Combinatorial Routines

SUBSET is a C++ library which enumerates, generates, randomizes, ranks and unranks combinatorial objects including combinations, compositions, Gray codes, index sets, partitions, permutations, polynomials, subsets, and Young tables. Backtracking routines are included to solve some combinatorial problems.

These include the enumeration, generation, random selection, ranking and unranking of

Other objects considered include


The computer code and data files made available on this web page are distributed under the GNU LGPL license.


SUBSET is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BACKTRACK_BINARY_RC, a C++ library which carries out a backtrack search for a set of binary decisions, using reverse communication.

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.

COMBO, a C++ library which includes many combinatorial routines.

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.

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.

UBVEC, a C++ library which demonstrates how unsigned binary vectors, strings of 0's and 1's, can represent nonnegative integers or subsets or other mathematical objects, for which various arithmetic and logical operations can be defined.

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


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Source Code:

Examples and Tests:

List of Routines:

You can go up one level to the C++ source codes.

Last revised on 11 December 2013.