Data Structures and Algorithms in Python

Preface v

1 Python Primer 1

1.1 Python Overview 2

1.2 Objects in Python 4

1.3 Expressions, Operators, and Precedence 12

1.4 Control Flow 18

1.5 Functions 23

1.6 Simple Input and Output 30

1.7 Exception Handling 33

1.8 Iterators and Generators 39

1.9 Additional Python Conveniences 42

1.10 Scopes and Namespaces 46

1.11 Modules and the Import Statement 48

1.12 Exercises 51

2 Object-Oriented Programming 56

2.1 Goals, Principles, and Patterns 57

2.2 Software Development 62

2.3 Class Definitions 69

2.4 Inheritance 82

2.5 Namespaces and Object-Orientation 96

2.6 Shallow and Deep Copying101

2.7 Exercises 103

3 Algorithm Analysis 109

3.1 Experimental Studies 111

3.1.1 Moving Beyond Experimental Analysis 113

3.2 The Seven Functions Used in This Book 115

3.3 Asymptotic Analysis 123

3.4 Simple Justification Techniques 137

3.5 Exercises 141

4 Recursion 148

4.1 Illustrative Examples 150

4.2 Analyzing Recursive Algorithms 161

4.3 Recursion Run Amok 165

4.4 Further Examples of Recursion 169

4.5 Designing Recursive Algorithms 177

4.6 Eliminating Tail Recursion 178

4.7 Exercises 180

5 Array-Based Sequences 183

5.1 Python’s Sequence Types 184

5.2 Low-Level Arrays 185

5.3 Dynamic Arrays and Amortization 192

5.4 Efficiency of Python's Sequence Types 202

5.5 Using Array-Based Sequences 210

5.6 Multidimensional Data Sets 219

5.7 Exercises 224

6 Stacks, Queues, and Deques 228

6.1 Stacks 229

6.2 Queues 239

6.3 Double-Ended Queues 247

6.4 Exercises 250

7 Linked Lists 255

7.1 Singly Linked Lists 256

7.2 Circularly Linked Lists 266

7.3 Doubly Linked Lists 270

7.4 The Positional List ADT 277

7.5 Sorting a Positional List 285

7.6 Case Study: Maintaining Access Frequencies 286

7.7 Link-Based vs Array-Based Sequences 292

7.8 Exercises 294

8 Trees 299

8.1 General Trees 300

8.2 Binary Trees 311

8.3 Implementing Trees 317

8.4 Tree Traversal Algorithms 328

8.5 Case Study: An Expression Tree 348

8.6 Exercises 352

9 Priority Queues 362

9.1 The Priority Queue Abstract Data Type 363

9.2 Implementing a Priority Queue 365

9.3 Heaps 370

9.4 Sorting with a Priority Queue 385

9.5 Adaptable Priority Queues 390

9.6 Exercises 395

10 Maps, Hash Tables, and Skip Lists 401

10.1 Maps and Dictionaries 402

10.2 Hash Tables 410

10.3 Sorted Maps 427

10.4 Skip Lists 437

10.5 Sets, Multisets, and Multimaps 446

10.6 Exercises 452

11 Search Trees 459

11.1 Binary Search Trees 460

11.2 Balanced Search Trees 475

11.2.1 Python Framework for Balancing Search Trees 478

11.3 AVL Trees 481

11.4 Splay Trees 490

11.5 (2,4) Trees 502

11.6 Red-Black Trees 512

11.7 Exercises 528

12 Sorting and Selection 536

12.1 Why Study Sorting Algorithms? 537

12.2 Merge-Sort 538

12.3 Quick-Sort 550

12.4 Studying Sorting through an Algorithmic Lens 562

12.5 Comparing Sorting Algorithms567

12.6 Python's Built-In Sorting Functions 569

12.7 Selection 571

12.8 Exercises 574

13 Text Processing 581

13.1 Abundance of Digitized Text 582

13.2 Pattern-Matching Algorithms 584

13.3 Dynamic Programming 594

13.4 Text Compression and the Greedy Method 601

13.5 Tries 604

13.6 Exercises 613

14 Graph Algorithms 619

14.1 Graphs 620

14.2 Data Structures for Graphs627

14.3 Graph Traversals 638

14.4 Transitive Closure 651

14.5 Directed Acyclic Graphs 655

14.6 Shortest Paths 659

14.7 Minimum Spanning Trees 670

14.8 Exercises 686

15 Memory Management and B-Trees 697

15.1 Memory Management 698

15.2 Memory Hierarchies and Caching 705

15.3 External Searching and B-Trees 711

15.4 External-Memory Sorting 715

15.5 Exercises 717

A Character Strings in Python 721

B Useful Mathematical Facts 725

Bibliography 732

Index 737