6. See the Forest for the Trees | Learning F# Functional Data Structures and Algorithms

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Learning F# Functional Data Structures and Algorithms

By : Adnan Masood

4 (9)

Learning F# Functional Data Structures and Algorithms

4 (9)

By: Adnan Masood

Overview of this book

If you have just started your adventure with F#, then this book will help you take the right steps to become a successful F# coder. An intermediate knowledge of imperative programming concepts, and a basic understanding of the algorithms and data structures in .NET environments using the C# language and BCL (Base Class Library), would be helpful.

Preface

Preface

What this book covers

What you need for this book

Who this book is for

Conventions

Reader feedback

Customer support

Free Chapter

1. Embrace the Truth

1. Embrace the Truth

Exploring the functional programming paradigm

Thinking functional – why functional programming matters

A historical primer of F#

The Hello World example

A brief F# language primer

Syntactical similarities and differences

Benefits of using F# over C#

Summary

2. Now Lazily Get Over It, Again

2. Now Lazily Get Over It, Again

Setting up the IDE

Your first F# project

Talk is cheap, show me some code

To understand recursion, you must understand recursion

Memoization with Fibonacci

Towers of Hanoi

Sorting lazily

F# 4.0 – new features

Summary

3. What's in the Bag Anyway?

3. What's in the Bag Anyway?

Exploring data structures in F#

F# implementation of sorting algorithms

Algorithmic complexity and the Big-O notation

Summary

4. Are We There Yet?

4. Are We There Yet?

Diving deep into enumerations and sequences

Enumerating a CSV file

Query expressions

Creating sequences from collections

Usage considerations for sequences

Summary

5. Let's Stack Up

5. Let's Stack Up

Let's build a stack

Stack with concurrency support

Testing the stack

Algorithm – parenthesis matching using stacks

Summary

6. See the Forest for the Trees

6. See the Forest for the Trees

Tree as a data structure

The binary search tree

Navigating the tree

Abstract syntax trees

Summary

7. Jumping the Queue

7. Jumping the Queue

Let's make a functional queue

The FSharpx.Collections library

Summary

8. Quick Boost with Graph

8. Quick Boost with Graph

Graphs

Modeling graphs using F#

The shortest path algorithm

Finding the minimal path sum

Summary

9. Sets, Maps, and Vectors of Indirections

9. Sets, Maps, and Vectors of Indirections

Sets and maps

Vectors

F# and the Intermediate Language

Summary

10. Where to Go Next?

10. Where to Go Next?

References and further readings

F# language resources

Component design guidelines

Functional programming guides

Books and interactive tutorials

Video tutorials

Community projects – development tools

Community projects – functional programming

Community projects – data science programming

Community projects – the GPU execution

General functional programming

Academic resources

Summary

Index

Index

Navigating the tree

Consider the tree in the following figure. Our objective is to traverse the tree, that is, iterate through the nodes. There are several different approaches to do so but some of the most common ones are in-order, post-order, and pre-order traversal:

In the in-order traversal, we start from the root node and traverse to left subtree, and then we visit the root node and then traverse to right subtree as seen in the following. The nodes are traversed in this order: A, B, C, D, …, H, I:

An in-order traversal algorithm can be implemented in F# as the following recursive function. In this function, we utilize the power of sequences, and the match expressions to implement the in-order traversal algorithm:

type Tree<'a> =
  | Tree of 'a * Tree<'a> * Tree<'a>
  | Leaf of 'a

let rec inorder tree =
  seq {
    match tree with
      | Tree(x, left, right) ->
      yield! inorder left
      yield x
      yield! inorder right
   | Leaf x -> yield x
  }

As you have...

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