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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

Unfolding recurrence functions

So far, we have discussed the recursive structures in algorithm design and introduced different types of recursions. We then focused on two types of recurrence functions: subtractive and divide-and-conquer. Table 4.2 provides a summary of the properties of these two recurrence functions. As the table illustrates, divide-and-conquer recurrences generally offer more efficient solutions, although the efficiency highly depends on the specific problem being solved.

In this section, we will demystify recurrence functions. This understanding will be essential in the next chapter, where we will solve recurrence functions and estimate their computational complexity, or in other words, their rate of growth. By unfolding these functions, we can gain insights into how recursive algorithms operate and how their performance scales with input size. This knowledge will enable us to analyze and optimize algorithms more effectively.

Regardless of the type of recurrence...

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Efficient Algorithm Design
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