Pearls of Functional Algorithm Design

by Richard Bird

Overview

Richard Bird takes a radically new approach to algorithm design, namely, design by calculation. These 30 short chapters each deal with a particular programming problem drawn from sources as diverse as games and puzzles, intriguing combinatorial tasks, and more familiar areas such as data compression and string matching. Each pearl starts with the statement of the problem expressed using the functional programming language Haskell, a powerful yet succinct language for capturing algorithmic ideas clearly and simply. The novel aspect of the book is that each solution is calculated from an initial formulation of the problem in Haskell by appealing to the laws of functional programming. Pearls of Functional Algorithm Design will appeal to the aspiring functional programmer, students and teachers interested in the principles of algorithm design, and anyone seeking to master the techniques of reasoning about programs in an equational style.

Product Details

ISBN-13:	9780521513388
Publisher:	Cambridge University Press
Publication date:	09/16/2010
Pages:	290
Product dimensions:	6.70(w) x 9.90(h) x 0.80(d)

About the Author

Richard Bird is Professor of Computer Science at Oxford University Computing Laboratory.

Table of Contents

Preface ix

1 The smallest free number 1

2 A surpassing problem 7

3 Improving on saddleback search 12

4 A selection problem 21

5 Sorting pairwise sums 27

6 Making a century 33

7 Building a tree with minimum height 41

8 Unravelling greedy algorithms 50

9 Finding celebrities 56

10 Removing duplicates 64

11 Not the maximum segment sum 73

12 Ranking suffixes 79

13 The Burrows-Wheeler transform 91

14 The last tail 102

15 All the common prefixes 112

16 The Boyer-Moore algorithm 117

17 The Knuth-Morris-Pratt algorithm 127

18 Planning solves the Rush Hour problem 136

19 A simple Sudoku solver 147

20 The Countdown problem 156

21 Hylomorphisms and nexuses 168

22 Three ways of computing determinants 180

23 Inside the convex hull 188

24 Rational arithmetic coding 198

25 Integer arithmetic coding 208

26 The Schorr-Waite algorithm 221

27 Orderly insertion 231

28 Loopless functional algorithms 242

29 The Johnson-Trotter algorithm 251

30 Spider spinning for dummies 258

Index 275

Editorial Reviews

"Though the writing is crisp, and the explanations lucid, this is not an easy book to read. The difficulty lies in the density of ideas presented. The rewards of persevering are definitely worth it, though. In fact, once immersed, I started to ponder where this material would lead to: which algorithms could be even further generalized, what would many of these algorithms look like if implemented in Coq or Agda, and so forth. This is the effect that all good books have on me: well-presented and well-motivated material strives to become a stepping stone to further discovery. Any serious computer scientist would benefit from reading and properly understanding this book.
Jacques Carette, Computing Reviews

From the Publisher