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## Problem Solving with Algorithms and Data Structures using Python ¶

By Brad Miller and David Ranum, Luther College

There is a wonderful collection of YouTube videos recorded by Gerry Jenkins to support all of the chapters in this text.

- 1.1. Objectives
- 1.2. Getting Started
- 1.3. What Is Computer Science?
- 1.4. What Is Programming?
- 1.5. Why Study Data Structures and Abstract Data Types?
- 1.6. Why Study Algorithms?
- 1.7. Review of Basic Python
- 1.8.1. Built-in Atomic Data Types
- 1.8.2. Built-in Collection Data Types
- 1.9.1. String Formatting
- 1.10. Control Structures
- 1.11. Exception Handling
- 1.12. Defining Functions
- 1.13.1. A Fraction Class
- 1.13.2. Inheritance: Logic Gates and Circuits
- 1.14. Summary
- 1.15. Key Terms
- 1.16. Discussion Questions
- 1.17. Programming Exercises
- 2.1.1. A Basic implementation of the MSDie class
- 2.2. Making your Class Comparable
- 3.1. Objectives
- 3.2. What Is Algorithm Analysis?
- 3.3. Big-O Notation
- 3.4.1. Solution 1: Checking Off
- 3.4.2. Solution 2: Sort and Compare
- 3.4.3. Solution 3: Brute Force
- 3.4.4. Solution 4: Count and Compare
- 3.5. Performance of Python Data Structures
- 3.7. Dictionaries
- 3.8. Summary
- 3.9. Key Terms
- 3.10. Discussion Questions
- 3.11. Programming Exercises
- 4.1. Objectives
- 4.2. What Are Linear Structures?
- 4.3. What is a Stack?
- 4.4. The Stack Abstract Data Type
- 4.5. Implementing a Stack in Python
- 4.6. Simple Balanced Parentheses
- 4.7. Balanced Symbols (A General Case)
- 4.8. Converting Decimal Numbers to Binary Numbers
- 4.9.1. Conversion of Infix Expressions to Prefix and Postfix
- 4.9.2. General Infix-to-Postfix Conversion
- 4.9.3. Postfix Evaluation
- 4.10. What Is a Queue?
- 4.11. The Queue Abstract Data Type
- 4.12. Implementing a Queue in Python
- 4.13. Simulation: Hot Potato
- 4.14.1. Main Simulation Steps
- 4.14.2. Python Implementation
- 4.14.3. Discussion
- 4.15. What Is a Deque?
- 4.16. The Deque Abstract Data Type
- 4.17. Implementing a Deque in Python
- 4.18. Palindrome-Checker
- 4.19. Lists
- 4.20. The Unordered List Abstract Data Type
- 4.21.1. The Node Class
- 4.21.2. The Unordered List Class
- 4.22. The Ordered List Abstract Data Type
- 4.23.1. Analysis of Linked Lists
- 4.24. Summary
- 4.25. Key Terms
- 4.26. Discussion Questions
- 4.27. Programming Exercises
- 5.1. Objectives
- 5.2. What Is Recursion?
- 5.3. Calculating the Sum of a List of Numbers
- 5.4. The Three Laws of Recursion
- 5.5. Converting an Integer to a String in Any Base
- 5.6. Stack Frames: Implementing Recursion
- 5.7. Introduction: Visualizing Recursion
- 5.8. Sierpinski Triangle
- 5.9. Complex Recursive Problems
- 5.10. Tower of Hanoi
- 5.11. Exploring a Maze
- 5.12. Dynamic Programming
- 5.13. Summary
- 5.14. Key Terms
- 5.15. Discussion Questions
- 5.16. Glossary
- 5.17. Programming Exercises
- 6.1. Objectives
- 6.2. Searching
- 6.3.1. Analysis of Sequential Search
- 6.4.1. Analysis of Binary Search
- 6.5.1. Hash Functions
- 6.5.2. Collision Resolution
- 6.5.3. Implementing the Map Abstract Data Type
- 6.5.4. Analysis of Hashing
- 6.6. Sorting
- 6.7. The Bubble Sort
- 6.8. The Selection Sort
- 6.9. The Insertion Sort
- 6.10. The Shell Sort
- 6.11. The Merge Sort
- 6.12. The Quick Sort
- 6.13. Summary
- 6.14. Key Terms
- 6.15. Discussion Questions
- 6.16. Programming Exercises
- 7.1. Objectives
- 7.2. Examples of Trees
- 7.3. Vocabulary and Definitions
- 7.4. List of Lists Representation
- 7.5. Nodes and References
- 7.6. Parse Tree
- 7.7. Tree Traversals
- 7.8. Priority Queues with Binary Heaps
- 7.9. Binary Heap Operations
- 7.10.1. The Structure Property
- 7.10.2. The Heap Order Property
- 7.10.3. Heap Operations
- 7.11. Binary Search Trees
- 7.12. Search Tree Operations
- 7.13. Search Tree Implementation
- 7.14. Search Tree Analysis
- 7.15. Balanced Binary Search Trees
- 7.16. AVL Tree Performance
- 7.17. AVL Tree Implementation
- 7.18. Summary of Map ADT Implementations
- 7.19. Summary
- 7.20. Key Terms
- 7.21. Discussion Questions
- 7.22. Programming Exercises
- 8.1. Objectives
- 8.2. Vocabulary and Definitions
- 8.3. The Graph Abstract Data Type
- 8.4. An Adjacency Matrix
- 8.5. An Adjacency List
- 8.6. Implementation
- 8.7. The Word Ladder Problem
- 8.8. Building the Word Ladder Graph
- 8.9. Implementing Breadth First Search
- 8.10. Breadth First Search Analysis
- 8.11. The Knight’s Tour Problem
- 8.12. Building the Knight’s Tour Graph
- 8.13. Implementing Knight’s Tour
- 8.14. Knight’s Tour Analysis
- 8.15. General Depth First Search
- 8.16. Depth First Search Analysis
- 8.17. Topological Sorting
- 8.18. Strongly Connected Components
- 8.19. Shortest Path Problems
- 8.20. Dijkstra’s Algorithm
- 8.21. Analysis of Dijkstra’s Algorithm
- 8.22. Prim’s Spanning Tree Algorithm
- 8.23. Summary
- 8.24. Key Terms
- 8.25. Discussion Questions
- 8.26. Programming Exercises

## Acknowledgements ¶

We are very grateful to Franklin Beedle Publishers for allowing us to make this interactive textbook freely available. This online version is dedicated to the memory of our first editor, Jim Leisy, who wanted us to “change the world.”

## Indices and tables ¶

Search Page

- Table of Contents
- Scratch ActiveCode
- Navigation Help
- Help for Instructors
- About Runestone
- Report A Problem
- 1. Introduction
- 2. Analysis
- 3. Basic Data Structures
- 4. Recursion
- 5. Sorting and Searching
- 6. Trees and Tree Algorithms
- 7. Graphs and Graph Algorithms

## Problem Solving with Algorithms and Data Structures using Python ¶

By Brad Miller and David Ranum, Luther College (as remixed by Jeffrey Elkner)

- 1.1. Objectives
- 1.2. Getting Started
- 1.3. What Is Computer Science?
- 1.4. What Is Programming?
- 1.5. Why Study Data Structures and Abstract Data Types?
- 1.6. Why Study Algorithms?
- 1.7. Review of Basic Python
- 1.8.1. Built-in Atomic Data Types
- 1.8.2. Built-in Collection Data Types
- 1.9.1. String Formatting
- 1.10. Control Structures
- 1.11. Exception Handling
- 1.12. Defining Functions
- 1.13.1. A Fraction Class
- 1.13.2. Inheritance: Logic Gates and Circuits
- 1.14. Summary
- 1.15. Key Terms
- 1.16. Discussion Questions
- 1.17. Programming Exercises
- 2.1. Objectives
- 2.2. What Is Algorithm Analysis?
- 2.3. Big-O Notation
- 2.4.1. Solution 1: Checking Off
- 2.4.2. Solution 2: Sort and Compare
- 2.4.3. Solution 3: Brute Force
- 2.4.4. Solution 4: Count and Compare
- 2.5. Performance of Python Data Structures
- 2.7. Dictionaries
- 2.8. Summary
- 2.9. Key Terms
- 2.10. Discussion Questions
- 2.11. Programming Exercises
- 3.1. Objectives
- 3.2. What Are Linear Structures?
- 3.3. What is a Stack?
- 3.4. The Stack Abstract Data Type
- 3.5. Implementing a Stack in Python
- 3.6. Simple Balanced Parentheses
- 3.7. Balanced Symbols (A General Case)
- 3.8. Converting Decimal Numbers to Binary Numbers
- 3.9.1. Conversion of Infix Expressions to Prefix and Postfix
- 3.9.2. General Infix-to-Postfix Conversion
- 3.9.3. Postfix Evaluation
- 3.10. What Is a Queue?
- 3.11. The Queue Abstract Data Type
- 3.12. Implementing a Queue in Python
- 3.13. Simulation: Hot Potato
- 3.14.1. Main Simulation Steps
- 3.14.2. Python Implementation
- 3.14.3. Discussion
- 3.15. What Is a Deque?
- 3.16. The Deque Abstract Data Type
- 3.17. Implementing a Deque in Python
- 3.18. Palindrome-Checker
- 3.19. Lists
- 3.20. The Unordered List Abstract Data Type
- 3.21.1. The Node Class
- 3.21.2. The Unordered List Class
- 3.22. The Ordered List Abstract Data Type
- 3.23.1. Analysis of Linked Lists
- 3.24. Summary
- 3.25. Key Terms
- 3.26. Discussion Questions
- 3.27. Programming Exercises
- 4.1. Objectives
- 4.2. What Is Recursion?
- 4.3. Calculating the Sum of a List of Numbers
- 4.4. The Three Laws of Recursion
- 4.5. Converting an Integer to a String in Any Base
- 4.6. Stack Frames: Implementing Recursion
- 4.7. Introduction: Visualizing Recursion
- 4.8. Sierpinski Triangle
- 4.9. Complex Recursive Problems
- 4.10. Tower of Hanoi
- 4.11. Exploring a Maze
- 4.12. Dynamic Programming
- 4.13. Summary
- 4.14. Key Terms
- 4.15. Discussion Questions
- 4.16. Glossary
- 4.17. Programming Exercises
- 5.1. Objectives
- 5.2. Searching
- 5.3.1. Analysis of Sequential Search
- 5.4.1. Analysis of Binary Search
- 5.5.1. Hash Functions
- 5.5.2. Collision Resolution
- 5.5.3. Implementing the Map Abstract Data Type
- 5.5.4. Analysis of Hashing
- 5.6. Sorting
- 5.7. The Bubble Sort
- 5.8. The Selection Sort
- 5.9. The Insertion Sort
- 5.10. The Shell Sort
- 5.11. The Merge Sort
- 5.12. The Quick Sort
- 5.13. Summary
- 5.14. Key Terms
- 5.15. Discussion Questions
- 5.16. Programming Exercises
- 6.1. Objectives
- 6.2. Examples of Trees
- 6.3. Vocabulary and Definitions
- 6.4. List of Lists Representation
- 6.5. Nodes and References
- 6.6. Parse Tree
- 6.7. Tree Traversals
- 6.8. Priority Queues with Binary Heaps
- 6.9. Binary Heap Operations
- 6.10.1. The Structure Property
- 6.10.2. The Heap Order Property
- 6.10.3. Heap Operations
- 6.11. Binary Search Trees
- 6.12. Search Tree Operations
- 6.13. Search Tree Implementation
- 6.14. Search Tree Analysis
- 6.15. Balanced Binary Search Trees
- 6.16. AVL Tree Performance
- 6.17. AVL Tree Implementation
- 6.18. Summary of Map ADT Implementations
- 6.19. Summary
- 6.20. Key Terms
- 6.21. Discussion Questions
- 6.22. Programming Exercises
- 7.1. Objectives
- 7.2. Vocabulary and Definitions
- 7.3. The Graph Abstract Data Type
- 7.4. An Adjacency Matrix
- 7.5. An Adjacency List
- 7.6. Implementation
- 7.7. The Word Ladder Problem
- 7.8. Building the Word Ladder Graph
- 7.9. Implementing Breadth First Search
- 7.10. Breadth First Search Analysis
- 7.11. The Knight’s Tour Problem
- 7.12. Building the Knight’s Tour Graph
- 7.13. Implementing Knight’s Tour
- 7.14. Knight’s Tour Analysis
- 7.15. General Depth First Search
- 7.16. Depth First Search Analysis
- 7.17. Topological Sorting
- 7.18. Strongly Connected Components
- 7.19. Shortest Path Problems
- 7.20. Dijkstra’s Algorithm
- 7.21. Analysis of Dijkstra’s Algorithm
- 7.22. Prim’s Spanning Tree Algorithm
- 7.23. Summary
- 7.24. Key Terms
- 7.25. Discussion Questions
- 7.26. Programming Exercises

## Acknowledgements ¶

We are very grateful to Franklin Beedle Publishers for allowing us to make this interactive textbook freely available. This online version is dedicated to the memory of our first editor, Jim Leisy, who wanted us to “change the world.”

## Indices and tables ¶

- Module Index
- Search Page

## Challenging Programming in Python: A Problem Solving Perspective

- © 2024
- Habib Izadkhah 0 ,
- Rashid Behzadidoost 1

## Department of Computer Science, University of Tabriz, Tabriz, Iran

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- Demonstrates with a lot of examples how to solve problems with Python
- Provides an accessible introduction to Python
- Presents challenging problems and its programming solutions from different areas of applied sciences

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## About this book

This book aims to strengthen programming skills and foster creative thinking by presenting and solving 90 challenging problems. The book is intended for individuals with elementary, intermediate, and advanced Python programming skills who aspire to take their abilities to the next level. Additionally, the book is valuable for individuals interested in enhancing their creative thinking and logical reasoning skills. It is a self-instructional book meant to provide readers with the ability to solve challenging problems independently. The presented challenges are lucidly and succinctly expressed, facilitating readers to follow along and comprehend the problem-solving process. The challenges cover various fields, making it suitable for a wide range of individuals.

The book is divided into eight chapters, beginning with an introduction in chapter one. The second chapter presents essential Python basics for programming challenging problems, while the subsequent chapters focuson specific types of challenges. These include math-based challenges in chapter three, number-based challenges in chapter four, string-based challenges in chapter five, game-based challenges in chapter six, count-based challenges in chapter seven, and miscellaneous challenges in chapter eight. Each chapter comprises a set of challenges with examples, hints, algorithms, and Python code solutions. The target audience of the book includes computer science and engineering students, teachers, software developers, and participants in programming competitions.

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## Table of contents (8 chapters)

Front matter, introduction.

Habib Izadkhah, Rashid Behzadidoost

## Python Basics

Miscellaneous problems, authors and affiliations, about the authors.

Dr. Habib Izadkhah is an associate professor at the Department of Computer Science, University of Tabriz, Iran. He worked in the industry for a decade as a software engineer before becoming an academic. His research interests include algorithms and graphs, software engineering, and bioinformatics. More recently, he has been working on developing and applying deep learning to a variety of problems, dealing with biomedical images, speech recognition, text understanding, and generative models. He has contributed to various research projects, authored a number of research papers in international conferences, workshops, and journals, and also has written five books, including Source Code Modularization: Theory and Techniques from Springer and Deep Learning in Bioinformatics from Elsevier.

Rashid Behzadidoost is a Ph.D. candidate in Computer Science at the University of Tabriz, Iran. He is currently pursuing his doctoral degree in Computer Science, specializing in artificial intelligence and natural language processing. Rashid has a deep passion for coding and enjoys solving challenging problems. He has obtained his skills through years of study, practice, and teaching. He has taught several courses on computer sciences including challenging programming, microprocessor, and data structure at the University of Tabriz.

## Problem Solving and Python Programming PDF

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Table of contents.

Title Contents Unit 1 Introduction to Computing and Algorithmic Problem Solving 1 Introduction to Digital Computer 2 Problem Solving Strategies Appendix A Practice Exercises with Algorithm and Flow Chart Appendix B Problem Solving Exercises with Algorithms and Pseudocode Unit 2 Introduction to Python and Data, Expressions, Statements 3 Introduction to Python Unit 3 Functions 4 Functions Unit 4 Lists, Tuples and Dictionaries 5 Strings and Lists 6 Tuples and Dictionaries Unit 5 Files, Modules and Packages 7 Files and Exceptions 8 Classes and Objects Appendix C Fundamental Standard Library Modules

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Algorithmic Problem Solving with Python John B. Schneider Shira Lynn Broschat Jess Dahmen February 22, 2019

Each exercise has 10-20 Questions. The solution is provided for every question. Practice each Exercise in Online Code Editor. These Python programming exercises are suitable for all Python developers. If you are a beginner, you will have a better understanding of Python after solving these exercises. Below is the list of exercises.

Problem Solving with Algorithms and Data Structures using Python¶. By Brad Miller and David Ranum, Luther College. Assignments; There is a wonderful collection of YouTube videos recorded by Gerry Jenkins to support all of the chapters in this text.

Python currently is one of the most popular programming languages, and as such, it has become vital for students to understand this concept in this language. This student-friendly textbook provides a complete view of data structures and algorithms using the Python programming language, striking a balance between theory and practical application.

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Unit 1 Introduction to Computing and Algorithmic Problem Solving 1 Introduction to Digital Computer 2 Problem Solving Strategies Appendix A Practice Exercises with Algorithm and Flow Chart Appendix B Problem Solving Exercises with Algorithms and Pseudocode Unit 2 Introduction to Python and Data, Expressions, Statements 3 Introduction to Python

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1.1Introduction to Problem Solving 1.1.1. Problem Analysis The key dimensions basis on which an appropriate method is applied are as follows Decomposable/non decomposable : Analyze whether the problem is decomposable, i.e, whether it can be broken into sub-problems. If cannot be decomposed then such problem is non-decomposable.

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