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Efficient Algorithm Design

Efficient Algorithm Design

By : Masoud Makrehchi
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Efficient Algorithm Design

Efficient Algorithm Design

By: Masoud Makrehchi

Overview of this book

Efficient Algorithm Design redefines algorithms, tracing the evolution of computer science as a discipline bridging natural science and mathematics. Author Masoud Makrehchi, PhD, with his extensive experience in delivering publications and presentations, explores the duality of computers as mortal hardware and immortal algorithms. The book guides you through essential aspects of algorithm design and analysis, including proving correctness and the importance of repetition and loops. This groundwork sets the stage for exploring algorithm complexity, with practical exercises in design and analysis using sorting and search as examples. Each chapter delves into critical topics such as recursion and dynamic programming, reinforced with practical examples and exercises that link theory with real-world applications. What sets this book apart is its focus on the practical application of algorithm design and analysis, equipping you to solve real programming challenges effectively. By the end of this book, you’ll have a deep understanding of algorithmic foundations and gain proficiency in designing efficient algorithms, empowering you to develop more robust and optimized software solutions.
Table of Contents (21 chapters)
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1
Part 1: Foundations of Algorithm Analysis
7
Part 2: Deep Dive in Algorithms
13
Part 3: Fundamental Data Structures
17
Part 4: Next Steps

Summary

In Chapter 3, we examined the concept of the rate of growth in algorithmic complexity, highlighting its importance for understanding how an algorithm’s running time scaled with increasing input size. This understanding was crucial for predicting algorithm behavior and making informed design decisions. We covered a range of growth rates, from constant time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>O</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:mfenced></mml:math> to factorial time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>O</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>n</mml:mi><mml:mo>!</mml:mo></mml:mrow></mml:mfenced></mml:math>, and discussed how these rates impacted the efficiency and practicality of algorithms, particularly when dealing with large datasets.

We also introduced various asymptotic notations, such as Big <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>O</mml:mi></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>Ω</mml:mi></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>ϴ</mml:mi></mml:math>, to formally describe the upper, lower, and tight bounds of an algorithm’s running time. Through examples and comparisons, we demonstrated how different growth rates influenced computational resources and performance. This chapter laid the foundation for recognizing and analyzing the complexity of algorithms, providing the necessary tools to evaluate and compare their efficiency in real...

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Efficient Algorithm Design
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