Data Structures

Data Structures

Theory and Practice

1st Edition - January 1, 1971

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  • Author: A. T. Berztiss
  • eBook ISBN: 9781483264721

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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


    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



    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



    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



    Chapter 4. Strings

    4a. Algebraic Structures

    4b. Algebra of Strings

    4c. Markov Algorithms

    4d. Languages and Grammars

    4e. Languages and Automata



    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



    Chapter 6. Paths and Cycles in Digraphs

    6a. Shortest Path Problems

    6b. Cycles

    6c. A Scheduling Problem

    6d. Critical Path Scheduling



    Chapter 7. Digraphs of Programs

    7a. Flowchart Digraphs

    7b. Detection of Programming Errors

    7c. Segmentation of Programs

    7d. Automatic Flowcharting



    Chapter 8. Other Applications of Graphs

    8a. Flow Problems

    8b. Graphs in Chemistry

    8c. Graphs in Information Retrieval



    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



    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



    Chapter 11. Organization of Files

    11a. Records and Files

    11b. Indexed Files

    11c. Scatter Storage Techniques

    11d. Sorting

    11e. Files and Secondary Storage



    Chapter 12. Programming Languages for Information Structures

    12a. List Processing Languages

    12b. String Processing Languages

    12c. Extension of General Purpose Languages


    Solutions to Selected Exercises



Product details

  • No. of pages: 458
  • Language: English
  • Copyright: © Academic Press 1971
  • Published: January 1, 1971
  • Imprint: Academic Press
  • eBook ISBN: 9781483264721

About the Author

A. T. Berztiss

About the Editor

Werner Rheinboldt

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