What s New in the Second Edition

Transcription

1 What s New in the Second Edition This second edition of Data Structures and Algorithms in Java has been augmented to make it easier for the reader and for instructors using it as a text in computer science classes. Besides coverage of additional topics, we ve added end-of-chapter questions, experiments, and programming projects. Additional Topics We ve added a variety of interesting new topics to the book. Many provide a basis for programming projects. se new topics include Depth-first-search and game simulations Josephus problem Huffman codes for data compression Traveling Salesman problem Hamiltonian cycles Knight s Tour puzzle Floyd s algorithm Warshall s algorithm knapsack problem Listing N things taken K at a time Folding-digits hash functions radix sort End-of-Chapter Questions Short questions covering the key points of each chapter are included at the end of each chapter. answers can be found in Appendix C, Answers to Questions. se questions are intended as a self-test for readers, to ensure that they have understood the material. Experiments We include some suggested activities for the reader. se experiments often involve using the Workshop applets or example programs to examine certain features of an algorithm s operation, but some are pencil-and-paper or thought experiments. Programming Projects Most importantly, we have included at the end of each chapter a number (usually five) of challenging programming projects. y cover a range of difficulty. easiest are simple variations on the example programs. most challenging are implementations of topics discussed in the text but for which there are no example programs. Solutions to the Programming Projects are not provided in this book, but see the adjacent note..

2 What This Book Is About This book is about data structures and algorithms as used in computer programming. Data structures are ways in which data is arranged in your computer s memory (or stored on disk). Algorithms are the procedures a software program uses to manipulate the data in these structures. Almost every computer program, even a simple one, uses data structures and algorithms. For example, consider a program that prints address labels. program might use an array containing the addresses to be printed and a simple for loop to step through the array, printing each address. array in this example is a data structure, and the for loop, used for sequential access to the array, executes a simple algorithm. For uncomplicated programs with small amounts of data, such a simple approach might be all you need. However, for programs that handle even moderately large amounts of data, or which solve problems that are slightly out of the ordinary, more sophisticated techniques are necessary. Simply knowing the syntax of a computer language such as Java or C++ isn t enough. This book is about what you need to know after you ve learned a programming language. material we cover here is typically taught in colleges and universities as a second-year course in computer science, after a student has mastered the fundamentals of programming. What s Different About This Book re are dozens of books on data structures and algorithms. What s different about this one? Three things: Our primary goal in writing this book is to make the topics we cover easy to understand. Demonstration programs called Workshop applets bring to life the topics we cover, showing you step by step, with moving pictures, how data structures and algorithms work. example code is written in Java, which is easier to understand than C, C++, or Pascal, the languages traditionally used to demonstrate computer science topics. Let s look at these features in more detail. Easy to Understand Typical computer science textbooks are full of theory, mathematical formulas, and abstruse examples of computer code. This book, on the other hand, concentrates on simple explanations of techniques that can be applied to real-world problems. We avoid complex proofs and heavy math. re are lots of figures to augment the text. Many books on data structures and algorithms include considerable material on software engineering. Software engineering is a body of study concerned with designing and implementing large and complex software projects. However, it s our belief that data structures and algorithms are complicated enough without involving this additional discipline, so we have deliberately de-emphasized software engineering in this book. (We ll discuss the relationship of data structures and algorithms to software engineering in Chapter 1, Overview. ) Of course, we do use an object-oriented approach, and we discuss various aspects of object-oriented design as we go along, including a mini-tutorial on OOP in Chapter 1. Our primary emphasis, however, is on the data structures and algorithms themselves.

3 Who This Book Is For This book can be used as a text in a Data Structures and Algorithms course, typically taught in the second year of a computer science curriculum. However, it is also designed for professional programmers and for anyone else who needs to take the next step up from merely knowing a programming language. Because it s easy to understand, it is also appropriate as a supplemental text to a more formal course. What You Need to Know Before You Read This Book only prerequisite for using this book is a knowledge of some programming language. Although the example code is written in Java, you don t need to know Java to follow what s happening. Java is not hard to understand, and we ve tried to keep the syntax as general as possible, avoiding baroque or Java-specific constructions whenever possible. Of course, it won t hurt if you re already familiar with Java. Knowing C++ is essentially just as good, because Java syntax is based so closely on C++. differences are minor as they apply to our example programs (except for the welcome lamination of pointers), and we ll discuss them in Chapter 1. Software You Need to Use This Book To run the Workshop applets, you need a Web browser such as Microsoft Internet Explorer or Netscape Communicator. You can also use an applet viewer utility. Applet viewers are available with various Java development systems, including the free system from Sun Microsystems, which we ll discuss in Appendix A. To run the example programs, you can use the MS-DOS utility in Microsoft Windows (called MS-DOS Prompt) or a similar text-oriented environment. If you want to modify the source code for the example programs or write your own programs, you ll need a Java development system. Such systems are available commercially, or you can download an excellent basic system from Sun Microsystems, as described in Appendix A.

4 Contents at a Glance Introduction Overview Arrays Simple Sorting Stacks and Queues Linked Lists Recursion Advanced Sorting Binary Trees Red-Black Trees Trees and External Storage Hash Tables Heaps Graphs Weighted Graphs When to Use What Appendixes A Running the Workshop Applets and Example Programs B Further Reading C Answers to Questions Index Table of Contents Introduction 1 What s New in the Second Edition...1 Additional Topics...1 End-of-Chapter Questions...2 Experiments...2 Programming Projects...2 What This Book Is About...2 What s Different About This Book...3 Easy to Understand...3 Workshop Applets...4 Java Example Code...5 Who This Book Is For...5 What You Need to Know Before You Read This Book...5 Software You Need to Use This Book...6 How This Book Is Organized...6 Enjoy Yourself! Overview 9

5 What Are Data Structures and Algorithms Good For?...9 Real-World Data Storage...10 Programmer s Tools...11 Real-World Modeling...11 Overview of Data Structures...11 Overview of Algorithms...12 Some Definitions...13 Database...13 Record...13 Field...13 Key...14 Object-Oriented Programming...14 Problems with Procedural Languages...14 Objects in a Nutshell...15 A Runnable Object-Oriented Program...18 Inheritance and Polymorphism...21 Software Engineering...21 Java for C++ Programmers...22 No Pointers...22 Overloaded Operators...25 Primitive Variable Types...25 Input/Output...26 Java Library Data Structures...29 Summary...30 Questions A rrays 33 Array Workshop Applet...33 Insertion...35 Searching...36 Deletion...36 Duplicates Issue...37 Not Too Swift...39 Basics of Arrays in Java...39 Creating an Array...40 Accessing Array Elements...40 Initialization...41 An Array Example...41 Dividing a Program into Classes...44 Classes LowArray and LowArray App...46 Class Interfaces...46 Not So Convenient...47 Who s Responsible for What?...48 higharray.java

6 Example...48 User s Life Made Easier...52 Abstraction...52 Ordered Workshop Applet...52 Linear Search...53 Binary Search...54 Java Code for an Ordered Array...56 Binary Search with the find() Method...56 OrdArray Class...58 Advantages of Ordered Arrays...61 Logarithms...62 Equation...63 Opposite of Raising Two to a Power...64 Storing Objects...64 Person Class...65 classdataarray.java Program...65 Big O Notation...70 Insertion in an Unordered Array: Constant...70 Linear Search: Proportional to N...70 Binary Search: Proportional to log(n)...71 Don t Need the Constant...71 Why Not Use Arrays for Everything?...72 Summary...73 Questions...74 Experiments...75 Programming Projects S imple Sorting 77 How Would You Do It?...78 Bubble Sort...79 Bubble Sort on the Baseball Players...79 BubbleSort Workshop Applet...81 Java Code for a Bubble Sort...85 Invariants...88 Efficiency of the Bubble Sort...88 Selection Sort...89 Selection Sort on the Baseball Players...89 SelectSort Workshop Applet...90 Java Code for Selection Sort...92 Invariant...95

7 Efficiency of the Selection Sort...95 Insertion Sort...95 Insertion Sort on the Baseball Players...95 InsertSort Workshop Applet...97 Java Code for Insertion Sort...99 Invariants in the Insertion Sort Efficiency of the Insertion Sort Sorting Objects Java Code for Sorting Objects Lexicographical Comparisons Stability Comparing the Simple Sorts Summary Questions Experiments Programming Projects Stacks and Queues 115 A Different Kind of Structure Programmer s Tools Restricted Access More Abstract Stacks Postal Analogy Stack Workshop Applet Java Code for a Stack Stack Example 1: Reversing a Word Stack Example 2: Delimiter Matching Efficiency of Stacks Queues Queue Workshop Applet A Circular Queue Java Code for a Queue Efficiency of Queues Deques Priority Queues PriorityQ Workshop Applet Java Code for a Priority Queue Efficiency of Priority Queues Parsing Arithmetic Expressions Postfix Notation Translating Infix to Postfix Evaluating Postfix Expressions Summary Questions Experiments Programming Projects L

8 inked Lists 179 Links References and Basic Types Relationship, Not Position LinkList Workshop Applet Insert Button Find Button Delete Button A Simple Linked List Link Class LinkList Class insertfirst() Method deletefirst() Method displaylist() Method linklist.java Program Finding and Deleting Specified Links find() Method delete() Method Other Methods Double-Ended Lists Linked-List Efficiency Abstract Data Types A Stack Implemented by a Linked List A Queue Implemented by a Linked List Data Types and Abstraction ADT Lists ADTs as a Design Tool Sorted Lists Java Code to Insert an Item in a Sorted List sortedlist.java Program Efficiency of Sorted Linked Lists...218

9 List Insertion Sort Doubly Linked Lists Traversal Insertion Deletion doublylinked.java Program Doubly Linked List as Basis for Deques Iterators A Reference in the List Itself? An Iterator Class Additional Iterator Features Iterator Methods interiterator.java Program Where Does the Iterator Point? atend() Method Iterative Operations Other Methods Summary Questions Experiments Programming Projects Recursion 251 Triangular Numbers Finding the n th Term Using a Loop Finding the n th Term Using Recursion triangle.java Program What s Really Happening? Characteristics of Recursive Methods Is Recursion Efficient? Mathematical Induction Factorials Anagrams A Recursive Binary Search Recursion Replaces the Loop Divide-and-Conquer Algorithms Towers of Hanoi...273

10 Towers Workshop Applet Moving Subtrees Recursive Algorithm towers.java Program mergesort Merging Two Sorted Arrays Sorting by Merging MergeSort Workshop Applet mergesort.java Program Efficiency of the mergesort Eliminating Recursion Recursion and Stacks Simulating a Recursive Method What Does This Prove? Some Interesting Recursive Applications Raising a Number to a Power Knapsack Problem Combinations: Picking a Team Summary Questions Experiments Programming Projects A dvanced Sorting 315 Shellsort Insertion Sort: Too Many Copies N-Sorting Diminishing Gaps Shellsort Workshop Applet Java Code for the Shellsort Other Interval Sequences Efficiency of the Shellsort Partitioning Partition Workshop Applet partition.java Program Partition Algorithm Efficiency of the Partition Algorithm Quicksort Quicksort Algorithm Choosing a Pivot Value QuickSort1 Workshop Applet Degenerates to O(N2) Performance...344

11 Median-of-Three Partitioning Handling Small Partitions Removing Recursion Efficiency of Quicksort Radix Sort Algorithm for the Radix Sort Designing a Program Efficiency of the Radix Sort Summary Questions Experiments Programming Projects Binary Trees 365 Why Use Binary Trees? Slow Insertion in an Ordered Array Slow Searching in a Linked List Trees to the Rescue What Is a Tree? Tree Terminology Path Root Parent Child Leaf Subtree Visiting Traversing Levels Keys Binary Trees An Analogy How Do Binary Search Trees Work? Binary Tree Workshop Applet Representing the Tree in Java Code Finding a Node Using the Workshop Applet to Find a Node Java Code for Finding a Node Tree Efficiency Inserting a Node Using the Workshop Applet to Insert a Node Java Code for Inserting a Node Traversing the Tree Inorder Traversal Java Code for Traversing Traversing a Three-Node Tree Traversing with the Workshop Applet Preorder and Postorder Traversals...385

12 Finding Maximum and Minimum Values Deleting a Node Case 1: Node to Be Deleted Has No Children Case 2: Node to Be Deleted Has One Child Case 3: Node to Be Deleted Has Two Children Efficiency of Binary Trees Trees Represented as Arrays Duplicate Keys Complete tree.java Program Huffman Code Character Codes Decoding with the Huffman Tree Creating the Huffman Tree Coding the Message Creating the Huffman Code Summary Questions Experiments Programming Projects Red-Black Trees 429 Our Approach to the Discussion Conceptual Top-Down Insertion Balanced and Unbalanced Trees Degenerates to O(N) Balance to the Rescue Red-Black Tree Characteristics Fixing Rule Violations Using the RBTree Workshop Applet Clicking on a Node Start Button Ins Button Del Button Flip Button RoL Button RoR Button R/B Button Text Messages Where s the Find Button? Experimenting with the Workshop Applet Experiment 1: Inserting Two Red Nodes Experiment 2: Rotations Experiment 3: Color Flips Experiment 4: An Unbalanced Tree More Experiments...440

13 Red-Black Rules and Balanced Trees Null Children Rotations Simple Rotations Weird Crossover Node Subtrees on the Move Human Beings Versus Computers Inserting a New Node Preview of the Insertion Process Color Flips on the Way Down Rotations After the Node Is Inserted Rotations on the Way Down Deletion Efficiency of Red-Black Trees Red-Black Tree Implementation Other Balanced Trees Summary Questions Experiments Trees and External Storage 463 Introduction to Trees What s in a Name? Tree Organization Searching a Tree Insertion Node Splits Splitting the Root Splitting on the Way Down Tree234 Workshop Applet Fill Button Find Button Ins Button Zoom Button Viewing Different Nodes Experiments Java Code for a Tree DataItem Class Node Class Tree234 Class...476

14 Tree234App Class Complete tree234.java Program Trees and Red-Black Trees Transformation from to Red-Black Operational Equivalence Efficiency of Trees Speed Storage Requirements Trees Node Splits Implementation External Storage Accessing External Data Sequential Ordering B-Trees Indexing Complex Search Criteria Sorting External Files Summary Questions Experiments Programming Projects Hash Tables 519 Introduction to Hashing Employee Numbers as Keys A Dictionary Hashing Collisions Open Addressing Linear Probing Java Code for a Linear Probe Hash Table Quadratic Probing Double Hashing Separate Chaining HashChain Workshop Applet Java Code for Separate Chaining Hash Functions Quick Computation Random Keys Non-Random Keys Hashing Strings Folding Hashing Efficiency Open Addressing...566

15 Separate Chaining Open Addressing Versus Separate Chaining Hashing and External Storage Table of File Pointers Non-Full Blocks Full Blocks Summary Questions Experiments Programming Projects Heaps 579 Introduction to Heaps Priority Queues, Heaps, and ADTs Weakly Ordered Removal Insertion Not Really Swapped Heap Workshop Applet Fill Button Change Button Remove Button Insert Button Java Code for Heaps Insertion Removal Key Change Array Size heap.java Program Expanding the Heap Array Efficiency of Heap Operations A Tree-based Heap Heapsort Trickling Down in Place Using the Same Array heapsort.java Program Efficiency of Heapsort Summary Questions Experiments Programming Projects Graphs 615 Introduction to Graphs Definitions...616

16 Historical Note Representing a Graph in a Program Adding Vertices and Edges to a Graph Graph Class Searches Depth-First Search Breadth-First Search Minimum Spanning Trees GraphN Workshop Applet Java Code for the Minimum Spanning Tree mst.java Program Topological Sorting with Directed Graphs An Example: Course Prerequisites Directed Graphs Topological Sorting GraphD Workshop Applet Cycles and Trees Java Code Connectivity in Directed Graphs Connectivity Table Warshall s Algorithm Implementation of Warshall s Algorithm Summary Questions Experiments Programming Projects Weighted Graphs 669 Minimum Spanning Tree with Weighted Graphs An Example: Cable TV in the Jungle GraphW Workshop Applet Send Out the Surveyors Creating the Algorithm Java Code mstw.java Program Shortest-Path Problem Railroad Line Dijkstra s Algorithm Agents and Train Rides Using the GraphDW Workshop Applet Java Code...698

17 path.java Program All-Pairs Shortest-Path Problem Efficiency Intractable Problems Knight s Tour Traveling Salesman Problem Hamiltonian Cycles Summary Questions Experiments Programming Projects When to Use What 717 General-Purpose Data Structures Speed and Algorithms Libraries Arrays Linked Lists Binary Search Trees Balanced Trees Hash Tables Comparing the General-Purpose Storage Structures Special-Purpose Data Structures Stack Queue Priority Queue Comparison of Special-Purpose Structures Sorting Graphs External Storage Sequential Storage Indexed Files B-trees Hashing Virtual Memory Onward Appendixes A Running the Workshop Applets and Example Programs 729 Workshop Applets Example Programs Sun Microsystem s Software Development Kit Command-line Programs Setting the Path Viewing the Workshop Applets Operating the Workshop Applets...732

18 Running the Example Programs Compiling the Example Programs Editing the Source Code Terminating the Example Programs Multiple Class Files Other Development Systems B Further Reading 735 Data Structures and Algorithms Object-Oriented Programming Languages Object-Oriented Design (OOD) and Software Engineering C Answers to Questions 739 Chapter 1, Overview Answers to Questions Chapter 2, Arrays Answers to Questions Chapter 3, Simple Sorting Answers to Questions Chapter 4, Stacks and Queues Answers to Questions Chapter 5, Linked Lists Answers to Questions Chapter 6, Recursion Answers to Questions Chapter 7, Advanced Sorting Answers to Questions Chapter 8, Binary Trees Answers to Questions Chapter 9, Red-Black Trees Answers to Questions Chapter 10, Trees and External Storage Answers to Questions Chapter 11, Hash Tables Answers to Questions Chapter 12, Heaps Answers to Questions Chapter 13, Graphs Answers to Questions Chapter 14, Weighted Graphs Answers to Questions...747