COMBO Kreher and Stinson Combinatorial Routines

COMBO, a C library which includes routines for ranking, unranking, enumerating and randomly selecting balanced sequences, cycles, graphs, Gray codes, subsets, partitions, permutations, restricted growth functions, Pruefer codes and trees.

Routines are available to count, list, rank and unrank such objects

• BAL, balanced sequences;
• CYCLE, permutations of the first N integers in cycle form;
• GRAPH, graphs stored as a list of edges.
• GRAY, Gray codes;
• KNAPSACK, optimally filling a knapsack of given size using a set of smaller objects;
• KSUBSET, subsets of size exactly K from a set of N objects;
• NPART, partitions of an integer having exactly N parts;
• PART, partitions of an integer;
• PERM, permutations of the first N integers in standard form;
• PRUEFER, Pruefer codes;
• RGF, restricted growth functions;
• SETPART, partitions of a set;
• SUBSET, subsets of a set of N objects;
• TABLEAU, tableaus;
• TREE, trees;

Some of these sets of objects can be ordered in several different ways, and in some cases, a separate set of ranking, unranking, and successor routines are available for the various orderings (lexical, colexical, revolving door, Trotter-Johnson).

Kreher and Stinson provide C source-code for the routines, as well as other information, at their web site.

Languages:

COMBO is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

CHANGE_MAKING, a C library which considers the change making problem, in which a given sum is to be formed using coins of various denominations.

FLOYD, a C library which implements Floyd's algorithm for finding the shortest distance between pairs of nodes on a directed graph.

GRAFPACK, a FORTRAN90 library which carries out computations involving graphs.

KNAPSACK, a FORTRAN77 library which solves a variety of knapsack problems.

KNAPSACK_01, a C library which uses brute force to solve small versions of the 0/1 knapsack problem;

LEGENDRE_PRODUCT_POLYNOMIAL, a C library which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

MONOMIAL, a C library which enumerates, lists, ranks, unranks and randomizes multivariate monomials in a space of M dimensions, with total degree less than N, equal to N, or lying within a given range.

PARTITION_PROBLEM, a C library which seeks solutions of the partition problem, splitting a set of integers into two subsets with equal sum.

POLYNOMIAL, a C library which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of M dimensions.

SELECT, a FORTRAN90 library which generates various combinatorial objects.

SET_THEORY, a C library which demonstrates various set theoretic operations using several models of a set.

SUBSET, a C library which generates, ranks and unranks various combinatorial objects.

SUBSET_SUM, a C library which seeks solutions of the subset sum problem.

TOMS515, a C library which can select subsets of size K from a set of size N. This is a version of ACM TOMS Algorithm 515, by Bill Buckles, Matthew Lybanon.

UNICYCLE, a C library which considers permutations containing a single cycle, sometimes called cyclic permutations.

Reference:

1. Donald Kreher, Douglas Simpson,
Combinatorial Algorithms,
CRC Press, 1998,
ISBN: 0-8493-3988-X,
LC: QA164.K73.

Source Code:

Last revised on 15 June 2019.