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Learning Functional Data Structures and Algorithms
Learning Functional Data Structures and Algorithms

Learning Functional Data Structures and Algorithms: Learn functional data structures and algorithms for your applications and bring their benefits to your work now

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Learning Functional Data Structures and Algorithms

Chapter 2.  Building Blocks

This chapter serves as a refresher on some fundamentals concepts.

How fast could an algorithm run? How does it fare when you have ten input elements versus a million? To answer such questions, we need to be aware of the notion of algorithmic complexity, which is expressed using the Big O notation. An O(1) algorithm is faster than O(logn), for example.

What is this notation? It talks about measuring the efficiency of an algorithm, which is proportional to the number of data items, N, being processed.

This chapter starts with a look at the O notation. Space/time trade-off is another important aspect of algorithm design. Let's look at a dynamic programming problem to better understand this fundamental notion.

Next, we will look at vectors and list data structures and note the trade-offs.

We will conclude by looking at the complexities of some functional idioms.

By the end of this chapter, you will have a good understanding of algorithmic complexities....

The Big O notation

In simple words, this notation is used to describe how fast an algorithm will run. It describes the growth of the algorithm's running time versus the size of input data.

Here is a simple example. Consider the following Scala snippet, reversing a linked list:

scala> def revList(list: List[Int]): List[Int] = list match { 
     |   case x :: xs => revList(xs) ++ List(x) 
     |   case Nil => Nil 
     | } 
revList: (list: List[Int])List[Int] 
scala> revList(List(1,2,3,4,5,6)) 
res0: List[Int] = List(6, 5, 4, 3, 2, 1) 

A quick question for you: how many times does the first case clause, namely case x :: xs => revList(xs) ++ List(x), match a list of six elements? Note that the clause matches when the list is non-empty. When it matches, we reduce the list by one element and recursively call the method.

It is easy to see the clause matches six times. As a result, the list method, ++, also gets invoked four times. The ++ method takes time and is directly proportional...

Space/time trade-off

A trade-off is a balancing act: when we take something, we give away another thing!

Algorithm designs too, at times, trade-off some amount of memory to save on the overall time. Let's look at two problems to better appreciate this important concept.

A word frequency counter

Let's say we have a list of words. The task is to find how many times a word occurs in the list in order to compute every word's frequency.

Here is a brute force approach:

    w <- each word in the list, count <- 1  
      w1 <- all other words in the list 
        If (w == w1)  
           Increment count  
                  println(w, " = ", count) 

The following diagram shows the comparisons for the first two elements:

A word frequency counter

The preceding diagram shows how the algorithm works for the first two words. Each word ends up being compared with other words. Note that even if we know the answer for the word "is," we end up recomputing it again.

The algorithm performs O...

Referential transparency

We appreciate the virtues of caching, but we do this to look at referential transparency, a cornerstone of functional programming.

In the preceding example, note that we are able to cache the results, as the results of the computation are not going to change for the same input. We need not repeat the computations; instead, we could compute the answer once and save and substitute it.

In the FP world, where we can substitute a function by its value, the function is called referentially transparent. Just like we avoid repeated calls in the previous algorithm, repeated calls to such functions could be avoided by caching the result.

Mathematical functions are referentially transparent. For example, the following Clojure functions are referentially transparent:

user=> (* 3 4) 
12 
user=> (apply + [1 2 3 4 5 6]) 
21 

You will always get 21 when you add up 1,2,3,4,5, and 6. Multiplying 3 and 4 will always give the result 12.

Note

Note that the preceding functions are pure...

Vectors versus lists

Prepending an element to a linked list is very fast. In fact, it is an O(1) operation, meaning the original list is simply pointed at by the new element node. The change happens only at the head of the list. As we don't need to traverse the list at all, this is a fixed cost, that is, O(1) operation.

Accessing an element at some index n is slower, meaning it is proportional to the number of elements in the list. We need to start at the head and keep traversing the nodes and keep counting. We do this until we reach the nth node. If we access the second last node, we will have traversed almost all of the list.

When any operation could make us look at almost all the elements, the complexity would be O(n). This means it would be proportional to the number of elements.

On the other hand, appending an element to a list is costly when we need to preserve the original list. In the next chapter, we need to traverse and copy all the elements, so we will preserve the current...

The Big O notation


In simple words, this notation is used to describe how fast an algorithm will run. It describes the growth of the algorithm's running time versus the size of input data.

Here is a simple example. Consider the following Scala snippet, reversing a linked list:

scala> def revList(list: List[Int]): List[Int] = list match { 
     |   case x :: xs => revList(xs) ++ List(x) 
     |   case Nil => Nil 
     | } 
revList: (list: List[Int])List[Int] 
scala> revList(List(1,2,3,4,5,6)) 
res0: List[Int] = List(6, 5, 4, 3, 2, 1) 

A quick question for you: how many times does the first case clause, namely case x :: xs => revList(xs) ++ List(x), match a list of six elements? Note that the clause matches when the list is non-empty. When it matches, we reduce the list by one element and recursively call the method.

It is easy to see the clause matches six times. As a result, the list method, ++, also gets invoked four times. The ++ method takes time and is directly proportional...

Space/time trade-off


A trade-off is a balancing act: when we take something, we give away another thing!

Algorithm designs too, at times, trade-off some amount of memory to save on the overall time. Let's look at two problems to better appreciate this important concept.

A word frequency counter

Let's say we have a list of words. The task is to find how many times a word occurs in the list in order to compute every word's frequency.

Here is a brute force approach:

    w <- each word in the list, count <- 1  
      w1 <- all other words in the list 
        If (w == w1)  
           Increment count  
                  println(w, " = ", count) 

The following diagram shows the comparisons for the first two elements:

The preceding diagram shows how the algorithm works for the first two words. Each word ends up being compared with other words. Note that even if we know the answer for the word "is," we end up recomputing it again.

The algorithm performs O(n2) comparison. Thus, the runtime complexity...

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Key benefits

  • Moving from object-oriented programming to functional programming? This book will help you get started with functional programming.
  • Easy-to-understand explanations of practical topics will help you get started with functional data structures.
  • Illustrative diagrams to explain the algorithms in detail.
  • Get hands-on practice of Scala to get the most out of functional programming.

Description

Functional data structures have the power to improve the codebase of an application and improve efficiency. With the advent of functional programming and with powerful functional languages such as Scala, Clojure and Elixir becoming part of important enterprise applications, functional data structures have gained an important place in the developer toolkit. Immutability is a cornerstone of functional programming. Immutable and persistent data structures are thread safe by definition and hence very appealing for writing robust concurrent programs. How do we express traditional algorithms in functional setting? Won’t we end up copying too much? Do we trade performance for versioned data structures? This book attempts to answer these questions by looking at functional implementations of traditional algorithms. It begins with a refresher and consolidation of what functional programming is all about. Next, you’ll get to know about Lists, the work horse data type for most functional languages. We show what structural sharing means and how it helps to make immutable data structures efficient and practical. Scala is the primary implementation languages for most of the examples. At times, we also present Clojure snippets to illustrate the underlying fundamental theme. While writing code, we use ADTs (abstract data types). Stacks, Queues, Trees and Graphs are all familiar ADTs. You will see how these ADTs are implemented in a functional setting. We look at implementation techniques like amortization and lazy evaluation to ensure efficiency. By the end of the book, you will be able to write efficient functional data structures and algorithms for your applications.

Who is this book for?

This book is for those who have some experience in functional programming languages. The data structures in this book are primarily written in Scala, however implementing the algorithms in other functional languages should be straight forward.

What you will learn

  • Learn to think in the functional paradigm
  • Understand common data structures and the associated algorithms, as well as the context in which they are commonly used
  • Take a look at the runtime and space complexities with the O notation
  • See how ADTs are implemented in a functional setting
  • Explore the basic theme of immutability and persistent data structures
  • Find out how the internal algorithms are redesigned to exploit structural sharing, so that the persistent data structures perform well, avoiding needless copying.
  • Get to know functional features like lazy evaluation and recursion used to implement efficient algorithms
  • Gain Scala best practices and idioms
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Length: 318 pages
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Language : English
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Length: 318 pages
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Language : English
ISBN-13 : 9781785888731
Category :
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Table of Contents

13 Chapters
1. Why Functional Programming? Chevron down icon Chevron up icon
2. Building Blocks Chevron down icon Chevron up icon
3. Lists Chevron down icon Chevron up icon
4. Binary Trees Chevron down icon Chevron up icon
5. More List Algorithms Chevron down icon Chevron up icon
6. Graph Algorithms Chevron down icon Chevron up icon
7. Random Access Lists Chevron down icon Chevron up icon
8. Queues Chevron down icon Chevron up icon
9. Streams, Laziness, and Algorithms Chevron down icon Chevron up icon
10. Being Lazy - Queues and Deques Chevron down icon Chevron up icon
11. Red-Black Trees Chevron down icon Chevron up icon
12. Binomial Heaps Chevron down icon Chevron up icon
13. Sorting Chevron down icon Chevron up icon

Customer reviews

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Bookreader Apr 02, 2018
Full star icon Full star icon Full star icon Full star icon Full star icon 5
This is not a perfect book, but it's really good for being a Packt book. It's a nicer read than all other functional programming books I have. I've never written this about a book before - but reading this one actually makes me happy. It's simply a fun read! Not full of jokes, but fun in the way that every page makes me really curious about what's in the next page. And every chapter makes me curious about what's in the next chapter. I usually only review bad books, to warn others, but I think this one deserves a good review because it stands out so strongly among the competition when it comes to Packt books. Another reviewer said that it's more like a Manning book, but I disagree. I like this one more than I like the Manning books I've read. There are a few errors in the book (not many) and at some points the explanations could be better / clearer. But if you stop and think a bit you will probably manage fine without a perfect explanation. Everything is in there to be able to figure the missing parts out yourself (contrary to the Functional Programming in Scala book from Manning, to take an example of a book with way too many missing explanations).
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This is by far the best Packt publishing book I've ever read. This is comparable to the quality of a Manning Press book. I highly recommend this book and it's especially useful if you are preparing for technical interviews.
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