Data Structures - 1st Edition - ISBN: 9780120935505, 9781483264721

Data Structures

1st Edition

Theory and Practice

Authors: A. T. Berztiss
Editors: Werner Rheinboldt
eBook ISBN: 9781483264721
Imprint: Academic Press
Published Date: 1st January 1971
Page Count: 458
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Description

Computer Science and Applied Mathematics: Data Structures: Theory and Practice focuses on the processes, methodologies, principles, and approaches involved in data structures, including algorithms, decision trees, Boolean functions, lattices, and matrices.

The book first offers information on set theory, functions, and relations, and graph theory. Discussions focus on linear formulas of digraphs, isomorphism of digraphs, basic definitions in the theory of digraphs, Boolean functions and forms, lattices, indexed sets, algebra of sets, and order pair and related concepts. The text then examines strings, trees, and paths and cycles in digraphs. Topics include algebra of strings, Markov algorithms, algebraic structures, languages and grammars, decision trees and decision tables, trees as grammatic markers, shortest path problems, and representation of prefix formulas.

The publication ponders on digraphs of programs, arrays, pushdown stores, lists, and list structures, and organization of files. Concerns include scatter storage techniques, files and secondary storage, representation of digraphs as list structures, storage of arrays, and sparse matrices.

The text is a valuable reference for computer science experts, mathematicians, and researchers interested in data structures.

Table of Contents


Preface

Acknowledgments

Part I Discrete Structures in Mathematics

Chapter 1. Set Theory

1a. Basic Definitions

1b. Indexed Sets

1c. Complement of a Set

1d. Algebra of Sets

1e. Algebra of Sets as an Axiomatic Theory

1f. Venn Diagrams

1g. The Ordered Pair and Related Concepts

1h. Permutations and Combinations

Notes

Exercises

Chapter 2. Functions and Relations

2a. Functions

2b. Boolean Functions and Forms

2c. Applications of Boolean Functions

2d. Relations

2e. The Equivalence Relation

2f. Ordering Relations

2g. Lattices

2h. Abstract Algebras

Notes

Exercises

Chapter 3. Graph Theory

3a. Diagrams and Graphs

3b. Basic Definitions in the Theory of Digraphs

3c. Digraphs, Matrices, and Relations

3d. Connectedness in a Digraph

3e. Linear Formulas of Digraphs

3f. Trees

3g. Isomorphism of Digraphs

3h. Planar Graphs

Notes

Exercises

Chapter 4. Strings

4a. Algebraic Structures

4b. Algebra of Strings

4c. Markov Algorithms

4d. Languages and Grammars

4e. Languages and Automata

Notes

Exercises

Part II Applications of Structures

Chapter 5. Trees

5a. Trees as Grammatic Markers

5b. Representation of Prefix Formulas

5c. Sort Trees and Dictionaries

5d. Decision Trees and Decision Tables

Notes

Exercises

Chapter 6. Paths and Cycles in Digraphs

6a. Shortest Path Problems

6b. Cycles

6c. A Scheduling Problem

6d. Critical Path Scheduling

Notes

Exercises

Chapter 7. Digraphs of Programs

7a. Flowchart Digraphs

7b. Detection of Programming Errors

7c. Segmentation of Programs

7d. Automatic Flowcharting

Notes

Exercises

Chapter 8. Other Applications of Graphs

8a. Flow Problems

8b. Graphs in Chemistry

8c. Graphs in Information Retrieval

Notes

Exercises

Part III Computer Representation of Structures

Chapter 9. Arrays

9a. Storage Media and Their Properties

9b. Storage of Arrays

9c. Sparse Matrices

9d. Storage Allocation at Execution Time

Notes

Exercises

Chapter 10. Pushdown Stores, Lists and List Structures

10a. Pushdown Stores

10b. Prefix, Postfix, and Infix Formulas

10c. Storage Levels for a Pushdown Store

10d. Lists—Introductory Concepts

10e. Formats of List Elements

10f. List Structures

10g. Threaded and Symmetric Lists

10h. Representation of Digraphs as List Structures

10i. Multiword List Elements

10j. Management of List Stores

10k. PL/I-Type Data Structures

Notes

Exercises

Chapter 11. Organization of Files

11a. Records and Files

11b. Indexed Files

11c. Scatter Storage Techniques

11d. Sorting

11e. Files and Secondary Storage

Notes

Exercises

Chapter 12. Programming Languages for Information Structures

12a. List Processing Languages

12b. String Processing Languages

12c. Extension of General Purpose Languages

Notes

Solutions to Selected Exercises

Bibliography

Index

Details

No. of pages:
458
Language:
English
Copyright:
© Academic Press 1971
Published:
Imprint:
Academic Press
eBook ISBN:
9781483264721

About the Author

A. T. Berztiss

About the Editor

Werner Rheinboldt