Preface

In the second chapter of this book, we explore the concept of the “loop invariant,” which refers to an attribute within a changing process that remains constant. If we look at human progress since the Industrial Revolution, despite the volatility and constant change, we can identify a few unchanging attributes. One is our drive to automate more and more, and the other is our systematic approach to problem-solving, which took a formal direction with the invention of the digital computer. This is what we now call algorithms.

This book is another contribution to the world of algorithms. It’s not meant to replace the existing and remarkable works that I have enjoyed reading and teaching. Instead, it offers an alternative approach to learning algorithms by merging theoretical concepts with practical applications. It also represents the culmination of 30 years of experience in research, industry, and academia, particularly in computer science and artificial intelligence, as well as 12 years of continuous teaching of algorithms to students.

If it were possible, I would add my students as co-authors, because I have learned more from their challenging questions than I could ever teach them. Their inquiries have pushed me to uncover the deeper explanations and logic behind every aspect of algorithms. Yes, I do mean every aspect. Algorithms are about making human-made machines function correctly and deliver the results we expect. Here, nothing short of a logical process and behavior is acceptable.

This book does not claim to cover every aspect or topic in the vast field of algorithms. Instead, it narrows its focus to the design and analysis of algorithms, seeking to address the essential questions we must always consider when evaluating them. First and foremost, can we prove that the algorithm functions correctly and as intended? It’s crucial to establish that the algorithm reliably produces the expected results for all possible inputs.

Next, we must ask how we can ensure the algorithm consistently behaves as we anticipate. This involves scrutinizing its logic, understanding its steps, and confirming that each part contributes to the overall goal. Finally, we need to consider whether the algorithm terminates within an acceptable timeframe. No matter how elegantly an algorithm is designed, if it doesn’t complete its task efficiently, it becomes impractical for real-world use. By concentrating on these fundamental questions, this book aims to guide you through the process of designing robust, reliable, and efficient algorithms.