combo

combo, a C++ code which ranks, unranks, enumerates, lists and randomly selects balanced sequences, cycles, graphs, Gray codes, subsets, partitions, permutations, restricted growth functions, Pruefer codes and trees.

The objects include:

• BAL, balanced sequences, included nested parentheses, Dyck lattice paths, ballot paths;
• 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.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

combo is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

combo_test

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

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

knapsack_01_brute, a C++ code which uses brute force to solve small versions of the 0/1 knapsack problem;

legendre_product_polynomial, a C++ code which defines Legendre product polynomials, creating a multivariate polynomial as the product of univariate Legendre polynomials.

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

polynomial, a C++ code which adds, multiplies, differentiates, evaluates and prints multivariate polynomials in a space of M dimensions.

subset, a C++ code which generates, ranks and unranks various combinatorial objects.

subset_sum, a C++ code which seeks solutions of the subset sum problem.

toms515, a C++ code 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++ code 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:

• combo.cpp, the source code;
• combo.sh, compiles the source code;
• combo.hpp, the include file;