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Data Structures & Algorithms in Python

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Description

  • Copyright 2023
  • Pages: 928
  • Edition: 1st
  • eBook
  • ISBN-10: 0-13-485592-2
  • ISBN-13: 978-0-13-485592-9

LEARN HOW TO USE DATA STRUCTURES IN WRITING HIGH PERFORMANCE PYTHON PROGRAMS AND ALGORITHMS

This practical introduction to data structures and algorithms can help every programmer who wants to write more efficient software. Building on Robert Lafore's legendary Java-based guide, this book helps you understand exactly how data structures and algorithms operate. You'll learn how to efficiently apply them with the enormously popular Python language and scale your code to handle today's big data challenges.

Throughout, the authors focus on real-world examples, communicate key ideas with intuitive, interactive visualizations, and limit complexity and math to what you need to improve performance. Step-by-step, they introduce arrays, sorting, stacks, queues, linked lists, recursion, binary trees, 2-3-4 trees, hash tables, spatial data structures, graphs, and more. Their code examples and illustrations are so clear, you can understand them even if you're a near-beginner, or your experience is with other procedural or object-oriented languages.

Build core computer science skills that take you beyond merely "writing code"

Learn how data structures make programs (and programmers) more efficient

See how data organization and algorithms affect how much you can do with today's, and tomorrow's, computing resources

Develop data structure implementation skills you can use in any language

Choose the best data structure(s) and algorithms for each programming problemand recognize which ones to avoid

Data Structures & Algorithms in Python is packed with examples, review questions, individual and team exercises, thought experiments, and longer programming projects. It's ideal for both self-study and classroom settings, and either as a primary text or as a complement to a more formal presentation.

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Sample Content

Table of Contents

MC1000049826

1 Overview 1

What Are Data Structures and Algorithms?. . . . . . . . . . . . . . . . . . . . . . . 1

Overview of Data Structures.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Overview of Algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Some Definitions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Programming in Python.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Object-Oriented Programming.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2 Arrays 29

The Array Visualization Tool.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

Using Python Lists to Implement the Array Class.. . . . . . . . . . . . . . . . . 37

The OrderedArray Visualization Tool.. . . . . . . . . . . . . . . . . . . . . . . . . . 47

Binary Search.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

Python Code for an OrderedArray Class.. . . . . . . . . . . . . . . . . . . . . . . . 52

Logarithms.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Storing Objects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

Big O Notation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

Why Not Use Arrays for Everything?.. . . . . . . . . . . . . . . . . . . . . . . . . . 69

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

3 Simple Sorting 75

How Would You Do It?.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

Bubble Sort. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

Selection Sort.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

Insertion Sort.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Comparing the Simple Sorts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4 Stacks and Queues 103

Different Structures for Different Use Cases.. . . . . . . . . . . . . . . . . . . . . 103

Stacks.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

Queues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

Priority Queues.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

Parsing Arithmetic Expressions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

5 Linked Lists 157

Links.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

The LinkedList Visualization Tool.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 164

A Simple Linked List.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Double-Ended Lists.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

Linked List Efficiency.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183

Abstract Data Types and Objects. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

Ordered Lists.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

Doubly Linked Lists.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

Insertion and Deletion at the Ends.. . . . . . . . . . . . . . . . . . . . . . . 201

Insertion and Deletion in the Middle.. . . . . . . . . . . . . . . . . . . . . 204

Doubly Linked List as Basis for Deques.. . . . . . . . . . . . . . . . . . . . 208

Circular Lists.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

Iterators.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

6 Recursion 229

Triangular Numbers.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

Factorials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237

Anagrams.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

A Recursive Binary Search.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

The Tower of Hanoi.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245

Sorting with mergesort.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255

Eliminating Recursion.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267

Some Interesting Recursive Applications.. . . . . . . . . . . . . . . . . . . . . . . 275

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

7 Advanced Sorting 285

Shellsort.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

Partitioning.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

Quicksort.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302

Radix Sort.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

Timsort.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

8 Binary Trees 335

Why Use Binary Trees?.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

Tree Terminology.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337

An Analogy.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340

How Do Binary Search Trees Work?.. . . . . . . . . . . . . . . . . . . . . . . . . . 341

Finding a Node.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346

Inserting a Node.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 350

Traversing the Tree.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353

Finding Minimum and Maximum Key Values. . . . . . . . . . . . . . . . . . . 365

Deleting a Node.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

The Efficiency of Binary Search Trees.. . . . . . . . . . . . . . . . . . . . . . . . . 375

Trees Represented as Arrays.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377

Printing Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379

Duplicate Keys.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

The BinarySearchTreeTester.py Program. . . . . . . . . . . . . . . . . . . . . . . . 382

The Huffman Code.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 397

9 2-3-4 Trees and External Storage 401

Introduction to 2-3-4 Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401

The Tree234 Visualization Tool. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408

Python Code for a 2-3-4 Tree.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

Efficiency of 2-3-4 Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

2-3 Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432

External Storage.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460

10 AVL and Red-Black Trees 463

Our Approach to the Discussion.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463

Balanced and Unbalanced Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 464

AVL Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470

The Efficiency of AVL Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

Red-Black Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487

Using the Red-Black Tree Visualization Tool.. . . . . . . . . . . . . . . . . . . . 489

Experimenting with the Visualization Tool.. . . . . . . . . . . . . . . . . . . . . 492

Rotations in Red-Black Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497

Inserting a New Node.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498

Deletion.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

The Efficiency of Red-Black Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 509

2-3-4 Trees and Red-Black Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510

Red-Black Tree Implementation.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 517

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

11 Hash Tables 525

Introduction to Hashing.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526

Open Addressing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536

Separate Chaining.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 565

Hash Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575

Hashing Efficiency.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581

Hashing and External Storage.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 588

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595

12 Spatial Data Structures 597

Spatial Data.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597

Computing Distances Between Points.. . . . . . . . . . . . . . . . . . . . . . . . . 599

Circles and Bounding Boxes.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601

Searching Spatial Data.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 611

Lists of Points.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 612

Grids.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617

Quadtrees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633

Theoretical Performance and Optimizations.. . . . . . . . . . . . . . . . . . . . 656

Practical Considerations.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 656

Further Extensions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 658

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 659

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 662

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

13 Heaps 665

Introduction to Heaps.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 666

The Heap Visualization Tool.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674

Python Code for Heaps.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677

A Tree-Based Heap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 684

Heapsort.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 686

Order Statistics.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 700

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703

14 Graphs 705

Introduction to Graphs.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705

Traversal and Search.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 718

Minimum Spanning Trees.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734

Topological Sorting.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 740

Connectivity in Directed Graphs.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 753

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 760

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763

15 Weighted Graphs 767

Minimum Spanning Tree with Weighted Graphs.. . . . . . . . . . . . . . . . . 767

The All-Pairs Shortest-Path Problem.. . . . . . . . . . . . . . . . . . . . . . . . . . 797

Efficiency.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 800

Intractable Problems.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 801

Summary.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805

Questions.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806

Experiments.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 808

Programming Projects.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 809

16 What to Use and Why 813

Analyzing the Problem.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814

Foundational Data Structures.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 818

Special-Ordering Data Structures.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 824

Sorting.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826

Specialty Data Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828

External Storage.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829

Onward. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 831

A Running the Visualizations 833

B Further Reading 841

C Answers to Questions 845

9780134855684, TOC, 8/3/2022

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