Book Image

R Data Structures and Algorithms

By : PKS Prakash, Achyutuni Sri Krishna Rao
Book Image

R Data Structures and Algorithms

By: PKS Prakash, Achyutuni Sri Krishna Rao

Overview of this book

In this book, we cover not only classical data structures, but also functional data structures. We begin by answering the fundamental question: why data structures? We then move on to cover the relationship between data structures and algorithms, followed by an analysis and evaluation of algorithms. We introduce the fundamentals of data structures, such as lists, stacks, queues, and dictionaries, using real-world examples. We also cover topics such as indexing, sorting, and searching in depth. Later on, you will be exposed to advanced topics such as graph data structures, dynamic programming, and randomized algorithms. You will come to appreciate the intricacies of high performance and scalable programming using R. We also cover special R data structures such as vectors, data frames, and atomic vectors. With this easy-to-read book, you will be able to understand the power of linked lists, double linked lists, and circular linked lists. We will also explore the application of binary search and will go in depth into sorting algorithms such as bubble sort, selection sort, insertion sort, and merge sort.
Table of Contents (17 chapters)
R Data Structures and Algorithms
Credits
About the Authors
Acknowledgments
About the Reviewer
www.PacktPub.com
Preface

Lower bounds for sorting


So far, we have covered performance assessment of algorithms based on their time complexity (number of operations). Empirical analysis shows the performance based on actual system runtime, while asymptotic analysis evaluates the performance based on the number of operations (or comparisons). However, for non-comparison-based sorts, such as bin sort and radix sort, the asymptotic complexity is evaluated using the number of iterations based on the value of specific digits as against the whole element itself. Table 5.3 summarizes the asymptotes of sorting algorithms based on the best, average, and worst-case scenarios depending on their type of sort:

Table 5.3: Asymptotic complexities of various sorting algorithms

Now, let's analyze the complexity induced by the problem (of sorting) itself. The upper bound of the sorting problem is the asymptotic complexity of the fastest known algorithm, whereas the lower bound is the best possible efficiency that can be achieved using...