subset_sum


subset_sum, an Octave code which seeks solutions of the subset sum problem, in which it is desired to find a subset of integers which has a given sum.

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.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

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

Related Data and Programs:

subset_sum_test

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

combo, a MATLAB code which includes many combinatorial routines.

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. Alexander Dewdney,
    The Turing Omnibus,
    Freeman, 1989,
    ISBN13: 9780716781547,
    LC: QA76.D45.
  2. Donald Kreher, Douglas Simpson,
    Combinatorial Algorithms,
    CRC Press, 1998,
    ISBN: 0-8493-3988-X,
    LC: QA164.K73.
  3. Silvano Martello, Paolo Toth,
    Knapsack Problems: Algorithms and Computer Implementations,
    Wiley, 1990,
    ISBN: 0-471-92420-2,
    LC: QA267.7.M37.

Source Code:


Last modified on 23 September 2022.