SUBSET_SUM
The Subset Sum Problem

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

This function tries to compute a target value as the sum of a selected subset of a given set of weights.

This function works by brute force, that is, it tries every possible subset to see if it sums to the desired value.

Given N weights, every possible selection can be described by one of the N-digit binary numbers from 0 to 2^N-1.

This function includes a range, which allows the user to control which subsets are to be checked. Thus, if there are N weights, specifying a range of [ 0, 2^N-1] indicates that all subsets should be checked. On the other hand, this full range could be broken down into smaller subranges, each of which could be checked independently.

It is possible that, in the given range, there may be multiple solutions of the problem. This function will only return one such solution, if found. However, the function may be called again, with an appropriate restriction of the range, to continue the search for other solutions.

Licensing:

The computer code and data files described and 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 FORTRAN77 version and a MATLAB 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.

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.

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:

• subset_sum.cpp, the source code.
• subset_sum.hpp, the include file.
• subset_sum.sh, BASH commands to compile the source code.

Examples and Tests:

• subset_sum_prb.cpp, a sample calling program.
• subset_sum_prb.sh, BASH commands to compile and run the sample program.
• subset_sum_prb_output.txt, the output file.

List of Routines:

• I4_MAX returns the maximum of two I4's.
• I4_MIN returns the minimum of two I4's.
• I4_POWER returns the value of I^J.
• I4_TO_DIGITS_BINARY produces the binary digits of an I4.
• I4VEC_COPY_NEW copies an I4VEC to a "new" I4VEC.
• I4VEC_DOT_PRODUCT computes the dot product of two I4VEC's.
• I4VEC_PRINT prints an I4VEC.
• SUBSET_SUM_COUNT counts solutions to the subset sum problem in a range.
• SUBSET_SUM seeks a subset of a set that has a given sum.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.