes the inorder traversal of a binary heap, using the proof rules for program inversion by W. Chen and J.T. Udding. This results in a linear-time solution in terms of binary trees. Subsequently, we...

It is well-known that, given inorder traversal along with one of the preorder or postorder traversals of a binary tree, the tree can be determined uniquely. Several algorithms have been proposed to reconstruct a binary tree from its inorder and preorder traversals. There is one study to reconstruct a binary tree from its inorder and postorder traversals, and this algorithm takes running time of...

It is known that to traverse a binary tree in inorder, by repeated splay-to-root, uses O(n) rotations. Estimates vary from 15n to 4.5n in proofs of varying length and difficulty. We present a fairly easy estimate of 6n rotations. (1) The process under consideration is inorder traversal of a binary tree using repeated splay-to-root: n is the number of nodes in the tree. Call the operation of see...

Given the inorder and preorder traversal of a binary tree whose labels are all distinct, one can reconstruct the tree. This article examines two existing algorithms for rebuilding the tree in a functional framework, using existing theory on function inversion. We also present a new, although complicated, algorithm by trying another possibility not explored before.

The aim of this note is to generalize some recent results for binary trees by Panholzer and Prodinger [15] to a larger class of rooted trees. The number of descendants of a node j is the number of nodes in the subtree rooted at j, and the number of ascendants is the number of nodes between j and the root. Recently, Panholzer and Prodinger [15] studied the behavior of these parameters in binary ...

Abstract Real-time applications such as streaming media and voice require encryption algorithms that do not propagate errors and support fast encryption on small blocks. Since IP packets are delivered out-of-order in routed networks it is difficult to synchronize the source and the destination, therefore requiring encryption algorithms to support out-of-order generation of key stream. In this p...

We have proposed a novel way of symmetric encryption utilizing interleaving salting, Binary Tree traversal, and an Artificial Neural Network in sequential manner. presented the use as invertible(reversible) mathematical function so that decryption encrypted output may be possible. Knowledge pipeline, salt, neural network weights is required for decryption. As same set values decryption, our app...