R Data Structures and Algorithms

Table of Contents

R Data Structures and Algorithms

Credits

About the Authors

Acknowledgments

About the Reviewer

www.PacktPub.com

Why subscribe?

Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Reader feedback

Customer support

Downloading the example code

Downloading the color images of this book

Errata

Piracy

Questions

1. Getting Started

Introduction to data structure

Abstract data type and data structure

Relationship between problem and algorithm

Basics of R

Installation of R

Basic data types in R

Operations in R

Control structures in R

If condition

If...else condition

Ifelse function

For() loop

Nested for( ) loop

While loop

Special statements in loops

Break statement

Next statement

Repeat loop

First class functions in R

Exercises

Summary

2. Algorithm Analysis

Getting started with data structure

Memory management in R

System runtime in R

Best, worst, and average cases

Computer versus algorithm

Algorithm asymptotic analysis

Upper bounds or Big O notation

Lower bounds or Big Omega notation (Ω)

Big θ notation

Simplifying rules

Classifying rules

Computation evaluation of a program

Component 1 - Assignment operator

Component 2 - Simple loop

Component 3 - Complex loop

Component 4 - Loops with conditional statements

Component 5 - Recursive statements

Analyzing problems

Space bounds

Exercises

Summary

3. Linked Lists

Data types in R

Vector and atomic vector

Element data types

Factor

Matrix

Array

Dataframes

List

Object-oriented programming using R

Linked list

Linear linked list

Doubly linked list

Circular linked list

Array-based list

Analysis of list operations

Exercises

Summary

4. Stacks and Queues

Stacks

Array-based stacks

Linked stacks

Comparison of array-based and linked stacks

Implementing recursion

Queues

Array-based queues

Linked queues

Comparison of array-based and linked queues

Dictionaries

Exercises

Summary

5. Sorting Algorithms

Sorting terminology and notation

Three Θ(n²) sorting algorithms

Insertion sort

Bubble sort

Selection sort

The cost of exchange sorting

Shell sort

Merge sort

Quick sort

Heap sort

Bin sort and radix sort

An empirical comparison of sorting algorithms

Lower bounds for sorting

Exercises

Summary

6. Exploring Search Options

Searching unsorted and sorted vectors

Self-organizing lists

Heuristic 1 - Count

Heuristic 2 - Move-to-front

Heuristic 3 - Transpose

Hashing

Hash functions

Open hashing

Closed hashing

Bucket hashing

Linear probing

Analysis of closed hashing

Deletion

Exercises

Summary

7. Indexing

Linear indexing

ISAM

Tree-based indexing

2-3 trees

B-trees

B+ trees

B-tree analysis

Exercises

Summary

8. Graphs

Terminology and representations

Graph implementations

Graph traversals

Depth-first search

Breadth-first search

Topological sort

Shortest path problems

Single-source shortest paths

Minimum-cost spanning tree

Prim's algorithm

Kruskal's algorithm

Exercises

Summary

9. Programming and Randomized Algorithms

Dynamic programming

The knapsack problem

All pairs shortest paths

Randomized algorithms

Randomized algorithms for finding large values

Skip lists

Probabilistic analysis of skip lists

Exercises

Summary

10. Functional Data Structures

Functional data structure

Lazy evaluation

Functional stacks

Functional queues

Fast fully-persistent queues

Slowly-persistent queues and deques

Summary

R Data Structures and Algorithms

R Data Structures and Algorithms

Copyright © 2016 Packt Publishing

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Credits

About the Authors

Dr. PKS Prakash has pursued his PhD in industrial and system engineering at Wisconsin-Madison, US. He defended his second PhD in engineering from University of Warwick, UK. He has provided data science support to numerous leading companies in healthcare, manufacturing, pharmaceutical, and e-commerce domains on a wide range of business problems related to predictive and prescriptive modeling, virtual metrology, predictive maintenance, root cause analysis, process simulations, fraud detection, early warning systems, and so on. Currently, he is working as the Vice President and Practice Lead for data science at Dream11. Dream11 offers the world's largest fantasy cricket, football, and kabaddi games of skill. He has published widely in research areas of operational research and management, soft computing tools, and advanced algorithms in the manufacturing and healthcare domains in leading journals such as IEEE-Trans, EJOR, and IJPR, among others. He has contributed a chapter in Evolutionary Computing in Advanced Manufacturing and edited an issue of Intelligent Approaches to Complex Systems.

Achyutuni Sri Krishna Rao has an MS in enterprise business analytics (data science) from National University of Singapore. He has worked on a wide range of data science problems in the domain of manufacturing, healthcare and pharmaceuticals. He is an R enthusiast and loves to contribute to the open source community. His passions include freelancing, technical blogs (http://rcodeeasy.blogspot.com) and marathon runs. Currently he works as a data science consultant at a leading consulting firm.

Acknowledgments

The completion of this book wouldn't have been possible without the participation and assistance of so many people whose names may not all be enumerated. Their contribution is sincerely appreciated and gratefully acknowledged. However, we would like to express our deep appreciation and indebtedness to all the members of the Packt team involved in this project. The book arose with an idea with an early discussion with Denim Pinto (acquisition editor), so we want to extend special thanks to him; without his input, this book would never have happened. We also want to thank Pooja Mhapsekar and Siddhi Chavan (content editor) and Sunith Shetty (technical editor) for ensuring the timely publication of this book. We would like to extend thanks to Vahid Mirjalili (reviewer), whose feedback has helped us tremendously improve this book.

About the Reviewer

Dr. Vahid Mirjalili is a software engineer/data scientist, currently working toward his PhD in computer science at Michigan State University. His research at the Integrated Pattern Recognition and Biometrics (i-PRoBE) lab involves attribute classification of face images from large image datasets.  Furthermore, he teaches Python programming, as well as computing concepts for data analysis and databases. With his specialty in data mining, he is very interested in predictive modeling and getting insights from data. He is also a Python developer and likes to contribute to the open source community. Furthermore, he enjoys making tutorials for different areas of data science and computer algorithms, which can be found in his GitHub repository (http://github.com/mirjalil/DataScience).

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Preface

Data structures represent a way to organize and access particular data efficiently. They are critical to any problem solving and provide a complete solution to implement reusable codes. R Data Structures and Algorithms aims at strengthening the data structure skills among R users working in the analytics and intelligence domains. R is a well-designed language and environment for statistical computing and graphics developed at Bell Laboratories (formerly AT&T, now Lucent Technologies). This book will allow users to design optimized algorithms from the computational efficiency and resource usage perspective of an algorithm. This book puts forward the processes of building algorithms by introducing several data structures and their relationship with algorithms, followed by their analysis and evaluation. This book intends to cover not only the classical data structures, but also understand the integrities of functional data structures. We will cover the fundamentals of data structures, such as lists, stacks, queues, and dictionaries, followed by topics such as indexing, sorting, and searching in depth. Readers will also be exposed to advanced topics such as graphs, dynamic programming, and randomized algorithms.

The objective of this book is to build data structure concepts using R.

What this book covers

Chapter 1, Getting Started, builds a background for the aspects of data structures that are important to develop basics of R, as well as why they are important.

Chapter 2, Algorithm Analysis, talks about motivation, basic notation, and fundamental techniques for algorithm analysis.

Chapter 3, Linked Lists, builds a foundation of linked lists and will cover multiple variants of linked lists, such as linear linked lists, doubly linked lists, and circular linked lists.

Chapter 4, Stacks and Queues, introduces you to array-based and linked list-based stacks and queues and their implementation in R.

Chapter 5, Sorting Algorithms, explains various sorting algorithms, such as insertion sort, bubble sort, selection sort, and shell sort, and provides an empirical comparison between different algorithms.

Chapter 6, Exploring Search Options, provides details about search operations carried out on both vectors and lists, including linked lists. It also introduces you to self-organizing lists and hashing concepts.

Chapter 7, Indexing, covers indexing concepts, which are essential in file structuring, and organize large amounts of data on disk. It will also cover ISAM, 2-3 trees, B-tree, and B+ tree in detail.

Chapter 8, Graphs, builds a foundation for the graph data structure and its implementation. It also covers various algorithms for traversals, shortest-paths problems, and minimum-cost spanning trees in detail.

Chapter 9, Programming and Randomized Algorithms, extends the concept of a static data structure to randomize data structure, such as randomized skip lists. The chapter will also introduce programming concepts and several applications of it.

Chapter 10, Functional Data Structures, introduces you to functional data structures and lazy evaluation. It will also cover functional stacks and queues in R.

What you need for this book

You will need inquisitiveness, perseverance, and a passion for algorithm design and data science. The scope and application of data structures is quite broad and wide.

You will need a good understanding of R or another programming language. Preliminary experience of programming and data analysis will be helpful as well. You will need to appreciate algorithms that can be applied in scale to build applications.

Who this book is for

This book is for R developers who want to use data structures efficiently. Basic knowledge of R is expected.

Conventions

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pip3 install -upgrade pip

pip3 install jupyter

New terms and important words are shown in bold. Words that you see on the screen, for example, in menus or dialog boxes, appear in the text like this: To start a new R Notebook, click on right hand side New tab and select R kernel as shown in Figure 1.7.

Note

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Tip

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Chapter 1. Getting Started

Faster and efficient information retrieval is the primary objective of most computer programs. Data structures and algorithms help us in achieving the objective by processing and retrieving data faster. Information retrieval can easily be integrated with algorithms to answer inferential questions from data such as:

How are sales increasing over time?

What is customer's arrival distribution over time?

Out of all the customers who visit between 3:00 and 6:00 PM, how many order Asian versus Chinese?

Of all the customers visiting, how many are from the same city?

In the efficient processing of the preceding queries, especially in big data scenarios, data structures and algorithms utilized for data retrieval play a significant role. This book will introduce primary data structures such as lists, queues, and stacks, which are used for information retrieval and trade-off of different data structures. We will also introduce the data structure and algorithms evaluation approach for retrieval and processing of defined data structures.

Algorithms are evaluated based on complexity and efficiency, where complexity refers to an algorithm design which is easy to program and debug, and efficacy ensures that the algorithm is utilizing computer resources optimally. This book will focus on the efficiency part of algorithms using data structures, and the current chapter introduces the importance of data structure and the algorithms used for retrieval of data from data structures.

Introduction to data structure

Moore's law in 1965 observed that the number of transistors per square inch in a dense integrated circuit (IC) had doubled every year since its invention, thus enhancing computational power per computer. He revised his forecast in 1975, stating that the number of transistors would double every 2 years, instead of every year, due to saturation:

Figure 1.1: Moore's law (Ref: data credit - Transistor count, Wikipedia)

Also, although the computational power has been increasing, problem complexity and data sources have also been increasing exponentially over the decade, enforcing the need for efficient algorithms:

Figure 1.2: Increase in size of unstructured data (Ref: Enterprise strategy group 2010)

This explosion in data from 2008 to 2015 has led to a new field of data science where people put in a lot of effort to derive insights using all kinds of datasets such as structured, semi-structured, and unstructured. Thus, to efficiently deal with data scalability, it is important to efficiently store and retrieve datasets. For example, searching for a word in a dictionary would take a long time if the data is randomly organized; thus, sorted list data structures are utilized to ensure a faster search of words. Similarly, searching for an optimal path in a city based on the input location requires data about road network, position, and so on to be stored in the form of geometries. Ideally, even a variable stored as any built-in data type such as character, integer, or float can be considered as a data structure of scalar nature. However, data structure is formally defined as a scheme of organizing related information in a computer so that it can be used efficiently.

Similarly, for algorithms, given sufficient space and time, any dataset can be stored and processed to