# SUBSET_SUM The Subset Sum Problem

SUBSET_SUM is a FORTRAN90 library which seeks solutions of the subset sum problem.

This function tries to compute a target value as the sum of a selected subset of a given set of weights.

This function works by brute force, that is, it tries every possible subset to see if it sums to the desired value.

Given N weights, every possible selection can be described by one of the N-digit binary numbers from 0 to 2^N-1.

This function includes a range, which allows the user to control which subsets are to be checked. Thus, if there are N weights, specifying a range of [ 0, 2^N-1] indicates that all subsets should be checked. On the other hand, this full range could be broken down into smaller subranges, each of which could be checked independently.

It is possible that, in the given range, there may be multiple solutions of the problem. This function will only return one such solution, if found. However, the function may be called again, with an appropriate restriction of the range, to continue the search for other solutions.

### Languages:

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

### Related Data and Programs:

COMBINATION_LOCK, a FORTRAN90 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_TASKS, a MATLAB program which runs in parallel, seeking solutions of the "subset sum" version of the knapsack 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.

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

LAU_NP, a FORTRAN90 library which implements heuristic algorithms for various NP-hard combinatorial problems.

PARTITION_PROBLEM, a FORTRAN90 library which seeks solutions of the partition problem, splitting a set of integers into two subsets with equal sum.

SATISFY, a FORTRAN90 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.

SUBSET_SUM, a dataset directory which contains examples of the subset sum problem, in which a set of numbers is given, and is desired to find at least one subset that sums to a given target value.

### Reference:

1. Donald Kreher, Douglas Simpson,
Combinatorial Algorithms,
CRC Press, 1998,
ISBN: 0-8493-3988-X,
LC: QA164.K73.
2. Silvano Martello, Paolo Toth,
Knapsack Problems: Algorithms and Computer Implementations,
Wiley, 1990,
ISBN: 0-471-92420-2,
LC: QA267.7.M37.

### List of Routines:

• SUBSET_SUM_COUNT counts solutions to the subset sum problem in a range.
• SUBSET_SUM seeks a subset of a set that has a given sum.
• I4_TO_BINARY_DIGITS produces the binary digits of an I4.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.

Last revised on 09 December 2010.