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Practical Discrete Mathematics

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

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Product type Paperback
Published in Feb 2021
Publisher Packt
ISBN-13 9781838983147
Length 330 pages
Edition 1st Edition
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Authors (2):
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Ryan T. White Ryan T. White
Author Profile Icon Ryan T. White
Ryan T. White
Archana Tikayat Ray Archana Tikayat Ray
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Archana Tikayat Ray
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Table of Contents (17) Chapters Close

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

Understanding Big-O Notation

Next, let's learn about Big-O Notation. Learning about this notation is crucial since it is used to describe the performance/complexity of an algorithm. This notation can be used to establish the relationship between the input to the algorithm and the steps required to execute the algorithm. Notation: O (relationship between the input and steps taken by the algorithm – denoted by "n").

For example: If there is a linear relationship between the input and the steps taken by the algorithm, then the Big-O notation will be O(n). Similarly, for a constant relationship, the notation will be O(constant).

The most frequently used Big-O notations are as follows:

Figure 7.3 – Big-O notation for different types of algorithms

We will now look into some of the complexities noted in the preceding table:

  • Constant complexity O(constant):

    The complexity of an algorithm is said to be constant if the steps...

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