# SUBSET_SUM_SERIAL Solve a Subset Sum Problem by Exhaustive Search

SUBSET_SUM_SERIAL is a MATLAB 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.

### 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 MATLAB program which demonstrates the computation of a Fast Fourier Transform (FFT), and is intended as a starting point for implementing a parallel version.

FIRE_SERIAL, a MATLAB 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.

ODE_SWEEP_SERIAL, a MATLAB program which computes a grid of solutions to a parameterized system of ordinary differential equations (ODE's).

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

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

QUAD2D_SERIAL, a MATLAB 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 MATLAB 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 MATLAB library which seeks solutions of the subset sum problem.

SUBSET_SUM_TASKS, a MATLAB program which solves the subset sum problem by exhaustive search, dividing the problem into subtasks, each of which is carried out as a separate program.

### Reference:

• Silvano Martello, Paolo Toth,
Knapsack Problems: Algorithms and Computer Implementations,
Wiley, 1990,
ISBN: 0-471-92420-2,
LC: QA267.7.M37.

### Examples and Tests:

You can go up one level to the MATLAB source codes.

Last revised on 01 July 2013.