Book Image

Applying Math with Python

By : Sam Morley
Book Image

Applying Math with Python

By: Sam Morley

Overview of this book

Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python’s scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science.
Table of Contents (12 chapters)

Finding the shortest paths in a network

A common problem where networks make an appearance is in the problem of finding the shortest – or perhaps more precisely, the highest reward – route between two nodes in a network. For instance, this could be the shortest distance between two cities, where the nodes represent the cities and the edges are roads connecting pairs of cities. In this case, the weights of the edges would be their lengths.

In this recipe, we will find the shortest path between two nodes in a network with weights.

Getting ready

For this recipe, we will need the NetworkX package imported, as usual, under the name nx, the Matplotlib pyplot module imported as plt, and a random number generator object from NumPy:

from numpy.random import default_rng
rng = default_rng(12345) # seed for reproducibility

How to do it...

Follow these steps to find the shortest path between...