Java 9 Data Structures and Algorithms

Table of Contents

Java 9 Data Structures and Algorithms

Credits

About the Author

About the Reviewer

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Why subscribe?

Customer Feedback

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. Why Bother? – Basic

The performance of an algorithm

Best case, worst case and the average case complexity

Analysis of asymptotic complexity

Asymptotic upper bound of a function

Asymptotic upper bound of an algorithm

Asymptotic lower bound of a function

Asymptotic tight bound of a function

Optimization of our algorithm

Fixing the problem with large powers

Improving time complexity

Summary

2. Cogs and Pulleys – Building Blocks

Arrays

Insertion of elements in an array

Insertion of a new element and the process of appending it

Linked list

Appending at the end

Insertion at the beginning

Insertion at an arbitrary position

Looking up an arbitrary element

Removing an arbitrary element

Iteration

Doubly linked list

Insertion at the beginning or at the end

Insertion at an arbitrary location

Removing the first element

Removing an arbitrary element

Removal of the last element

Circular linked list

Insertion

Removal

Rotation

Summary

3. Protocols – Abstract Data Types

Stack

Fixed-sized stack using an array

Variable-sized stack using a linked list

Queue

Fixed-sized queue using an array

Variable-sized queue using a linked list

Double ended queue

Fixed-length double ended queue using an array

Variable-sized double ended queue using a linked list

Summary

4. Detour – Functional Programming

Recursive algorithms

Lambda expressions in Java

Functional interface

Implementing a functional interface with lambda

Functional data structures and monads

Functional linked lists

The forEach method for a linked list

Map for a linked list

Fold operation on a list

Filter operation for a linked list

Append on a linked list

The flatMap method on a linked list

The concept of a monad

Option monad

Try monad

Analysis of the complexity of a recursive algorithm

Performance of functional programming

Summary

5. Efficient Searching – Binary Search and Sorting

Search algorithms

Binary search

Complexity of the binary search algorithm

Sorting

Selection sort

Complexity of the selection sort algorithm

Insertion sort

Complexity of insertion sort

Bubble sort

Inversions

Complexity of the bubble sort algorithm

A problem with recursive calls

Tail recursive functions

Non-tail single recursive functions

Summary

6. Efficient Sorting – quicksort and mergesort

quicksort

Complexity of quicksort

Random pivot selection in quicksort

mergesort

The complexity of mergesort

Avoiding the copying of tempArray

Complexity of any comparison-based sorting

The stability of a sorting algorithm

Summary

7. Concepts of Tree

A tree data structure

The traversal of a tree

The depth-first traversal

The breadth-first traversal

The tree abstract data type

Binary tree

Types of depth-first traversals

Non-recursive depth-first search

Summary

8. More About Search – Search Trees and Hash Tables

Binary search tree

Insertion in a binary search tree

Invariant of a binary search tree

Deletion of an element from a binary search tree

Complexity of the binary search tree operations

Self-balancing binary search tree

AVL tree

Complexity of search, insert, and delete in an AVL tree

Red-black tree

Insertion

Deletion

The worst case of a red-black tree

Hash tables

Insertion

The complexity of insertion

Search

Complexity of the search

Choice of load factor

Summary

9. Advanced General Purpose Data Structures

Priority queue ADT

Heap

Insertion

Removal of minimum elements

Analysis of complexity

Serialized representation

Array-backed heap

Linked heap

Insertion

Removal of the minimal elements

Complexity of operations in ArrayHeap and LinkedHeap

Binomial forest

Why call it a binomial tree?

Number of nodes

The heap property

Binomial forest

Complexity of operations in a binomial forest

Sorting using a priority queue

In-place heap sort

Summary

10. Concepts of Graph

What is a graph?

The graph ADT

Representation of a graph in memory

Adjacency matrix

Complexity of operations in a sparse adjacency matrix graph

More space-efficient adjacency-matrix-based graph

Complexity of operations in a dense adjacency-matrix-based graph

Adjacency list

Complexity of operations in an adjacency-list-based graph

Adjacency-list-based graph with dense storage for vertices

Complexity of the operations of an adjacency-list-based graph with dense storage for vertices

Traversal of a graph

Complexity of traversals

Cycle detection

Complexity of the cycle detection algorithm

Spanning tree and minimum spanning tree

For any tree with vertices V and edges E, |V| = |E| + 1

Any connected undirected graph has a spanning tree

Any undirected connected graph with the property |V| = |E| + 1 is a tree

Cut property

Minimum spanning tree is unique for a graph that has all the edges whose costs are different from one another

Finding the minimum spanning tree

Union find

Complexity of operations in UnionFind

Implementation of the minimum spanning tree algorithm

Complexity of the minimum spanning tree algorithm

Summary

11. Reactive Programming

What is reactive programming?

Producer-consumer model

Semaphore

Compare and set

Volatile field

Thread-safe blocking queue

Producer-consumer implementation

Spinlock and busy wait

Functional way of reactive programming

Summary

Index

Java 9 Data Structures and Algorithms

Java 9 Data Structures and Algorithms

Copyright © 2017 Packt Publishing

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First published: April 2017

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Credits

Author

Debasish Ray Chawdhuri

Reviewer

Miroslav Wengner

Commissioning Editor

Kunal Parikh

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About the Author

Debasish Ray Chawdhuri is an established Java developer and has been in the industry for the last 8 years. He has developed several systems, right from CRUD applications to programming languages and big data processing systems. He had provided the first implementation of extensible business reporting language specification, and a product around it, for the verification of company financial data for the Government of India while he was employed at Tata Consultancy Services Ltd. In Talentica Software Pvt. Ltd., he implemented a domain-specific programming language to easily implement complex data aggregation computation that would compile to Java bytecode. Currently, he is leading a team developing a new high-performance structured data storage framework to be processed by Spark. The framework is named Hungry Hippos and will be open sourced very soon. He also blogs at http://www.geekyarticles.com/ about Java and other computer science-related topics.

He has worked for Tata Consultancy Services Ltd., Oracle India Pvt. Ltd., and Talentica Software Pvt. Ltd.

I would like to thank my dear wife, Anasua, for her continued support and encouragement, and for putting up with all my eccentricities while I spent all my time writing this book. I would also like to thank the publishing team for suggesting the idea of this book to me and providing all the necessary support for me to finish it.

About the Reviewer

Miroslav Wengner has been a passionate JVM enthusiast ever since he joined SUN Microsystems in 2002. He truly believes in distributed system design, concurrency, and parallel computing. One of Miro's biggest hobby is the development of autonomic systems. He is one of the coauthors of and main contributors to the open source Java IoT/Robotics framework Robo4J.

Miro is currently working on the online energy trading platform for enmacc.de as a senior software developer.

I would like to thank my family and my wife, Tanja, for big support during reviewing this book.

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Preface

Java has been one of the most popular programming languages for enterprise systems for decades now. One of the reasons for the popularity of Java is its platform independence, which lets one write and compile code on any system and run it on any other system, irrespective of the hardware and the operating system. Another reason for Java's popularity is that the language is standardized by a community of industry players. The latter enables Java to stay updated with the most recent programming ideas without being overloaded with too many useless features.

Given the popularity of Java, there are plenty of developers actively involved in Java development. When it comes to learning algorithms, it is best to use the language that one is most comfortable with. This means that it makes a lot of sense to write an algorithm book, with the implementations written in Java. This book covers the most commonly used data structures and algorithms. It is meant for people who already know Java but are not familiar with algorithms. The book should serve as the first stepping stone towards learning the subject.

What this book covers

Chapter 1, Why Bother? – Basic, introduces the point of studying algorithms and data structures with examples. In doing so, it introduces you to the concept of asymptotic complexity, big O notation, and other notations.

Chapter 2, Cogs and Pulleys – Building Blocks, introduces you to array and the different kinds of linked lists, and their advantages and disadvantages. These data structures will be used in later chapters for implementing abstract data structures.

Chapter 3, Protocols – Abstract Data Types, introduces you to the concept of abstract data types and introduces stacks, queues, and double-ended queues. It also covers different implementations using the data structures described in the previous chapter.

Chapter 4, Detour – Functional Programming, introduces you to the functional programming ideas appropriate for a Java programmer. The chapter also introduces the lambda feature of Java, available from Java 8, and helps readers get used to the functional way of implementing algorithms. This chapter also introduces you to the concept of monads.

Chapter 5, Efficient Searching – Binary Search and Sorting, introduces efficient searching using binary searches on a sorted list. It then goes on to describe basic algorithms used to obtain a sorted array so that binary searching can be done.

Chapter 6, Efficient Sorting – Quicksort and Mergesort, introduces the two most popular and efficient sorting algorithms. The chapter also provides an analysis of why this is as optimal as a comparison-based sorting algorithm can ever be.

Chapter 7, Concepts of Tree, introduces the concept of a tree. It especially introduces binary trees, and also covers different traversals of the tree: breadth-first and depth-first, and pre-order, post-order, and in-order traversal of binary tree.

Chapter 8, More About Search – Search Trees and Hash Tables, covers search using balanced binary search trees, namely AVL, and red-black trees and hash-tables.

Chapter 9, Advanced General Purpose Data Structures, introduces priority queues and their implementation with a heap and a binomial forest. At the end, the chapter introduces sorting with a priority queue.

Chapter 10, Concepts of Graph, introduces the concepts of directed and undirected graphs. Then, it discusses the representation of a graph in memory. Depth-first and breadth-first traversals are covered, the concept of a minimum-spanning tree is introduced, and cycle detection is discussed.

Chapter 11, Reactive Programming, introduces the reader to the concept of reactive programming in Java. This includes the implementation of an observable pattern-based reactive programming framework and a functional API on top of it. Examples are shown to demonstrate the performance gain and ease of use of the reactive framework, compared with a traditional imperative style.

What you need for this book

To run the examples in this book, you need a computer with any modern popular operating system, such as some version of Windows, Linux, or Macintosh. You need to install Java 9 in your computer so that javac can be invoked from the command prompt.

Who this book is for

This book is for Java developers who want to learn about data structures and algorithms. A basic knowledge of Java is assumed.

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Chapter 1. Why Bother? – Basic

Since you already know Java, you have of course written a few programs, which means you have written algorithms. Well then, what is it? you might ask. An algorithm is a list of well-defined steps that can be followed by a processor mechanically, or without involving any sort of intelligence, which would produce a desired output in a finite amount of time. Well, that's a long sentence. In simpler words, an algorithm is just an unambiguous list of steps to get something done. It kind of sounds like we are talking about a program. Isn't a program also a list of instructions that we give the computer to follow, in order to get a desired result? Yes it is, and that means an algorithm is really just a program. Well not really, but almost. An algorithm is a program without the details of the particular programming language that we are coding it in. It is the basic idea of the program; think of it as an abstraction of a program where you don't need to bother about the program's syntactic details.

Well, since we already know about programming, and an algorithm is just a program, we are done with it, right? Not really. There is a lot to learn about programs and algorithms, that is, how to write an algorithm to achieve a particular goal. There are, of course, in general, many ways to solve a particular problem and not all ways may be equal. One way may be faster than another, and that is a very important thing about algorithms. When we study algorithms, the time it takes to execute is of utmost importance. In fact, it is the second most important thing about them, the first one being their correctness.

In this chapter, we will take a deeper look into the following ideas:

Measuring the performance of an algorithm

Asymptotic complexity

Why asymptotic complexity matters

Why an explicit study of algorithms is important

The performance of an algorithm

No one wants to wait forever to get something done. Making a program run faster surely is important, but how do we know whether a program runs fast? The first logical step would be to measure how many seconds the program takes to run. Suppose we have a program that, given three numbers, a, b, and c, determines the remainder when a raised to the power b is divided by c.

For example, say a=2, b=10, and c = 7, a raised to the power b = 2¹⁰ = 1024, 1024 % 7 = 2. So, given these values, the program needs to output 2. The following code snippet shows a simple and obvious way of achieving this:

public static long computeRemainder(long base, long power, long divisor){

  long baseRaisedToPower = 1;

  for(long i=1;i<=power;i++){

    baseRaisedToPower *= base;

  }

  return baseRaisedToPower % divisor;

}

We can now estimate the time it takes by running the program a billion times and checking how long it took to run it, as shown in the following code:

public static void main(String [] args){

  long startTime = System.currentTimeMillis();

  for(int i=0;i<1_000_000_000;i++){

    computeRemainder(2, 10, 7);

  }

  long endTime = System.currentTimeMillis();

  System.out.println(endTime - startTime);

}

On my computer, it takes 4,393 milliseconds. So the time taken per call is 4,393 divided by a billion, that is, about 4.4 nanoseconds. Looks like a very reasonable time to do any computation. But what happens if the input is different? What if I pass power = 1000? Let's check that out. Now it takes about 420,000 milliseconds to run a billion times, or about 420 nanoseconds per run. Clearly, the time taken to do this computation depends on the input, and that means any reasonable way to talk about the performance of a program needs to take into account the input to the program.

Okay, so we can say that the number of nanoseconds our program takes to run is 0.42 X power, approximately.

If you run the program with the input (2, 1000, and 7), you will get an output of 0, which is not correct. The correct output is 2. So, what is going on here? The answer is that the maximum value that a long type variable can hold is one less than 2 raised to the power 63, or 9223372036854775807L. The value 2 raised to the power 1,000 is, of course, much more than this, causing the value to overflow, which brings us to our next point: how much space does a program need in order to run?

In general, the memory space required to run a program can be measured in terms of the bytes required for the program to operate. Of course, it requires the space to at least store the input and the output. It may as well need some additional space to run, which is called auxiliary space. It is quite obvious that just like time, the space required to run a program would, in general, also be dependent on the input.

In the case of time, apart from the fact that the time depends on the input, it also depends on which computer you are running it on. The program that takes 4 seconds to run on my computer may take 40 seconds on a very old computer from the nineties and may run in 2 seconds in yours. However, the actual computer you run it on only improves the time by a constant multiplier. To avoid getting into too much detail about specifying the details of the hardware the program is running on, instead of saying the program takes 0.42 X power milliseconds approximately, we can say the time taken is a constant times the power, or simply say it is proportional to the power.

Saying the computation time is proportional to the power actually makes it so non-specific to hardware, or even the language the program is written in, that we can estimate this relationship by just looking at the program and analyzing it. Of course, the running time is sort of proportional to the power because there is a loop that executes power number of times, except, of course, when the power is so small that the other one-time operations outside the loop actually start to matter.

Best case, worst case and the average case complexity

In general, the time or space required for an algorithm to process a certain input depends not only on the size of the input, but also on the actual value of the input. For example, a certain algorithm to arrange a list of values in increasing order may take much less time if the input is already sorted than when it is an arbitrary unordered list. This is why, in general, we must have a different function representing the time or space required in the different cases of input. However, the best case scenario would be where the resources required for a certain size of an input take the least amount of resources. The would also be a worst case scenario, in which the algorithm needs the maximum amount of resources for a certain size of input. An average case is an estimation of the resources taken for a given size of inputs averaged over all values of the input with that size weighted by their probability of occurrence.

Analysis of asymptotic complexity

We seem to have hit upon an idea, an abstract sense of the running time. Let's spell it out. In an abstract way, we analyze the running time of and the space required by a program by using what is known as the asymptotic complexity.

We are only interested in what happens when the input is very large because it really does not matter how long it takes for a small input to be processed; it's going to be small anyway. So, if we have x³ + x², and if x is very large, it's almost the same as x3. We also don't want to consider constant factors of a function, as we have pointed out earlier, because it is dependent on the particular hardware we are running the program on and the particular language we have implemented it in. An algorithm implemented in Java will perform a constant times slower than the same algorithm written in C. The formal way of tackling these abstractions in defining the complexity of an algorithm is called an asymptotic bound. Strictly speaking, an asymptotic bound is for a function and not for an algorithm. The idea is to first express the time or space required for a given algorithm to process an input as a function of the size of the input in bits and then looking for an asymptotic bound of that function.

We will consider three types of asymptotic bounds—an upper bound, a lower bound and a tight bound. We will discuss these in the following sections.

Asymptotic upper bound of a function

An upper bound, as the name suggests, puts an upper limit of a function's growth. The upper bound is another function that grows at least as fast as the original function. What is the point of talking about one function in place of another? The function we use is in general a lot more simplified than the actual function for computing running time or space required to process a certain size of input. It is a lot easier to compare simplified functions than to compare complicated functions.

For a function f, we define the notation O, called big O, in the following ways:

f(x) = O(f(x)).

For example, x³ = O(x³).

If f(x) = O(g(x)), then k f(x) = O(g(x)) for any non-zero constant k.

For example, 5x³ = O(x³) and 2 log x = O(log x) and -x³ = O(x³)