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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 this chapter, we discussed the important concepts of mathematical induction and loop invariants as foundational tools for verifying the correctness of algorithms. The chapter started by explaining mathematical induction, describing its two primary steps: the base case, which establishes the initial validity of the proposition, and the induction step, which demonstrates the proposition’s maintenance across successive iterations. It then introduces loop invariants, expanding on mathematical induction by including the additional step of termination to ensure that the algorithm’s properties hold from initiation through termination. Through detailed examples, such as a binary search algorithm, the chapter illustrates how these principles are applied to prove that algorithms perform correctly and efficiently, emphasizing their importance in developing reliable software. The chapter aimed to equip you with the methodologies to rigorously assess the integrity and operational...

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Tech Concepts
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Programming languages
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Efficient Algorithm Design
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