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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

Non-comparison-based sorting

We have noted that all comparison-based sorting algorithms have a lower-bound time complexity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi mathvariant="normal">Ω</mml:mi><mml:mfenced separators="|"><mml:mrow><mml:mi>n</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">log</mml:mi></mml:mrow><mml:mo>⁡</mml:mo><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:mfenced></mml:math>, which means no comparison-based algorithm can achieve better performance than <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://schemas.openxmlformats.org/officeDocument/2006/math"><mml:mi>n</mml:mi><mml:mrow><mml:mrow><mml:mi mathvariant="normal">log</mml:mi></mml:mrow><mml:mo>⁡</mml:mo><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:mrow></mml:math> in the general case. However, there are sorting algorithms that do not depend on comparisons. These non-comparison-based algorithms leverage certain assumptions or information about the data to achieve better performance.

Unlike comparison-based algorithms, non-comparison-based algorithms can achieve a lower bound as efficiently as linear time. This remarkable efficiency is why they are sometimes referred to as linear-time sorting algorithms. By making use of specific properties of the data, such as a limited range of integer values or the distribution of digits, these algorithms can bypass the comparison limit and sort much faster under the right conditions. In this section, we will explore three well-known non-comparison-based sorting algorithms: counting sort, Radix sort,...

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Efficient Algorithm Design
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