# PARTITION_PROBLEM The Partition Problem

PARTITION_PROBLEM is a FORTRAN77 library which seeks solutions of the partition problem, splitting a set of integers into two subsets with equal sum.

### Licensing:

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

### Languages:

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

### Related Data and Programs:

CHANGE_MAKING, a FORTRAN77 library which considers the change making problem, in which a given sum is to be formed using coins of various denominations.

COMBINATION_LOCK, a FORTRAN77 program which simulates the process of determining the secret combination of a lock.

COMBO, a FORTRAN90 library which includes many combinatorial routines.

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

KNAPSACK_01, a FORTRAN77 library which uses brute force to solve small versions of the 0/1 knapsack problem;

LAMP, a FORTRAN77 library which solves linear assignment and matching problems.

PARTITION_PROBLEM, a dataset directory which contains examples of the partition problem, in which a set of numbers is given, and it is desired to break the set into two subsets with equal sum.

SATISFY, a FORTRAN77 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.

SUBSET, a FORTRAN77 library which enumerates, generates, ranks and unranks combinatorial objects including combinations, partitions, subsets, index sets, and trees.

SUBSET_SUM, a FORTRAN77 library which seeks solutions of the subset sum problem.

SUBSET_SUM_TASKS, a MATLAB program which runs in parallel, seeking solutions of the subset sum problem. Instructions are available on how to run the job, via MATLAB's BATCH facility, on a remote system such as Virginia Tech's ITHACA cluster.

TSP_BRUTE, a FORTRAN77 program which reads a file of city-to-city distances and solves the traveling salesperson problem, using brute force.

### Reference:

1. Alexander Dewdney,
The Turing Omnibus,
Freeman, 1989,
ISBN13: 9780716781547,
LC: QA76.D45.
2. Brian Hayes,
The Easiest Hard Problem,
American Scientist,
Volume 90, Number 2, March-April 2002, pages 113-117.
3. Silvano Martello, Paolo Toth,
Knapsack Problems: Algorithms and Computer Implementations,
Wiley, 1990,
ISBN: 0-471-92420-2,
LC: QA267.7.M37.

### List of Routines:

• I4VEC_COPY copies an I4VEC.
• I4VEC_DOT_PRODUCT computes the dot product of two I4VEC's.
• I4VEC_SUM returns the sum of the entries of an I4VEC.
• PARTITION_BRUTE approaches the partition problem using brute force.
• PARTITION_COUNT counts the solutions to a partition problem.
• SUBSET_NEXT computes the subset lexicographic successor.
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.

Last revised on 10 May 2012.