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<html>
<head>
<title>
SUBSET_SUM_SERIAL - Solve a Subset Sum Problem by Exhaustive Search
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
SUBSET_SUM_SERIAL <br>
Solve a Subset Sum Problem by Exhaustive Search
</h1>
<hr>
<p>
<b>SUBSET_SUM_SERIAL</b>
is a C++ library which
illustrates how a subset sum problem can be solved by exhaustive search.
</p>
<p>
We are given a collection of (21) weights and a
<i>target value</i> (24639098). We seek a combination of the weights which
adds up to the target value.
</p>
<p>
The function <i>subset_sum_serial.m</i> 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.
</p>
<p>
This program, which solves the problem serially, is primarily intended to
be a starting point for a parallel programming approach.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>SUBSET_SUM_SERIAL</b> is available in
<a href = "../../c_src/subset_sum_serial/subset_sum_serial.html">a C version</a> and
<a href = "../../cpp_src/subset_sum_serial/subset_sum_serial.html">a C++ version</a> and
<a href = "../../f77_src/subset_sum_serial/subset_sum_serial.html">a FORTRAN77 version</a> and
<a href = "../../f_src/subset_sum_serial/subset_sum_serial.html">a FORTRAN90 version</a> and
<a href = "../../m_src/subset_sum_serial/subset_sum_serial.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/fft_serial/fft_serial.html">
FFT_SERIAL</a>,
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.
<p>
<p>
<a href = "../../cpp_src/fire_serial/fire_serial.html">
FIRE_SERIAL</a>,
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.
</p>
<p>
<a href = "../../cpp_src/heated_plate/heated_plate.html">
HEATED_PLATE</a>,
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.
</p>
<p>
<a href = "../../cpp_src/md/md.html">
MD</a>,
a C++ program which
carries out a molecular dynamics simulation, and is intended as
a starting point for implementing an OpenMP parallel version.
</p>
<p>
<a href = "../../cpp_src/mxm_serial/mxm_serial.html">
MXM_SERIAL</a>,
a C++ program which
sets up a matrix multiplication problem A=B*C,
intended as a starting point for implementing a parallel version.
</p>
<p>
<a href = "../../cpp_src/poisson_serial/poisson_serial.html">
POISSON_SERIAL</a>,
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.
</p>
<p>
<a href = "../../cpp_src/prime_serial/prime_serial.html">
PRIME_SERIAL</a>,
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.
</p>
<p>
<a href = "../../cpp_src/quad_serial/quad_serial.html">
QUAD_SERIAL</a>,
a C++ program which
approximates an integral using a quadrature rule,
and is intended as a starting point for parallelization exercises.
</p>
<p>
<a href = "../../cpp_src/quad2d_serial/quad2d_serial.html">
QUAD2D_SERIAL</a>,
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.
</p>
<p>
<a href = "../../cpp_src/search_serial/search_serial.html">
SEARCH_SERIAL</a>,
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.
</p>
<p>
<a href = "../../cpp_src/subset_sum/subset_sum.html">
SUBSET_SUM</a>,
a C++ library which
seeks solutions of the subset sum problem.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ul>
<li>
Silvano Martello, Paolo Toth,<br>
Knapsack Problems: Algorithms and Computer Implementations,<br>
Wiley, 1990,<br>
ISBN: 0-471-92420-2,<br>
LC: QA267.7.M37.
</li>
</ul>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "subset_sum_serial.cpp">subset_sum_serial.cpp</a>, the source code.
</li>
<li>
<a href = "subset_sum_serial.hpp">subset_sum_serial.hpp</a>, the include file.
</li>
<li>
<a href = "subset_sum_serial.sh">subset_sum_serial.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "subset_sum_serial_prb.cpp">subset_sum_serial_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "subset_sum_serial_prb.sh">subset_sum_serial_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "subset_sum_serial_prb_output.txt">subset_sum_serial_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>I4_POWER</b> returns the value of I^J.
</li>
<li>
<b>I4VEC_DOT_PRODUCT</b> computes the dot product of two I4VEC's.
</li>
<li>
<b>SUBSET_SUM_SERIAL</b> seeks a subset of a set that has a given sum.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 01 July 2013.
</i>
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