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Practical Discrete Mathematics

You're reading from  Practical Discrete Mathematics

Product type Book
Published in Feb 2021
Publisher Packt
ISBN-13 9781838983147
Pages 330 pages
Edition 1st Edition
Languages
Authors (2):
Ryan T. White Ryan T. White
Profile icon Ryan T. White
Archana Tikayat Ray Archana Tikayat Ray
Profile icon Archana Tikayat Ray
View More author details
Toc

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 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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