Berztiss / Rheinboldt Data Structures

Theory and Practice
1. Auflage 2014
ISBN: 978-1-4832-6472-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 458 Seiten, Web PDF

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.

Autoren/Hrsg.

Berztiss, A. T.

Rheinboldt, Werner

Inhaltsverzeichnis

1;Front Cover;1
2;Data Structures: Theory and Practice;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;Acknowledgments;14
7;Part I: DISCRETE STRUCTURES IN MATHEMATICS;16
7.1;Chapter 1. Set Theory;18
7.1.1;1a. Basic Definitions;18
7.1.2;1b. Indexed Sets;22
7.1.3;1c. Complement of a Set;24
7.1.4;1d. Algebra of Sets;27
7.1.5;1e. Algebra of Sets as an Axiomatic Theory;30
7.1.6;1f. Venn Diagrams;38
7.1.7;1g. The Ordered Pair and Related Concepts;40
7.1.8;1h. Permutations and Combinations;43
7.1.9;Notes;54
7.1.10;Exercises;55
7.2;Chapter 2. Functions and Relations;58
7.2.1;2a. Functions;58
7.2.2;2b. Boolean Functions and Forms;62
7.2.3;2c. Applications of Boolean Functions;71
7.2.4;2d. Relations;85
7.2.5;2e. The Equivalence Relation;88
7.2.6;2f. Ordering Relations;91
7.2.7;2g. Lattices;97
7.2.8;2h. Abstract Algebras;101
7.2.9;Notes;108
7.2.10;Exercises;108
7.3;Chapter 3. Graph Theory;118
7.3.1;3a. Diagrams and Graphs;118
7.3.2;3b. Basic Definitions in the Theory of Digraphs;121
7.3.3;3c. Digraphs, Matrices, and Relations;127
7.3.4;3d. Connectedness in a Digraph;135
7.3.5;3e. Linear Formulas of Digraphs;138
7.3.6;3f. Trees;144
7.3.7;3g. Isomorphism of Digraphs;146
7.3.8;3h. Planar Graphs;150
7.3.9;Notes;155
7.3.10;Exercises;156
7.4;Chapter 4. Strings;160
7.4.1;4a. Algebraic Structures;160
7.4.2;4b. Algebra of Strings;166
7.4.3;4c. Markov Algorithms;168
7.4.4;4d. Languages and Grammars;174
7.4.5;4e. Languages and Automata;180
7.4.6;Notes;184
7.4.7;Exercises;184
8;Part II: APPLICATIONS OF STRUCTURES;188
8.1;Chapter 5. Trees;190
8.1.1;5a. Trees as Grammatic Markers;190
8.1.2;5b. Representation of Prefix Formulas;196
8.1.3;5c. Sort Trees and Dictionaries;200
8.1.4;5d. Decision Trees and Decision Tables;208
8.1.5;Notes;215
8.1.6;Exercises;216
8.2;Chapter 6. Paths and Cycles in Digraphs;220
8.2.1;6a. Shortest Path Problems;220
8.2.2;6b. Cycles;231
8.2.3;6c. A Scheduling Problem;238
8.2.4;6d. Critical Path Scheduling;241
8.2.5;Notes;245
8.2.6;Exercises;247
8.3;Chapter 7. Digraphs of Programs;252
8.3.1;7a. Flowchart Digraphs;252
8.3.2;7b. Detection of Programming Errors;255
8.3.3;7c. Segmentation of Programs;257
8.3.4;7d. Automatic Flowcharting;260
8.3.5;Notes;262
8.3.6;Exercises;263
8.4;Chapter 8. Other Applications of Graphs;266
8.4.1;8a. Flow Problems;266
8.4.2;8b. Graphs in Chemistry;273
8.4.3;8c. Graphs in Information Retrieval;278
8.4.4;Notes;281
8.4.5;Exercises;282
9;Part III: COMPUTER REPRESENTATION OF STRUCTURES;284
9.1;Chapter 9. Arrays;286
9.1.1;9a. Storage Media and Their Properties;286
9.1.2;9b. Storage of Arrays;289
9.1.3;9c. Sparse Matrices;291
9.1.4;9d. Storage Allocation at Execution Time;294
9.1.5;Notes;301
9.1.6;Exercises;302
9.2;Chapter 10. Pushdown Stores, Lists and List Structures;304
9.2.1;10a. Pushdown Stores;304
9.2.2;10b. Prefix, Postfix, and Infix Formulas;307
9.2.3;10c. Storage Levels for a Pushdown Store;310
9.2.4;10d. Lists—Introductory Concepts;311
9.2.5;10e. Formats of List Elements;317
9.2.6;10f. List Structures;320
9.2.7;10g. Threaded and Symmetric Lists;323
9.2.8;10h. Representation of Digraphs as List Structures;328
9.2.9;10i. Multiword List Elements;330
9.2.10;10j. Management of List Stores;331
9.2.11;10k. PL/I-Type Data Structures;334
9.2.12;Notes;338
9.2.13;Exercises;340
9.3;Chapter 11. Organization of Files;344
9.3.1;11a. Records and Files;344
9.3.2;11b. Indexed Files;347
9.3.3;11e. Scatter Storage Techniques;350
9.3.4;11d. Sorting;354
9.3.5;11e. Files and Secondary Storage;364
9.3.6;Notes;366
9.3.7;Exercises;367
9.4;Chapter 12. Programming Languages for Information Structures;370
9.4.1;12a. List Processing Languages;370
9.4.2;12b. String Processing Languages;381
9.4.3;12c. Extension of General Purpose Languages;392
9.4.4;Notes;402
10;Solutions to Selected Exercises;406
11;Bibliography;430
12;Index;446