You're reading from Practical Discrete Mathematics Discover math principles that fuel algorithms for computer science and machine learning with Python

Product type Paperback

Published in Feb 2021

Publisher Packt

ISBN-13 9781838983147

Length 330 pages

Edition 1st Edition

Languages

Python

Tools

NumPy

Concepts

Data Science

Authors (2):

Ryan T. White

Archana Tikayat Ray

View More author details

Table of Contents (17) Chapters

Preface

1. Part I – Basic Concepts of Discrete Math

2. Chapter 1: Key Concepts, Notation, Set Theory, Relations, and Functions FREE CHAPTER

3. Chapter 2: Formal Logic and Constructing Mathematical Proofs

4. Chapter 3: Computing with Base-n Numbers

5. Chapter 4: Combinatorics Using SciPy

6. Chapter 5: Elements of Discrete Probability

7. Part II – Implementing Discrete Mathematics in Data and Computer Science

8. Chapter 6: Computational Algorithms in Linear Algebra

9. Chapter 7: Computational Requirements for Algorithms

10. Chapter 8: Storage and Feature Extraction of Graphs, Trees, and Networks

11. Chapter 9: Searching Data Structures and Finding Shortest Paths

12. Part III – Real-World Applications of Discrete Mathematics

13. Chapter 10: Regression Analysis with NumPy and Scikit-Learn

14. Chapter 11: Web Searches with PageRank

15. Chapter 12: Principal Component Analysis with Scikit-Learn

16. Other Books You May Enjoy

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Dijkstra's Algorithm for Finding Shortest Paths

In this section, we will learn about Dijkstra's algorithm for finding the shortest paths, consider the process in simple terms, and apply the algorithm by hand to a small network.

The most common algorithm for finding the shortest paths on a network is Dijkstra's algorithm. It was named after the Dutch computer scientist Edsger W. Dijkstra, who constructed it in 1956, but since computing was such a new field at the time, there were so few academic journals dedicated to computing that he did not publish his findings until 1959.

We will first learn about the method in intuitive terms using the small network from Figure 9.5 so that we can understand the ideas behind the approach. This understanding is important because there are many variations of the algorithm and we hope you will learn to adapt it to solve your own problems!

Just like the previous section, we will seek the shortest path from v1 to v2. Since it is...