Data Structures and Algorithms Using Python

Transcription

1 Data Structures and Algorithms Using Python Ranee D. Necaise Department of Computer Science College of William and Mary WILEY JOHN WILEY & SONS, INC.

2 Contents Preface xiii Chapter 1: Abstract Data Types Introduction Abstractions Abstract Data Types Data Structures General Definitions The Date Abstract Data Type Defining the ADT Using the ADT Preconditions and Postconditions Implementing the ADT Bags The Bag Abstract Data Type Selecting a Data Structure List-Based Implementation Iterators Designing an Iterator Using Iterators Application: Student Records Designing a Solution Implementation 26 Exercises 28 Programming Projects 29 Chapter 2: Arrays The Array Structure Why Study Arrays? The Array Abstract Data Type Implementing the Array The Python List 41 V

3 2.2.1 Creating a Python List Appending Items Extending A List Inserting Items List Slice Two-Dimensional Arrays The Array2D Abstract Data Type Implementing the 2-D Array The Matrix Abstract Data Type Matrix Operations Implementing the Matrix Application: The Game of Life Rules of the Game Designing a Solution Implementation 61 Exercises 64 Programming Projects 65 Chapter 3: Sets and Maps Sets The Set Abstract Data Type Selecting a Data Structure List-Based Implementation Maps The Map Abstract Data Type List-Based Implementation Multi-Dimensional Arrays The MultiArray Abstract Data Type Data Organization Variable-Length Arguments Implementing the MultiArray Application: Sales Reports 89 Exercises 95 Programming Projects 96 Chapter 4: Algorithm Analysis Complexity Analysis Big-0 Notation Evaluating Python Code Evaluating the Python List Amortized Cost Evaluating the Set ADT 113

4 4.5 Application: The Sparse Matrix List-Based Implementation Efficiency Analysis 120 Exercises 121 Programming Projects 122 Chapter 5: Searching and Sorting Searching The Linear Search The Binary Search Sorting Bubble Sort Selection Sort Insertion Sort Working with Sorted Lists Maintaining a Sorted List Merging Sorted Lists The Set ADT Revisited A Sorted List Implementation Comparing the Implementations 152 Exercises 152 Programming Projects 153 Chapter 6: Linked Structures Introduction The Singly Linked List Traversing the Nodes Searching for a Node Prepending Nodes Removing Nodes The Bag ADT Revisited A Linked List Implementation Comparing Implementations Linked List Iterators More Ways to Build a Linked List Using a Tail Reference The Sorted Linked List The Sparse Matrix Revisited An Array of Linked Lists Implementation Comparing the Implementations Application: Polynomials Polynomial Operations 179

5 viii CONTENTS The Polynomial ADT Implementation 181 Exercises 189 Programming Projects 190 Chapter 7: Stacks The Stack ADT Implementing the Stack Using a Python List Using a Linked List Stack Applications Balanced Delimiters Evaluating Postfix Expressions Application: Solving a Maze Backtracking Designing a Solution The Maze ADT Implementation 214 Exercises 218 Programming Projects 219 Chapter 8: Queues The Queue ADT Implementing the Queue Using a Python List Using a Circular Array Using a Linked List Priority Queues The Priority Queue ADT Implementation: Unbounded Priority Queue Implementation: Bounded Priority Queue Application: Computer Simulations Airline Ticket Counter Implementation 239 Exercises 244 Programming Projects 246 Chapter 9: Advanced Linked Lists The Doubly Linked List Organization List Operations The Circular Linked List 253

6 9.2.1 Organization List Operations Multi-Linked Lists Multiple Chains The Sparse Matrix Complex Iterators Application: Text Editor Typical Editor Operations The Edit Buffer ADT Implementation 268 Exercises 275 Programming Projects 275 Chapter 10: Recursion Recursive Functions Properties of Recursion Factorials Recursive Call Trees The Fibonacci Sequence How Recursion Works The Run Time Stack Using a Software Stack Tail Recursion Recursive Applications Recursive Binary Search Towers of Hanoi Exponential Operation Playing Tic-Tac-Toe Application: The Eight-Queens Problem Solving for Four-Queens Designing a Solution 303 Exercises 307 Programming Projects 308 Chapter 11: Hash Tables Introduction Hashing Linear Probing Clustering Rehashing Efficiency Analysis Separate Chaining 321

7 11.4 Hash Functions The HashMap Abstract Data Type Application: Histograms The Histogram Abstract Data Type The Color Histogram 334 Exercises 337 Programming Projects 338 Chapter 12: Advanced Sorting Merge Sort Algorithm Description Basic Implementation Improved Implementation Efficiency Analysis Quick Sort Algorithm Description Implementation Efficiency Analysis How Fast Can We Sort? Radix Sort Algorithm Description Basic Implementation Efficiency Analysis Sorting Linked Lists Insertion Sort Merge Sort 362 Exercises 367 Programming Projects 368 Chapter 13: Binary Trees The Tree Structure The Binary Tree Properties Implementation Tree Traversais Expression Trees Expression Tree Abstract Data Type String Representation Tree Evaluation Tree Construction Heaps Definition 391

8 Implementation The Priority Queue Revisited Heapsort Simple Implementation Sorting In Place Application: Morse Code Decision Trees The ADT Definition 406 Exercises 407 Programming Projects 410 Chapter 14: Search Trees The Binary Search Tree Searching Min and Max Values Insertions Deletions Efficiency of Binary Search Trees Search Tree Iterators AVL Trees Insertions Deletions Implementation The 2-3 Tree Searching Insertions Efficiency of the 2-3 Tree 449 Exercises 451 Programming Projects 452 Appendix A: Python Review 453 A.1 The Python Interpreter 453 A.2 The Basics of Python 454 A.2.1 Primitive Types 455 A.2.2 Statements 456 A.2.3 Variables 457 A.2.4 Arithmetic Operators 458 A.2.5 Logical Expressions 459 A.2.6 Using Functions and Methods 461 A.2.7 Standard Library 462 A.3 User Interaction 463 A.3.1 Standard Input 463

9 A.3.2 Standard Output 464 A.4 Control Structures 467 A.4.1 Selection Constructs 467 A.4.2 Repetition Constructs 469 A.5 Collections 472 A.5.1 Strings 472 A.5.2 Lists 473 A.5.3 Tuples 475 A.5.4 Dictionaries 475 A.6 Text Files 477 A.6.1 File Access 477 A.6.2 Writing to Files 478 A.6.3 Reading from Files 479 A.7 User-Defined Functions 480 A.7.1 The Function Definition 480 A.7.2 Variable Scope 483 A.7.3 Main Routine 483 Appendix B: User-Defined Modules 485 B.1 Structured Programs 485 B.2 Namespaces 486 Appendix C: Exceptions 489 C.1 Catching Exceptions 489 C.2 Raising Exceptions 490 C.3 Standard Exceptions 491 C.4 Assertions 491 Appendix D: Classes 493 D.1 The Class Definition 493 D.1.1 Constructors 494 D.1.2 Operations 495 D.1.3 Using Modules 497 D.1.4 Hiding Attributes 498 D.2 Overloading Operators 500 D.3 Inheritance 502 D.3.1 Deriving Child Classes 503 D.3.2 Creating Class Instances 504 D.3.3 Invoking Methods 505 D.4 Polymorphism 507