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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

Hashing

In the previous two sections, we explored two groups of search algorithms: those with linear time complexity and those with more efficient, sub-linear time complexity. Linear search algorithms, such as the simple sequential search, operate with <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:mo>(</mml:mo><mml:mi>n</mml:mi><mml:mo>)</mml:mo></mml:math> time complexity, making them straightforward but less efficient for large datasets. On the other hand, sub-linear search algorithms, such as binary search and jump search, offer significantly better time complexities, often <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mrow><mi>O</mi><mo>(</mo><mi>l</mi><mi>o</mi><mi>g</mi><mi>n</mi><mo>)</mo></mrow></mrow></mrow></math> or <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:msqrt><mml:mi>n</mml:mi></mml:msqrt></mml:mrow></mml:mfenced></mml:math>, by leveraging the properties of sorted data to minimize the number of comparisons needed.

However, achieving this improved time complexity comes with a cost: the time required to sort the data. Sorting is a prerequisite for the efficiency of sub-linear search algorithms. Without sorted data, the theoretical benefits of sub-linear time complexity cannot be realized. The process of sorting itself can be time-consuming, typically <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mrow><mi>O</mi><mfenced open="(" close=")"><mrow><mi>n</mi><mi>l</mi><mi>o</mi><mi>g</mi><mi>n</mi></mrow></mfenced></mrow></mrow></math> for efficient algorithms such as quick sort or merge sort. Therefore, while sub...

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Efficient Algorithm Design
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