Book Image

Practical Discrete Mathematics

By : Ryan T. White, Archana Tikayat Ray
Book Image

Practical Discrete Mathematics

By: Ryan T. White, Archana Tikayat Ray

Overview of this book

Discrete mathematics deals with studying countable, distinct elements, and its principles are widely used in building algorithms for computer science and data science. The knowledge of discrete math concepts will help you understand the algorithms, binary, and general mathematics that sit at the core of data-driven tasks. Practical Discrete Mathematics is a comprehensive introduction for those who are new to the mathematics of countable objects. This book will help you get up to speed with using discrete math principles to take your computer science skills to a more advanced level. As you learn the language of discrete mathematics, you’ll also cover methods crucial to studying and describing computer science and machine learning objects and algorithms. The chapters that follow will guide you through how memory and CPUs work. In addition to this, you’ll understand how to analyze data for useful patterns, before finally exploring how to apply math concepts in network routing, web searching, and data science. By the end of this book, you’ll have a deeper understanding of discrete math and its applications in computer science, and be ready to work on real-world algorithm development and machine learning.
Table of Contents (17 chapters)
1
Part I – Basic Concepts of Discrete Math
7
Part II – Implementing Discrete Mathematics in Data and Computer Science
12
Part III – Real-World Applications of Discrete Mathematics

Python Implementation of Dijkstra's Algorithm

We have now learned how Dijkstra's algorithm works, but we will now implement it in Python.

The input to the algorithm will be a network and a source vertex. The simplest way we can represent a network is with a weight matrix like we introduced in Chapter 8, Storage and Feature Extraction of Graphs, Trees, and Networks. For the graph in Figure 9.7, we have the following weight matrix:

Figure 9.17 – A small network and its weight matrix

In the context of a shortest-distance problem, this weight matrix may be called a distance matrix, but we will refrain from using this terminology because, as we have seen in previous sections, these shortest path problems may or may not actually refer to distances.

The output from the algorithm will be a table like the one at the upper right of Figure 9.15, giving the shortest distance from the source vertex to each of the other vertices.

The table in Figure...