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    Data Structures II Essentials
    Data Structures II Essentials
    Data Structures II Essentials
    Ebook149 pages53 minutes

    Data Structures II Essentials

    By Dennis C. Smolarski

    ()

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    About this ebook

    REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Data Structures II includes sets, trees, advanced sorting, elementary graph theory, hashing, memory management and garbage collection, and appendices on recursion vs. iteration, algebraic notation, and large integer arithmetic.
    LanguageEnglish
    PublisherResearch & Education Association
    Release dateJan 1, 2013
    ISBN9780738671727
    Data Structures II Essentials

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      Book preview

      Data Structures II Essentials - Dennis C. Smolarski

      These Little Books have rescued lots of grades and more!

      (a sample of the hundreds of letters REA receives each year)

      I can’t tell you how much that little book helped me. It saved my GPA and quite possibly my sanity.

      Student, Winchester, IN

      Your book has really helped me sharpen my skills and improve my weak areas. Definitely will buy more.

      Student, Buffalo, NY

      I think it’s the greatest study guide I have ever used!

      Student, Anchorage, AK

      I wish to congratulate you on publishing such excellent books.

      Instructor, Big Rapids, MI

      I found your Essentials book very helpful. Now tattered and covered with notes, I take it to class daily.

      Student, Huntington Beach, CA

      I bought The Essentials of Electric Circuits and was very impressed. Congratulations on such a well thought out summary.

      Engineer, Colorado Springs, CO

      (More on back cover)

      THE ESSENTIALS®

      OF DATA STRUCTURES II

      Copyright © 2000, 1990 by Research &

      Education Association. All rights reserved.

      No part of this book may be reproduced in any

      form without permission of the publisher.

      Printed in the United States of America

      Library of Congress Catalog Card Number 99-75138

      International Standard Book Number 0-87891-837-X

      ESSENTIALS is a registered trademark of

      Research & Education Association, Piscataway, New Jersey 08854

      9780738671727

      II-1

      WHAT THE ESSENTIALS WILL DO FOR YOU

      This book is a review and study guide. It is comprehensive and it is concise.

      It helps in preparing for exams, in doing homework, and remains a handy reference source at all times.

      It condenses the vast amount of detail characteristic of the subject matter and summarizes the essentials of the field.

      It will thus save hours of study and preparation time.

      The book provides quick access to the important facts, principles and concepts in the field.

      Materials needed for exams can be reviewed in summary form - eliminating the need to read and re-read many pages of textbook and class notes. The summaries will even tend to bring detail to mind that had been previously read or noted.

      This ESSENTIALS book has been prepared by an expert in the field, and has been carefully reviewed to assure accuracy and maximum usefulness.

      Dr. Max Fogiel

      Program Director

      Table of Contents

      These Little Books have rescued lots of grades and more!

      Title Page

      Copyright Page

      WHAT THE ESSENTIALS WILL DO FOR YOU

      CHAPTER 9 - SETS

      CHAPTER 10 - TREES

      CHAPTER 11 - ADVANCED SORTING

      CHAPTER 12 - ELEMENTARY GRAPH THEORY

      CHAPTER 13 - HASHING

      CHAPTER 14 - MEMORY MANAGEMENT AND GARBAGE COLLECTION

      APPENDIX C - RECURSION VS. ITERATION

      APPENDIX D - ALGEBRAIC NOTATION

      APPENDIX E - LARGE INTEGER ARITHMETIC

      INDEX

      CHAPTER 9

      SETS

      9.1 BASIC DEFINITIONS

      A set is an ADT (abstract data type) that consists of zero or more distinct items and that lacks any inherent ordering. The standard mathematical notation for sets is a pair of curly braces that enclose an exhaustive listing of the elements contained in that set. For example, the set that consists of the two integers 3 and 5 is written {3, 5}. Since a set lacks any ordering, {3, 5} is the same set as {5, 3}. Since a set contains distinct items, there are no duplicates among the items in a set. Either an item is a member of a set or it is not — there can never be multiple copies of any item in a set. Thus, {3, 3, 5} is normally never written, since it conveys the same information as {3, 5}.

      A set that contains no items is called the empty set or the null set and is frequently written φ or { }. If a set contains a subrange of some enumerable collection of items, such as letters or integers, an ellipsis can be indicated instead of an exhaustive listing. For example, {1, ... , 100} indicates the set of the first one hundred non-negative integers.

      9.2 OPERATIONS ON SETS AND ITEMS

      As with other ADTs, two elementary operations that can be performed on a set (to modify it) and on an item that can be contained in a set are the operations of inserting a single new item into an existing set, and of deleting an item from a set.

      Another operation is that of determining whether an item is in a set or not. This is sometimes called the member or element-of or in function. Note that since a set lacks inherent ordering, there is no operation to determine where an item resides in a set.

      9.3 OPERATIONS ON TWO SETS

      The simple operations of inserting and deleting are usually combined into functions that operate on two sets (rather than on a set and an item of a set). The most common of these operations are union, intersection, and difference.

      Given sets A and B, the union of A and B, written A ∪ B, is the new set that contains any element that was in A along with any element that was in B. (As mentioned above, duplicates are omitted.) Thus if A = {3, 4, 5} and B = {5, 6, 7}, then A ∪ B = {3, 4, 5, 6, 7},

      The intersection of A and B, written A ∩ B, is the new set that contains any element that was

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