Binary Trees

ACM SIGCSE Bulletin, 1996

By applying object-oriented design to the definition of a binary search tree, Berman and Duvall [1] designed a data structure comprised of three classes: (i) an EmptyBST class to model empty binary search trees, (ii) a NonEmptyBST class to model non-empty binary search trees, and (iii) a BST base class for common attributes of EmptyBST and NonEmptyBST objects. That paper noted the problem of inserting new values into such a structure: since insertions occur at an EmptyBST object, an EmptyBST would have to "turn into" a NonEmptyBST; a behavior beyond the capabilities of the classes in most languages.

1974

This project documents the results of an investigation into binary search trees. Because of their favourable characteristics binary search trees have become popular for information storage and retrieval applications in a one level store. The trees may be of two types, weighted and unweighted. Various algorithms are presented, in a machine independent context, for both types and an empirical evaluation is performed. An important software aid used for graphically displaying a binary tree is also described.

Computer Science Education

Background and Context: Recursion in binary trees has proven to be a hard topic. There was not much research on enhancing student understanding of this topic. Objective: We present a tutorial to enhance learning through practice of recursive operations in binary trees, as it is typically taught post-CS2. Method: We identified the misconceptions students have in recursive operations on binary trees. We designed a code writing exam question to measure those misconceptions. We built a tutorial that trains students on avoiding those misconceptions through the use of a semantic code analyzer that detects misconceptions and provides appropriate feedback. Findings: Our results show an improvement in student performance when using the tutorial along with the practice exercises, and even more improvement when the same exercises are used with a semantic code analyzer. Implications: The best way to use our tutorial to enhance student performance on advanced recursion is to allow students solving the tutorial exercises with the the semantic feedback.

Discrete Mathematics & Theoretical Computer Science, 1997

There are three classical algorithms to visit all the nodes of a binary tree - preorder, inorder and postorder traversal. From this one gets a natural labelling of the internal nodes of a binary tree by the numbers , indicating the sequence in which the nodes are visited. For given (size of the tree) and (a number between 1 and

The modeling of dynamical systems from a time series implemented by our DSA program introduces binary trees of height with all leaves on the same level, and the related subtrees of height L <= D. These are called epsilon-trees and epsilon-subtrees. The recursive and nonrecursive versions of the traversal algorithms for the trees with dynamically created nodes are discussed. The original nonrecursive algorithms that return the pointer to the next node in preorder, inorder and postorder traversals are presented. The space-time complexity analysis shows, and the execution time measurements confirm, that for these algorithms the recursive versions have approximately 10-25% better time constants. Still, the use of nonrecursive algorithms may be more appropriate in several occasions.

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 tree from its inorder and preorder traversals as well as inorder and postorder traversals. There is no study to focus on reconstructing a binary tree from both its preorder and postorder traversals. In this paper, we proved that given preorder and postorder traversals of a binary tree, the tree may not be identified uniquely, however, determining all the feasible solution(s) is possible. We present the PrePos algorithm, a novel algorithm to reconstruct all the possible binary tree(s) from its preorder and postorder traversals. PrePos algorithm not only finds the all the possible solutions, but also determines different types of the nodes in a binary tree; nodes with two children, nodes with one child, and node with no child. In the end, PrePos returns a matrix-based structure to represent all the binary tree solution(s). By this representation, the number of feasible solution can be counted in linear time.

ARTICLE INFO 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 binary tree can be determined. We present the algorithm BT-leaf, a novel one, to detect the leaf (leaves) of a binary tree from its preorder and postorder traversals in quadratic time and linear space.

A data structure is proposed to maintain a collection of vertex-disjoint trees under a sequence of two kinds of operations: a link operation that combines two trees into one by adding an edge, and a cut operation that divides one tree into two by deleting an edge. The tree is one of the most powerful of the advanced data structures and it often pops up in even more advanced subjects such as AI and compiler design. Surprisingly though the tree is important in a much more basic application-namely the keeping of an efficient index. This research paper gives us brief description of importance of tree in data structure, types of trees, implementation with their examples.

2016

There are many situations in which information has a hierarchical or nested structure like that found in family trees or organization charts. The abstraction that models hierarchical structure is called a tree and this data model is among the most fundamental in computer science. It is the model that underlies several programming languages, including Lisp. Trees of various types appear in many of the chapters of this book. For instance , in Section 1.3 we saw how directories and files in some computer systems are organized into a tree structure. In Section 2.8 we used trees to show how lists are split recursively and then recombined in the merge sort algorithm. In Section 3.7 we used trees to illustrate how simple statements in a program can be combined to form progressively more complex statements. The following themes form the major topics of this chapter: 3 The terms and concepts related to trees (Section 5.2). 3 The basic data structures used to represent trees in programs (Sect...

BIT, 1989

This paper shows that a binary tree can be constructed from its preorder and inorder traversals in linear time and space.