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...

We consider the following problem. For a binary tree T = (V; E) where V = f1; 2; :::; ng, given its inorder traversal and either its preorder or its postorder traversal, reconstruct the binary tree. We present a new parallel algorithm for this problem. Our algorithm requires O(n) space. The main idea of our algorithm is to reduce the reconstruction process to merging two sorted sequences. With ...

List or set comprehensions are a wonderful means to define nondeterministic or relational programs. Despite their beauty, comprehensions are somewhat underused in program calculation. The purpose of this paper is to remind the program-calculation community that comprehensions provide a convenient language for specifying and deriving nondeterministic programs in a pointwise manner. We illustrate...

In a new approach, functional correctness specifications of insert/update and delete operations on search trees are expressed on the level of lists by means of an inorder traversal function that projects trees to lists. With the help of a small lemma library, functional correctness and preservation of the search tree property are proved automatically (in Isabelle/HOL) for a range of data struct...

A number of algorithms are presented for obtaining~a~i&?ter representation for an image given its quadtree. The algorithms are given in an evolutionary manner starting with the straightforward top-down approach that visits each run in a row in succession starting at the root of the tree. The remaining algorithms proceed in a manner akin to an inorder tree traversal. All of the algorithms are an...

We consider random binary search trees when the input consists of a multiset, i.e. a set with multiple occurrences of equal elements, and prove that the randomized insertion and deletion algorithms produce random search trees regardless of multiplicities; even if all the elements are equal during the tree updates, a search tree will maintain its randomness. Thus, equal elements do not degenerat...

This week, we will work in a more restricted and abstract setting, namely the comparison model: elements can only be compared and the result is <,= or >. Furthermore, we only consider Binary Search Trees. In this model of computation, we are given n keys placed in the n nodes of a binary tree in symmetric order (an inorder traversal of the tree gives the elements in sorted order). We are also g...

In order to address this problem, our algorithm uses the rst element of preorder node sequence to nd the root of tree, and locate the root in the inorder node sequence. Then, in inorder sequence, everything on the left side of the root element is the inorder node sequence of the left subtree and everything on the right side of of the root element is the inorder node sequence of the right tree. ...

Binary trees are essential structures in Computer Science. The leaf (leaves) of a binary tree is one of the most significant aspects of it. In this study, we prove that the order of a leaf (leaves) of a binary tree is the same in the main tree traversals; preorder, inorder, and postorder. Then, we prove that given the preorder and postorder traversals of a binary tree, the leaf (leaves) of a bi...

one of the debates concerning concepts of “medial motion” and “traversal motion” is the question of which of these two concepts of motion corresponds to motion in the corporeal world. in the present article we intend to employ the language of mathematics to present a model for each of these two concepts to study the above mentioned problem. as a result, medial motion represents a covering funct...