Part V: Advanced Data Structures in Java

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Part V: Advanced Data Structures
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22 Splay Trees 795 221 Self-Adjustment and Amortized Analysis 795 221 I Amortized Time Bounds 797 2212 A Simple Self-Adjusting Strategy (That Does Not Work) 797 222 The Basic Bottom-Up Splay Tree 799 223 Basic Splay Tree Operations 802 224 Analysis of Bottom-Up Splaying 803 2241 Proof of the Splaying Bound 806 225 Top-Down Splay Trees 809 226 Implementation of Top-Down Splay Trees 81 2 227 Comparison of the Splay Tree with Other Search Trees 8 18 Summary 8 19 Objects of the Game 8 19 Common Errors 820 On the Internet 820 Exercises 820 References 822 23 Merging Priority Queues 823 231 The Skew Heap 823 2311 Merging Is Fundamental 823 2312 Simplistic Merging of Heap-Ordered Trees 824 2313 The Skew Heap: A Simple Modification 825 2314 Analysis of the Skew Heap 826 232 The Pairing Heap 828 2321 Pairing Heap Operations 829 2322 Implementation of the Pairing Heap 830 2323 Application: Dijkstra's Shortest Weighted Path Algorithm Summary 840 Objects of the Game 840 Common Errors 84 1 On the Internet 84 1 Exercises 84 1 References 842 24 The Disjoint Set Class 845 241 Equivalence Relations 845 242 Dynamic Equivalence and Two Applications
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contents
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2421 Application: Generating Mazes 847 2422 Application: Minimum Spanning Trees 850 2423 Application: The Nearest Common Ancestor Problem 243 The Quick-Find Algorithm 857 244 The Quick-Union Algorithm 858 2441 Smart Union Algorithms 860 2442 Path Compression 862 245 C++ Implementation 863 246 Worst Case for Union-by-Rank and Path Compression 865 2461 Analysis of the UnionIFind Algorithm 866 Summary 873 Objects of the Game 873 Common Errors 875 On the Internet 875 Exercises 875 References 877
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Appendices
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Appendix A Miscellaneous C++ Details A-3 A 1 None of the Compilers Implement the Standard A-3 A2 Unusual C++ Operators A-4 A21 Autoincrement and Autodecrement Operators A22 Type Conversions A-5 A23 Bitwise Operators A-6 A24 The Conditional Operator A-8 A3 Command-Line Arguments A-8 A4 Input and Output A-9 A41 Basic Stream Operations A-9 A42 Sequential Files A- 13 A43 String Streams A- 13 A5 Namespaces A-15 A6 New C++ Features A- 17 Common C++ Errors A- 17
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Appendix B
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Operators A-21
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Appendix C Some Library Routines A-23 Cl Routines Declared in <ctype h> and <cctype> A-23 C2 Constants Declared in <limits h> and <climits> A-24 C3 Routines Declared in <mathh> and <cmath> A-25 C4 Routines Declared in <stdlibh> and <cstdlib> A-26 Appendix D Primitive Arrays in C++ A-27 D1 Primitive Arrays A-27 The C++ Implementation: An Array Name Is a Pointer A-28 D 1 1 D 12 Multidimensional Arrays A-3 1 D I 3 The char * Type, const Pointers, and Constant Strings A-3 I D2 Dynamic Allocation of Arrays: new [ ] and delete [ I A-35 D3 Pointer Arithmetic, Pointer Hopping, and Primitive Iteration A-4 1 D31 Implications of the Precedence of *, &, and [ I A-41 D32 What Pointer Arithmetic Means A-42 D33 A Pointer-Hopping Example A-44 D34 Is Pointer Hopping Worthwhile A-45 Common C++ Errors A-47 On the Internet A-47
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I Preface
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This book is designed for a two-semester sequence in computer science, beginning with what is typically known as Data Structures (CS-2) and continuing with advanced data structures and algorithm analysis The content of the CS-2 course has been evolving for some time Although there is some general consensus concerning topic coverage, considerable disagreement still exists over the details One uniformly accepted topic is principles of software development, most notably the concepts of encapsulation and information hiding Algorithmically, all CS-2 courses tend to include an introduction to running-time analysis, recursion, basic sorting algorithms, and elementary data structures An advanced course is offered at many universities that covers topics in data structures, algorithms, and running-time analysis at a higher level The material in this text has been designed for use in both levels of courses, thus eliminating the need to purchase a second textbook Although the most passionate debates in CS-2 revolve around the choice of a programming language, other fundamental choices need to be made, including whether to introduce object-oriented design or object-based design early, the level of mathematical rigor, the appropriate balance between the implementation of data structures and their use, and programming details related to the language chosen My goal in writing this text was to provide a practical introduction to data structures and algorithms from the viewpoint of abstract thinking and problem solving I tried to cover all of the important details concerning the data structures, their analyses, and their C++ implementations, while staying
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away from data structures that are theoretically interesting but not widely used It is impossible to cover in a single course all the different data structures, including their uses and the analysis, described in this text So, I designed the textbook to allow instructors flexibility in topic coverage The instructor will need to decide on an appropriate balance between practice and theory and then choose those topics that best fit the course As I discuss later in this Preface, I organized the text to minimize dependencies among the various chapters
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