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

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### 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.