Contents Preface xi Synopsis xii Course Structure xiv Supplementary Materials xv Book Production xvi Acknowledgments xvi 1 Programming Principles 1 1.1 Introduction 2 1.2 The Game of Life 4 1.2.1 Rules for the Game of Life 4 1.2.2 Examples 5 1.2.3 The Solution: Classes, Objects, and Methods 7 1.2.4 Life: The Main Program 8 1.3 Programming Style 10 1.3.1 Names 10 1.3.2 Documentation and Format 13 1.3.3 Refinement and Modularity 15 1.4 Coding, Testing, and Further Refinement 20 1.4.1 Stubs 20 1.4.2 Definition of the Class Life 22 1.4.3 Counting Neighbors 23 1.4.4 Updating the Grid 24 1.4.5 Input and Output 25 1.4.6 Drivers 27 1.4.7 Program Tracing 28 1.4.8 Principles of Program Testing 29 1.5 Program Maintenance 33 1.5.1 Program Evaluation 34 1 .5.2 Review of the Life Program 35 1.5.3 Program Revision and Redevelopment 38 1.6 Conclusions and Preview 39 1.6.1 Software Engineering 39 1.6.2 Problem Analysis 40 1.6.3 Requirements Specification 41 1.6.4 Coding 41 Pointers and Pitfalls 45 Review Questions 46 References for Further Study 47 C++ 47 Programming Principles 47 The Game of Life 47 Software Engineering 48 2 Introduction to Stacks 49 2.1 Stack Specifications 50 2.1.1 Lists and Arrays 50 2.1.2 Stacks 50 2.1.3 First Example: Reversing a List 51 2.1.4 Information Hiding 54 2.1.5 The Standard T6mplate Library 55 2.2 Implementation of Stacks S7 2.2.1 Specification of Methods for Stacks 57 2.2.2 The Class Specification 60 2.2.3 Pushing, Popping, and Other Methods 61 2.2.4 Encapsulation 63 2.3 Application: A Desk Calculator 66 2.4 Application: Bracket Matching 69 2.5 Abstract Data Types and Their Implementations 71 2.5.1 Introduction 71 2.5.2 General Definitions 73 2.5.3 Refinement of Data Specification 74 Pointers and Pitfalls 76 Review Questions 76 References for Further Study 77 3 Queues 78 3.1 Definitions 79 3.1.1 Queue Operations 79 3.1.2 Extended Queue Operations 81 3.2 implementations of Queues 84 3.3 Circular Implementation of Queues in C++ 89 3.4 Demonstration and Testing 93 3.5 Application of Queues: Simulation 96 3.5.1 Introduction 96 3.5.2 Simulation of an Airport 96 3.5.3 Random Numbers 99 3.5.4 The Runway Class Specification 99 3.5.5 The Plane Class Specification 100 3.5.6 Functions and Methods of the Simulation 101 3.5.7 Sample Results 107 Pointers and Pitfalls 110 Review Questions 110 References for Further Study 111 4 Linked Stacks and Queues 119 4.1 Pointers and Linked Structures 113 4.1.1 Introduction and Survey 113 4.1.2 Pointers and Dynamic Memory in C++ 116 4.1.3 The Basics of Linked Structures 122 4.2 Linked Stacks 127 4.3 Linked Stacks with Safeguards 131 4.3.1 The Destructor 131 4.3.2 Overloading the Assignment Operator 132 4.3.3 The Copy Constructor 135 4.3.4 The Modified Linked-Stack Specification 136 4.4 Linked Queues 137 4.4.1 Basic Declarations 137 4.4.2 Extended Linked Queues 139 4.5 Application: Polynomial Arithmetic 141 4.5.1 Purpose of the Project 141 4.5.2 The Main Program 141 4.5.3 The Polynomial Data Structure 144 4.5.4 Reading and Writing Polynomials 147 4.5.5 Addition of Polynomials 148 4.5.6 Completing the Project 150 4.6 Abstract Data Types and Their implementations 152 Pointers and Pitfalls 154 Review Questions 155 5 Recursion 157 5.1 Introduction to Recursion 158 5.1.1 Stack Frames for Subprograms 158 5.1.2 Tree of Subprogram Calls 159 5.1.3 Factorials: A Recursive Definition 160 5.1.4 Divide and Conquer: The Towers of Hanoi 163 5.2 Principles of Recursion 170 5.2.1 Designing Recursive Algorithms 170 5.2.2 How Recursion Works 171 5.2.3 Tail Recursion 174 5.2.4 When Not to Use Recursion 176 5.2.5 Guidelines and Conclusions 180 5.3 Backtracking: Postponing the Work 183 5.3.1 Solving the Eight-Queens Puzzle 183 5.3.2 Example: Four Queens 184 5.3.3 Backtracking 185 5.3.4 Overall Outline 186 5.3.5 Refinement: The First Data Structure and its Methods 188 5.3.6 Review and Refinement 191 5.3.7 Analysis of Backtracking 194 5.4 Thee-Structured Programs: Look-Ahead in Games 198 5.4.1 Game Trees 198 5.4.2 The Minimax Method 199 5.4.3 Algorithm Development 201 5.4.4 Refinement 203 5.4.5 Tie-Tao-Toe 204 Pointers and Pitfalls 209 Review Questions 210 References for Further Study 211 6 Lists and Strings 212 6.1 List Definition 213 6.1.1 Method Specifications 214 6.2 implementation of Lists 217 6.2.1 Class Templates 218 6.2.2 Contiguous Implementation 219 6.2.3 Simply Linked implementation 221 6.2.4 Variation: Keeping the Current Position 225 6.2.5 Doubly Linked Lists 227 6.2.6 Comparison of Implementations 230 6.3 Strings 233 6.3.1 Strings in C++ 233 6.3.2 Implementation of Strings 234 6.3.3 Further String Operations 238 6.4 Application: A Text Editor 242 6.4.1 Specifications 242 6.4.2 Implementation 243 6.5 Linked Lists in Arrays 251 6.6 Application: Generating Permutations 260 Pointers and Pitfalls 265 Review Questions 266 References for Further Study 267 7 Searching 268 7.1 Searching: Introduction and Notation 269 7.2 Sequential Search 271 7.3 Binary Search 278 7.3.1 Ordered Lists 278 7.3.2 Algorithm Development 280 7.3.3 The Forgetful Version 281 7.3.4 Recognizing Equality 284. 7.4 Comparison Trees 286 7.4.1 Analysis for n = 10 287 7.4.2 Generalization 290 7.4.3 Comparison of Methods 294 7.4.4 A General Relationship 296 7.5 Lower Bounds 297 7.6 Asymptotics 302 7.6.1 introduction 302 7.6.2 Orders of Magnitude 304 7.6.3 The Big-O and Related Notations 310 7.6.4 Keeping the Dominant Term 311 Pointers and Pitfalls 314 Review Questions 315 References for Further Study 316 8 Sorting 317 8.1 Introduction and Notation 318 8.1.1 Sortable Lists 319 8.2 Insertion Sort 320 8.2.1 Ordered insertion 320 8.2.2 Sorting by insertion 321 8.2.3 Linked Version 323 8.2.4 Analysis 325 8.3 Selection Sort 329 8.3.1 The Algorithm 329 8.3.2 Contiguous Implementation 330 8.3.3 Analysis 331 8.3.4 Comparisons 332 8.4 Shell Sort 333 8.5 Lower Bounds 336 8.6 Divide-and-Conquer Sorting 339 8.6.1 The Main ideas 339 8.6.2 An Example 340 8.7 Mergesort for Linked Lists 344 8.7.1 The Functions 345 8.7.2 Analysis of Mergesort 348 8.8 Quicksort for Contiguous Lists 352 8.8.1 The Main Function 352 8.8.2 Partitioning the List 353 8.8.3 Analysis of Quicksort 356 8.8.4 Average-Case Analysis of Quicksort 358 8.8.5 Comparison with Mergesort 360 8.9 Heaps and Heapsort 363 8.9.1 Two-Way Trees as Lists 363 8.9.2 Development of Heapsort 365 8.9.3 Analysis of Heapsort 368 8.9.4 Priority Queues 369 8.10 Review: Comparison of Methods 372 Pointers and Pitfalls 375 Review Questions 376 References for Further Study 377 9 Tables and Information Retrieval 379 9.1 Introduction: Breaking the lg n Barrier 380 9.2 RectangularT8bles 381 9.3 T8bles of V8rious Shapes 383 9.3.1 Triangular T8bles 383 9.3.2 Jagged Tables 385 9.3.3 Inverted T8bles 386 9.4 Tables: A New Abstract Data Type 388 9.5 Application: Radix Sort 391 9.5.1 The idea 392 9.5.2 Implementation 393 9.5.3 Analysis 396 9.6 Hashing 397 9.6.1 Sparse T8bles 397 9.6.2 Choosing a Hash Function 399 9.6.3 Collision Resolution with Open Addressing 401 9.6.4 Collision Resolution by Chaining 406 9.7 Analysis of Hashing 411 9.8 Conclusions: Comparison of Methods 417 9.9 Application: The Life Game Revisited 418 9.9.1 Choice of Algorithm 418 9.9.2 Specification of Data Structures 9.9.3 The Life Class 421 9.9.4 The Life Functions 421 Pointers and Pitfalls 426 Review Questions 427 References for Further Study 428 10 Binary Trees 429 10.1 Binary Trees 430 10.1.1 Definitions 430 10.1.2 Traversal of Binary Trees 432 10.1.3 Linked implementation of Binary Trees 437 10.2 Binary Search Trees 444 10.2.1 Ordered Lists and Implementations 446 10.2.2 Tree Search 447 10.2.3 Insertion into a Binary Search Tree 451 10.2.4 Treesort 453 10.2.5 Removal from a Binary Search Tree 455 10.3 Building a Binary Search Tree 463 10.3.1 Getting Started 464 10.3.2 Declarations and the Main Function 465 10.3.3 Inserting a Node 466 10.3.4 Finishing the Task 467 10.3.5 Evaluation 469 10.3.6 Random Search Trees and Optimality 470 10.4 Height Balance: AVL Trees 473 10.4.1 Definition 473 10.4.2 Insertion of a Node 477 10.4.3 Removal of a Node 484 10.4.4 The Height of an AVL Tree 485 10.5 Splay Trees: A Self-Adjusting Data Structure 490 10.5.1 Introduction 490 10.5.2 Splaying Steps 491 10.5.3 Algorithm Development 495 10.5.4 Amortized Algorithm Analysis: Introduction 505 10.5.5 Amortized Analysis of Splaying 509 Pointers and Pitfalls 515 Review Questions 516 References for Further Study 518 11 Multiway Trees 520 11.1 Orchards, Trees, and Binary Trees 521 11.1.1 On the Classification of Species 521 11.1.2 Ordered Trees 522 11.1.3 Forests and Orchards 524 11.1.4 The Formal Correspondence 526 11.1.5 Rotations 527 11.1.6 Summary 527 11.2 Lexicographic Search Trees: Tries 530 11.2.1 Tries 530 11.2.2 Searching for a Key 530 11.2.3 C++ Algorithm 531 11.2.4 Searching a Trie 532 11.2.5 Insertion into a Trie 533 11.2.6 Deletion from a Trie 533 11.2.7 Assessment of Tries 534 11.3 External Searching: B-Trees 535 11.3.1 Access Time 535 11.3.2 Multiway Search Trees 535 11.3.3 Balanced Multiway Trees 536 11.3.4 Insertion into a B-Tree 537 11.3.5 C++ Algorithms: Searching and insertion 539 11.3.6 Deletion from a B-Tree 547 11.4 Red-Black Trees 556 11.4.1 Introduction 556 11.4.2 Definition and Analysis 557 11.4.3 Red-Black Tree Specification 559 11.4.4 Insertion 560 11.4.5 Insert
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