The Subset Sum Problem

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

The task is to compute a target value as the sum of a selected subset of a given set of weights.

SUBSET_SUM_NEXT works by backtracking, returning all possible solutions one at a time, keeping track of the selected weights using a 0/1 mask vector of size N.

SUBSET_SUM_TABLE works by a kind of dynamic programming approach, constructing a table of all possible sums from 1 to S. The storage required is N * S, so for large S this can be an issue.

SUBSET_SUM_FIND works by brute force, trying every possible subset to see if it sums to the desired value. It uses the bits of a 32 bit integer to keep track of the possibilities, and hence cannot work with more N = 31 weights.


I don't care what you do with this code.


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

Related Data and Programs:

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.

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

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;

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

SATISFY, a C 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.

TSP_BRUTE, a C 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 C source codes.

Last revised on 15 July 2017.