# Combinatorial Algorithms: For Computers and Calculators

1978 | ISBN: 0125192606 9780125192606 0125192509 9780125192507 | 317 pages | PDF | 5.63 MB

This book can be read at several levels. Those whose only need is to use one of the computer programs can turn immediately to those pages and satisfy their wants. Thus, on one level, this is a collection of subroutines, in FORTRAN, for the solution of combinatorial problems. At the other extreme, pure mathematicians with no need of computer programs will find much that is new and hopefully interesting in these pages.

Readers will want to follow the entire road from general mathematics to particular mathematics to informal algorithm to formal algorithm to computer program and back again, which occurs in virtually every chapter of the book.

Readers will view methods and programs as a beginning set of building blocks for their own kit of tools and will go on to add to these tools to meet their own needs, so that the contents of this book will be not a collection of pretty artifacts to be looked at but basic elements of the growing and working equipment of scientific investigation and learning.

Contents

Preface to Second Edition

Preface to First Edition

Introduction

Aims

Highlights

Categories of Usage (Part I)

Structure of the Chapters

The Specifications List

Structure of the "Next" Programs

Structure of the "Random" Programs

Arrays and Specifications

PART 1 COMBINATORIAL FAMILIES

1 Next Subset of an n-Set (NEXSUBILEXSUB)

(A) The Direct Approach

(B) The Gray Code

Algodthm NEXSUB

(C) Lexicographic Sequencing

Algorithm LEXSUB

Subroutine Specifications (NEXSUB)

Subroutine Specifications (LEXSUB)

Sample Output (NEXSUB)

2 Random Subset of an n-Set (RANSUB)

Algorithm RANSUB

Subroutine Specifications

Sample Output

3 Next k-Subset of an n-Set (NEXKSB/NXKSRD)

Algorithm NEXKSB (Lexicographic)

Flow Chart NXKSRD

Subroutine Specifications (NEXKSB)

Subroutine Specifications (NXKSRD)

Sample Output (NEXKSBj

Sample Output (NXKSRDj

4 Random k-Subset of an n-Set (RANKSB)

Algorithm RANKSB

Algorithm RKS2

Subroutine Specifications

Sample Intermediate Result

Sample Output

5 Next Composition of n into k Parts (NEXCOM)

Algorithm NEXCOM

Subroutine Specifications

Sample Output

6 Random Composition of n into k Parts (RANCOM)

Algorithm RANCOM

Subroutine Specifications

7 Next Permutation of n Letters (NEXPER)

Algorithm NEXPER

Subroutine Specifications

Sample Output

8 Random Permutation of n Letters (RANPER)

Algorithm RANPER

Subroutine Specifications

Sample Output

9 Next Partition of Integer n (NEXPAR)

Algorithm NEXPAR

Subroutine Specifications

10 Random Partition of an Integer n (RANPAR)

Algorithm RANPAR

Subroutine Specifications

Sample Output

Postscript: Deus ex Machina

Algorithm NEXT PLANE PARTITION

11 Next Partition of an n-Set (NEXEQU)

Algorithm NEXEQU

Subroutine Specifications

Sample Output

12 Random Partition of an n-Set (RANEQU)

Algorithm RANEQU

Flow Chart RANEQU

Subroutine Specifications

Sample Output

13 Sequencing, Ranking, and Selection Algorithms in General Combinatorial Families (SELECT)

(A) Introduction

(B) General Setting

Algorithm NEXT

(C) Examples

(D) The Formal Algorithms

Algorithm SELECT

Subroutine Specifications

(E) Decoding

Sample Output

14 Young Tableaux (NEXYTBIRANYTB)

(A) Introduction

(B) Lexicographic Sequencing

Algorithm NEXYTB

(e) Random Selection

Algorithm RANYTB

Subroutine Specifications (NEXYTB)

Subroutine Speciflcation.s (RANYTB)

Sample Output

PART 2 COMBINATORIAL STRUCTURES

15 Sorting (HPSORT/EXHEAP)

Algorithm [!F(l, 11)

Algorithm TOHEAP

Algorithm SORTHEAP

Subroutine Specifications (HPSORT)

Subroutine Specifications (EXHEAP)

Sample Output

16 The Cycle Structure of a Pennutation (CYCLES)

Algorithm TAG

Algorithm INVERT

Subroutine Specifications

Sample Output

17 Renumbering Rows and Columns ofan Array (RENUMB)

Algorithm RENUMB

Subroutine Specifications

Sample Output

18 Spanning Forest of a Graph (SPANFO)

(A) Introduction

(B) Depth-First-Search

Algorithm DEPTHFIRST

(C) A Breadth-First Algorithm

Algorithm LINK (x, e, n, E)

Algorithm VISIT (x, E. n, E, q, Ii> mil a)

Algorithm SCAN (x, E, n, E, p,Io, mo, m, r)

Algorithm COMPONENT (x, e, n, E, p, k, L)

Algorithm SPANFO (x, e, n, E, k)

Subroutine Specifications

Sample Output

19 Newton Fonns of a Polynomial (POLY)

Algorithm VALUE

Algorithm NEWTON

Algorithm TAYLOR

Algorithm STIRLING

Algorithm REVERSE STIRLING

Algorithm NWT (m, x, E, Y)

Subroutine Specincations

Sample Output

20 Chromatic Polynomial of a Graph (CHROMP)

Algorithm CHROMP

Subroutine Specifications

Sample Output

21 Composition of Power Series (POWSER)

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