SUBSET_SUM_SERIAL
Solve a Subset Sum Problem by Exhaustive Search

SUBSET_SUM_SERIAL is a C++ library which illustrates how a subset sum problem can be solved by exhaustive search.

We are given a collection of (21) weights and a target value (24639098). We seek a combination of the weights which adds up to the target value.

The function subset_sum_serial.m simply considers every possible subset of the weights, determines its sum, and compares that to the target value. The first case in which the target value is matched is returned as the solution.

This program, which solves the problem serially, is primarily intended to be a starting point for a parallel programming approach.

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_SERIAL is available in a C version and a C++ version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

FFT_SERIAL, a C++ program which demonstrates the computation of a Fast Fourier Transform, and is intended as a starting point for developing a parallel version using OpenMP.

FIRE_SERIAL, a C++ program which simulates a forest fire over a rectangular array of trees, starting at a single random location. It is intended as a starting point for the development of a parallel version.

HEATED_PLATE, a C++ program which solves the steady state heat equation in a 2D rectangular region, and is intended as a starting point for implementing an OpenMP parallel version.

MD, a C++ program which carries out a molecular dynamics simulation, and is intended as a starting point for implementing an OpenMP parallel version.

MXM_SERIAL, a C++ program which sets up a matrix multiplication problem A=B*C, intended as a starting point for implementing a parallel version.

POISSON_SERIAL, a C++ program which computes an approximate solution to the Poisson equation in a rectangle, and is intended as the starting point for the creation of a parallel version.

PRIME_SERIAL, a C++ program which counts the number of primes between 1 and N, intended as a starting point for the creation of a parallel version.

QUAD_SERIAL, a C++ program which approximates an integral using a quadrature rule, and is intended as a starting point for parallelization exercises.

QUAD2D_SERIAL, a C++ program which approximates an integral over a 2D region using a product quadrature rule, and is intended as a starting point for parallelization exercises.

SEARCH_SERIAL, a C++ program which searches the integers from A to B for a value J such that F(J) = C. this version of the program is intended as a starting point for a parallel approach.

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

Reference:

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

Examples and Tests:

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

List of Routines:

• I4_POWER returns the value of I^J.
• I4VEC_DOT_PRODUCT computes the dot product of two I4VEC's.
• SUBSET_SUM_SERIAL 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.