# Pearls of Functional Algorithm Design

Cambridge University Press, Sep 16, 2010 - Computers
Richard Bird takes a radical 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.

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### Contents

 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
 17 The KnuthMorrisPratt 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

 9 Finding celebrities 56 10 Removing duplicates 64 11 Not the maximum segment sum 73 12 Ranking suffixes 79 13 The BurrowsWheeler transform 91 14 The last tail 102 15 All the common prefixes 112 16 The BoyerMoore algorithm 117
 25 Integer arithmetic coding 208 26 The SchorrWaite algorithm 221 27 Orderly insertion 231 28 Loopless functional algorithms 242 29 The JohnsonTrotter algorithm 251 30 Spider spinning for dummies 258 Index 275 Copyright