subset_sum


subset_sum, a C 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 described and 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

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subset_sum_backtrack, a C code which uses backtracking to solve the subset sum problem, to find a subset of a set of integers which has a given sum.

subset_sum_brute, a C code which uses brute force to solve the subset sum problem, to find a subset of a set of integers which has a given sum.

tsp_brute, a C code which reads a file of city-to-city distances and solves the traveling salesperson problem, using brute force.

Reference:

  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:


Last revised on 11 August 2019.