The Subset Sum Problem

SUBSET_SUM is a FORTRAN77 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.


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


SUBSET_SUM 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:

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 FORTRAN77 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 FORTRAN77 library which seeks solutions of the partition problem, splitting a set of integers 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_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.

SUBSET_SUM_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.

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


  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.

Source Code:

Examples and Tests:

List of Routines:

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

Last revised on 02 February 2012.