subset_sum


subset_sum, a Python 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_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 information on this web page is 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:

python_combinatorics, a Python code which considers a variety of problems in combinatorics involving counting, combinations, permutations, and so on.

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 10 November 2015.