Pearls of Functional Algorithm Design

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.

Preface; 1. The smallest free number; 2. A surpassing problem; 3. Improving on saddleback search; 4. A selection problem; 5. Sorting pairwise sums; 6. Making a century; 7. Building a tree with minimum height; 8. Unravelling greedy algorithms; 9. Finding celebrities; 10. Removing duplicates; 11. Not the maximum segment sum; 12. Ranking suffixes; 13. The Burrows–Wheeler transform; 14. The last tail; 15. All the common prefixes; 16. The Boyer–Moore algorithm; 17. The Knuth–Morris–Pratt algorithm; 18. Planning solves the rush hour problem; 19. A simple Sudoku solver; 20. The countdown problem; 21. Hylomorphisms and nexuses; 22. Three ways of computing determinants; 23. Inside the convex hull; 24. Rational arithmetic coding; 25. Integer arithmetic coding; 26. The Schorr–Waite algorithm; 27. Orderly insertion; 28. Loopless functional algorithms; 29. The Johnson–Trotter algorithm; 30. Spider spinning for dummies; Index.

Richard Bird takes a radically new approach to algorithm design, namely, design by calculation. This unique collection of 30 programming problems draws from various sources including games and puzzles, sorting, and problems in data compression.

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