Ebook: Algorithms and data structures: the basic toolbox

Algorithms are at the heart of every nontrivial computer application, and algorithmics is a modern and active area of computer science. Every computer scientist and every professional programmer should know about the basic algorithmic toolbox: structures that allow efficient organization and retrieval of data, frequently used algorithms, and basic techniques for modeling, understanding and solving algorithmic problems.

This book is a concise introduction addressed to students and professionals familiar with programming and basic mathematical language. Individual chapters cover arrays and linked lists, hash tables and associative arrays, sorting and selection, priority queues, sorted sequences, graph representation, graph traversal, shortest paths, minimum spanning trees, and optimization. The algorithms are presented in a modern way, with explicitly formulated invariants, and comment on recent trends such as algorithm engineering, memory hierarchies, algorithm libraries and certifying algorithms. The authors use pictures, words and high-level pseudocode to explain the algorithms, and then they present more detail on efficient implementations using real programming languages like C++ and Java.

The authors have extensive experience teaching these subjects to undergraduates and graduates, and they offer a clear presentation, with examples, pictures, informal explanations, exercises, and some linkage to the real world. Most chapters have the same basic structure: a motivation for the problem, comments on the most important applications, and then simple solutions presented as informally as possible and as formally as necessary. For the more advanced issues, this approach leads to a more mathematical treatment, including some theorems and proofs. Finally, each chapter concludes with a section on further findings, providing views on the state of research, generalizations and advanced solutions.

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This book is a concise introduction to this basic toolbox, intended for studentsand professionals familiar with programming and basic mathematical language. Wehave used the book in undergraduate courses on algorithmics. In our graduate-levelcourses, we make most of the book a prerequisite, and concentrate on the starredsections and the more advanced material. We believe that, even for undergraduates,a concise yet clear and simple presentation makes material more accessible, as longas it includes examples, pictures, informal explanations, exercises, and some linkageto the real world.Most chapters have the same basic structure. We begin by discussing a problemas it occurs in a real-life situation. We illustrate the most important applications andthen introduce simple solutions as informally as possible and as formally as necessaryto really understand the issues at hand. When we move to more advanced andoptional issues, this approach gradually leads to a more mathematical treatment, includingtheorems and proofs. This way, the book should work for readers with a widerange of mathematical expertise. There are also advanced sections (marked with a *)where we recommend that readers should skip them on first reading. Exercises provideadditional examples, alternative approaches and opportunities to think about theproblems. It is highly recommended to take a look at the exercises even if there isno time to solve them during the first reading. In order to be able to concentrate onideas rather than programming details, we use pictures, words, and high-level pseudocodeto explain our algorithms. A section “implementation notes” links these abstractideas to clean, efficient implementations in real programming languages suchas C++ and Java. Each chapter ends with a section on further findings that providesa glimpse at the state of the art, generalizations, and advanced solutions.