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More About This Textbook
Overview
In this second edition of his bestselling book, Data Structures and Algorithm Analysis in C, Mark Allen Weiss, continues to refine and enhance his innovative approach to algorithms and data structures. Using a C implementation, he highlights conceptual topics, focusing on ADTs and the analysis of algorithms for efficiency as well as performance and running time. Dr. Weiss also distinguishes Data Structures and Algorithm Analysis in C with the extensive use of figures and examples showing the successive stages of an algorithm, his engaging writing style, and a logical organization of topics.
Features
0201498405B04062001
From a prominent expert in algorithm efficiency, this book discusses the use of modern data structures with a keen eye for issues of performance and running time. Abundant examples demonstrate the power and breadth of the C language in the hands of an experienced C programmer. The concepts behind data structures are illustrated with many diagrams and illustrations.
Editorial Reviews
Booknews
A textbook for an advanced undergraduate course in data structures, or a firstyear graduate course in algorithm analysis. Assumes an intermediate knowledge of programming, and some background in discrete math. Extensive diagrams illustrate the development and relative efficiency of algorithms. Continues Weiss's coverage of the major computer languages. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
Related Subjects
Meet the Author
Mark Allen Weiss is a Professor in the School of Computer Science at Florida International University. He received his Ph.D. in Computer Science from Princeton University where he studied under Robert Sedgewick. Dr.Weiss has received FIU's Excellence in Research Award, as well as the Teaching Incentive Program Award, which was established by the Florida Legislature to recognize teaching excellence. Mark Allen Weiss is on the Advanced Placement Computer Science Development Committee. He is the successful author of Algorithms, Data Structures, and Problem Solving with C++ and the series Data Structures and Algorithm Analysis in Pascal, Ada, C, and C++, with AddisonWesley.
0201498405AB04062001
Read an Excerpt
Purpose/Goals
This book describes data structures, methods of organizing large amounts of data, and algorithm analysis, the estimation of the running time of algorithms. As computers become faster and faster, the need for programs that can handle large amounts of input becomes more acute. Paradoxically, this requires more careful attention to efficiency, since inefficiencies in programs become most obvious when input sizes are large. By analyzing an algorithm before it is actually coded, students can decide if a particular solution will be feasible. For example, in this text students look at specific problems and see how careful implementations can reduce the time constraint for large amounts of data from 16 years to less than a second. Therefore, no algorithm or data structure is presented without an explanation of its running time. In some cases, minute details that affect the running time of the implementation are explored.
Once a solution method is determined, a program must still be written. As computers have become more powerful, the problems they must solve have become larger and more complex, requiring development of more intricate programs. The goal of this text is to teach students good programming and algorithm analysis skills simultaneously so that they can develop such programs with the maximum amount of efficiency.
This book is suitable for either an advanced data structures (CS7) course or a firstyear graduate course in algorithm analysis. Students should have some knowledge of intermediate programming, including such topics as pointers and recursion, and some background in discrete math.
Approach
I believe it is important for students to learn how to program for themselves, not how to copy programs from a book. On the other hand, it is virtually impossible to discuss realistic programming issues without including sample code. For this reason, the book usually provides about onehalf to threequarters of an implementation, and the student is encouraged to supply the rest. Chapter 12, which is new to this edition, discusses additional data structures with an emphasis on implementation details.
The algorithms in this book are presented in ANSI C, which, despite some flaws, is arguably the most popular systems programming language. The use of C instead of Pascal allows the use of dynamically allocated arrays (see, for instance, rehashing in Chapter 5). It also produces simplified code in several places, usually because the and (&&) operations is shortcircuited.
Most criticisms of C center on the fact that it is easy to write code that is barely readable. Some of the more standard tricks, such as the simultaneous assignment and testing against 0 via
if (x=y)
are generally not used in the text, since the loss of clarity is compensated by only a few keystrokes and no increased speed. I believe that this books demonstrates that unreadable code can be avoided by exercising reasonable care.
Overview
Chapter 1 contains review material on discrete math and recursion. I believe the only way to be comfortable with recursion is to see good uses over and over. Therefore, recursion is prevalent in this text, with examples in every chapter except Chapter 5.
Chapter 2 deals with algorithm analysis. This chapter explains asymptotic analysis and its major weaknesses. Many examples are provided, including an indepth explanation of logarithms running time. Simple recursive programs are analyzed by intuitively converting them into iterative programs. More complicated divideandconquer programs are introduced, but some of the analysis (solving recurrence relations) is implicitly delayed until Chapter 7, where it is performed in detail.
Chapter 3 covers lists, stacks, and queues. The emphasis here is on coding these data structures using ADTs, fast implementation of these data structures, and an exposition of some of their uses. There are almost no programs (just routines), but the exercises contain plenty of ideas for programming assignments.
Chapter 4 covers trees, with an emphasis on search trees, including external search trees (Btrees). The UNIX file system and expression trees are used as examples. AVL trees and splay trees are introduced but not analyzed. Seventyfive percent of the code is written, leaving similar cases to be completed by the student. More careful treatment of search tree implementation details is found in Chapter 12. Additional coverage of trees, such as file compression and game trees, is deferred until Chapter 10. Data structures for an external medium are considered as the final topic in several chapters.
Chapter 5 is relatively short chapter concerning hash tables. Some analysis is performed, and extendible hashing is covered at the end of the chapter.
Chapter 6 is about priority queues. Binary heaps are covered, and there is additional material on some of the theoretically interesting implementations of priority queues. The Fibonacci heap is discussed in Chapter 11, and the pairing heap is discussed in Chapter 12.
Chapter 7 covers sorting. It is very specific with respect to coding details and analysis. All the important generalpurpose sorting algorithms are covered and compared. Four algorithms are analyzed in detail: insertion sort, Shellsort, heapsort, and quicksort. The analysis of the averagecase running time of heapsort is new to this edition. External sorting is covered at the end of the chapter.
Chapter 8 discusses the disjoint set algorithm with proof of the running time. This is a short and specific chapter that can be skipped if Kruskal's algorithm is not discussed.
Chapter 9 covers graph algorithms. Algorithms on graphs are interesting, not only because they frequently occur in practice but also because their running time is so heavily dependent on the proper use of data structures. Virtually all of the standard algorithms are presented along with appropriate data structures, pseudocode, and analysis of running time. To place these problems in a proper context, a short discussion on complexity theory (including NPcompleteness and undecidability) is provided.
Chapter 10 covers algorithm design by examining common problemsolving techniques. This chapter is heavily fortified with examples. Pseudocode is used in these later chapters so that the student's appreciation of an example algorithm is not obscured by implementation details.
Chapter 11 deals with amortized analysis. Three data structures from Chapters 4 and 6 and the Fibonacci heap, introduced in this chapter, are analyzed.
Chapter 12 is new to this edition. It covers search tree algorithms, the kd tree, and the pairing heap. This chapter departs from the rest of the text by providing complete and careful implementations for the search trees and pairing heap. The material is structured so that the instructor can integrate sections into discussions from other chapters. For example, the topdown red black tree in Chapter 12 can be discussed under AVL trees (in Chapter 4).
Chapters 19 provide enough material for most onesemester data structures courses. If time permits, then Chapter 10 can be covered. A graduate course on algorithm analysis could cover Chapters 711. The advanced data structures analyzed in Chapter 11 can easily be referred to in the earlier chapters. The discussion of NPcompleteness in Chapter 9 is far too brief to be used in such a course. Garey and Johnson's book on NPcompleteness can be used to augment this text.
Exercises
Exercises, provided at the end of each chapter, match the order in which material is presented. The last exercises may address the chapter as a whole rather than a specific section. Difficult exercises are marked with an asterisk, and more challenging exercises have two asterisks.
A solutions manual containing solutions to almost all the exercises is available to instructors from the AddisonWesley Publishing Company.
References
References are placed at the end of each chapter. Generally the references either are historical, representing the original source of the material, or they represent extensions and improvements to the results given in the text. Some references represent solutions to exercises.
Code Availability
The example program code in this book is available via anonymous ftp at aw.com. It is also accessible through the World Wide Web; the URL is http://www.aw.com/cseng/authors/weiss/dsaac2/dsaac2e.sup.html (follow the links from there). The exact location of this material may change.
Acknowledgments
Many, many people have helped me in the preparation of books in this series. Some are listed in other versions of the book; thanks to all.
For this edition, I would like to thank my editors at AddisonWesley, Carter Shanklin and Susan Hartman. Teri Hyde did another wonderful job with the production, and Matthew Harris and his staff at Publication Services did their usual fine work putting the final pieces together.
M.A.W.
Miami, Florida July, 1996
Table of Contents
1. Introduction.
What’s the Book About?
Mathematics Review.
Exponents.
Logarithms.
Series.
Modular Arithmetic.
The P word.
A Brief Introduction to Recursion.
2. Algorithm Analysis.
Mathematical Background.
Model.
What to Analyze.
Running Time Calculations.
A Simple Example.
General Rules.
Solutions for the Maximum Subsequence Sum Problem.
Logarithms in the Running Time.
Checking Your Analysis.
A Grain of Salt.
3. Lists, Stacks, and Queues.
Abstract Data Types (ADTs).
The List ADT.
Simple Array Implementation of Lists.
Linked Lists.
Programming Details.
Common Errors.
Doubly Linked Lists.
Circularly Linked Lists.
Examples.
Cursor Implementation of Linked Lists.
The Stack ADT.
Stack Model.
Implementation of Stacks.
Applications.
The Queue ADT.
Queue Model.
Array Implementation of Queues.
Applications of Queues.
4. Trees.
Preliminaries.
Implementation of Trees.
Tree Traversals with an Application.
Binary Trees.
Implementation.
Expression Trees.
The Search Tree ADT—Binary Search Trees.
MakeEmpty.
Find.
FindMin and FindMax.
Insert.
Delete.
AverageCase Analysis.
AVL Trees.
Single Rotation.
Double Rotation.
Splay Trees.
A Simple Idea (That Does Not Work).
Splaying.
Tree Traversals (Revisited).
BTrees.
5. Hashing.
General Idea.
Hash Function.
Separate Chaining.
Open Addressing.
Linear Probing.
Quadratic Probing.
Double Hashing.
Rehashing.
Extendible Hashing.
6. Priority Queues (Heaps).
Model.
Simple Implementations.
Binary Heaps.
Structure Property.
Heap Order Property.
Basic Heap Operations.
Other Heap Operations.
Applications of Priority Queues.
The Selection Problem.
Event Simulation.
dHeaps.
Leftist Heaps.
Leftist Heap Property.
Leftist Heap Operations.
Skew Heaps.
Binomial Queues.
Binomial Queue Structure.
Binomial Queue Operations.
Implementations of Binomial Queues.
7. Sorting.
Preliminaries.
Insertion Sort.
The Algorithm.
Analysis of Insertion Sort.
A Lower Bound for Simple Sorting Algorithms.
Shellsort.
Analysis of Insertion Sort.
Heapsort.
Analysis of Heapsort.
Mergesort.
Analysis of Mergesort.
Quicksort.
Picking the Pivot.
Partitioning Strategy.
Small Arrays.
Actual Quicksort Routines.
Analysis of Quicksort.
A LinearExpectedTime Algorithm for Selection.
Sorting Large Structures.
A General Lower Bound for Sorting.
Decision Trees.
Bucket Sort.
External Sorting.
Why We Need New Algorithms.
Model for External Sorting.
The Simple Algorithm.
Multiway Merge.
Polyphase Merge.
Replacement Selection.
8. The Disjoint Set ADT.
Equivalence Relations.
The Dynamic Equivalence Problem.
Basic Data Structure.
Smart Union Algorithms.
Path Compression.
Worst Case for UnionbyRank and Path Compression.
Analysis of the Union/Find Algorithm.
An Application.
9. Graph Algorithms.
Definitions.
Representation of Graphs.
Topological Sort.
ShortestPath Algorithms.
Unweighted Shortest Paths.
Dijkstra’s Algorithm.
Graphs with Negative Edge Costs.
Acyclic Graphs.
AllPairs Shortest Path.
Network Flow Problems.
A Simple MaximumFlow Algorithm.
Minimum Spanning Tree.
Prim’s Algorithm.
Kruskal’s Algorithm.
Applications of DepthFirst Search.
Undirected Graphs.
Biconnectivity.
Euler Circuits.
Directed Graphs.
Finding Strong Components.
Introduction to the NPCompleteness.
Easy vs. Hard.
The Class NP.
NPComplete Problems.
10. Algorithm Design Techniques.
Greedy Algorithms.
A Simple Scheduling Problem.
Huffman Codes.
Approximate Bin Packing.
Divide and Conquer.
Running Time of Divide and Conquer Algorithms.
ClosestPoints Problem.
The Selection Problem.
Theoretical Improvements for Arithmetic Problems.
Dynamic Programming.
Using a Table Instead of Recursion.
Ordering Matrix Multiplications.
Optimal Binary Search Tree.
AllPairs Shortest Path.
Randomized Algorithms.
Random Number Generators.
Skip Lists.
Primality Testing.
Backtracking Algorithms.
The Turnpike Reconstruction Problem.
Games.
11. Amortized Analysis.
An Unrelated Puzzle.
Binomial Queues.
Skew Heaps.
Fibonacci Heaps.
Cutting Nodes in Leftist Heaps.
Lazy Merging for Binomial Queues.
The Fibonacci Heap Operations.
Proof of the Time Bound.
Splay Trees.
12. Advanced Data Structures and Implementation.
TopDown Splay Trees.
Red Black Trees.
BottomUp Insertion.
TopDown Red Black Trees.
TopDown Deletion.
Deterministic Skip Lists.
AATrees.
Treaps.
kd Trees.
Pairing Heaps.
Index. 0201498405T04062001
Preface
Purpose/Goals
This book describes data structures, methods of organizing large amounts of data, and algorithm analysis, the estimation of the running time of algorithms. As computers become faster and faster, the need for programs that can handle large amounts of input becomes more acute. Paradoxically, this requires more careful attention to efficiency, since inefficiencies in programs become most obvious when input sizes are large. By analyzing an algorithm before it is actually coded, students can decide if a particular solution will be feasible. For example, in this text students look at specific problems and see how careful implementations can reduce the time constraint for large amounts of data from 16 years to less than a second. Therefore, no algorithm or data structure is presented without an explanation of its running time. In some cases, minute details that affect the running time of the implementation are explored.
Once a solution method is determined, a program must still be written. As computers have become more powerful, the problems they must solve have become larger and more complex, requiring development of more intricate programs. The goal of this text is to teach students good programming and algorithm analysis skills simultaneously so that they can develop such programs with the maximum amount of efficiency.
This book is suitable for either an advanced data structures (CS7) course or a firstyear graduate course in algorithm analysis. Students should have some knowledge of intermediate programming, including such topics as pointers and recursion, and some background in discrete math.
Approach
I believe it is important for students to learn how to program for themselves, not how to copy programs from a book. On the other hand, it is virtually impossible to discuss realistic programming issues without including sample code. For this reason, the book usually provides about onehalf to threequarters of an implementation, and the student is encouraged to supply the rest. Chapter 12, which is new to this edition, discusses additional data structures with an emphasis on implementation details.
The algorithms in this book are presented in ANSI C, which, despite some flaws, is arguably the most popular systems programming language. The use of C instead of Pascal allows the use of dynamically allocated arrays (see, for instance, rehashing in Chapter 5). It also produces simplified code in several places, usually because the and (&&) operations is shortcircuited.
Most criticisms of C center on the fact that it is easy to write code that is barely readable. Some of the more standard tricks, such as the simultaneous assignment and testing against 0 via
if (x=y)
are generally not used in the text, since the loss of clarity is compensated by only a few keystrokes and no increased speed. I believe that this books demonstrates that unreadable code can be avoided by exercising reasonable care.
Overview
Chapter 1 contains review material on discrete math and recursion. I believe the only way to be comfortable with recursion is to see good uses over and over. Therefore, recursion is prevalent in this text, with examples in every chapter except Chapter 5.
Chapter 2 deals with algorithm analysis. This chapter explains asymptotic analysis and its major weaknesses. Many examples are provided, including an indepth explanation of logarithms running time. Simple recursive programs are analyzed by intuitively converting them into iterative programs. More complicated divideandconquer programs are introduced, but some of the analysis (solving recurrence relations) is implicitly delayed until Chapter 7, where it is performed in detail.
Chapter 3 covers lists, stacks, and queues. The emphasis here is on coding these data structures using ADTs, fast implementation of these data structures, and an exposition of some of their uses. There are almost no programs (just routines), but the exercises contain plenty of ideas for programming assignments.
Chapter 4 covers trees, with an emphasis on search trees, including external search trees (Btrees). The UNIX file system and expression trees are used as examples. AVL trees and splay trees are introduced but not analyzed. Seventyfive percent of the code is written, leaving similar cases to be completed by the student. More careful treatment of search tree implementation details is found in Chapter 12. Additional coverage of trees, such as file compression and game trees, is deferred until Chapter 10. Data structures for an external medium are considered as the final topic in several chapters.
Chapter 5 is relatively short chapter concerning hash tables. Some analysis is performed, and extendible hashing is covered at the end of the chapter.
Chapter 6 is about priority queues. Binary heaps are covered, and there is additional material on some of the theoretically interesting implementations of priority queues. The Fibonacci heap is discussed in Chapter 11, and the pairing heap is discussed in Chapter 12.
Chapter 7 covers sorting. It is very specific with respect to coding details and analysis. All the important generalpurpose sorting algorithms are covered and compared. Four algorithms are analyzed in detail: insertion sort, Shellsort, heapsort, and quicksort. The analysis of the averagecase running time of heapsort is new to this edition. External sorting is covered at the end of the chapter.
Chapter 8 discusses the disjoint set algorithm with proof of the running time. This is a short and specific chapter that can be skipped if Kruskal's algorithm is not discussed.
Chapter 9 covers graph algorithms. Algorithms on graphs are interesting, not only because they frequently occur in practice but also because their running time is so heavily dependent on the proper use of data structures. Virtually all of the standard algorithms are presented along with appropriate data structures, pseudocode, and analysis of running time. To place these problems in a proper context, a short discussion on complexity theory (including NPcompleteness and undecidability) is provided.
Chapter 10 covers algorithm design by examining common problemsolving techniques. This chapter is heavily fortified with examples. Pseudocode is used in these later chapters so that the student's appreciation of an example algorithm is not obscured by implementation details.
Chapter 11 deals with amortized analysis. Three data structures from Chapters 4 and 6 and the Fibonacci heap, introduced in this chapter, are analyzed.
Chapter 12 is new to this edition. It covers search tree algorithms, the kd tree, and the pairing heap. This chapter departs from the rest of the text by providing complete and careful implementations for the search trees and pairing heap. The material is structured so that the instructor can integrate sections into discussions from other chapters. For example, the topdown red black tree in Chapter 12 can be discussed under AVL trees (in Chapter 4).
Chapters 19 provide enough material for most onesemester data structures courses. If time permits, then Chapter 10 can be covered. A graduate course on algorithm analysis could cover Chapters 711. The advanced data structures analyzed in Chapter 11 can easily be referred to in the earlier chapters. The discussion of NPcompleteness in Chapter 9 is far too brief to be used in such a course. Garey and Johnson's book on NPcompleteness can be used to augment this text.
Exercises
Exercises, provided at the end of each chapter, match the order in which material is presented. The last exercises may address the chapter as a whole rather than a specific section. Difficult exercises are marked with an asterisk, and more challenging exercises have two asterisks.
A solutions manual containing solutions to almost all the exercises is available to instructors from the AddisonWesley Publishing Company.
References
References are placed at the end of each chapter. Generally the references either are historical, representing the original source of the material, or they represent extensions and improvements to the results given in the text. Some references represent solutions to exercises.
Code Availability
The example program code in this book is available via anonymous ftp at aw.com. It is also accessible through the World Wide Web; the URL is http://www.aw.com/cseng/authors/weiss/dsaac2/dsaac2e.sup.html (follow the links from there). The exact location of this material may change.
Acknowledgments
Many, many people have helped me in the preparation of books in this series. Some are listed in other versions of the book; thanks to all.
For this edition, I would like to thank my editors at AddisonWesley, Carter Shanklin and Susan Hartman. Teri Hyde did another wonderful job with the production, and Matthew Harris and his staff at Publication Services did their usual fine work putting the final pieces together.
M.A.W.
Miami, Florida
July, 1996
0201498405P04062001