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<html>
<head>
<title>
SUBSET_SUM - The Subset Sum Problem
</title>
</head>
<body bgcolor="#eeeeee" link="#cc0000" alink="#ff3300" vlink="#000055">
<h1 align = "center">
SUBSET_SUM <br> The Subset Sum Problem
</h1>
<hr>
<p>
<b>SUBSET_SUM</b>
is a C++ library which
seeks solutions of the subset sum problem.
</p>
<p>
This function tries to compute a target value as the sum of
a selected subset of a given set of weights.
</p>
<p>
This function works by brute force, that is, it tries every
possible subset to see if it sums to the desired value.
</p>
<p>
Given N weights, every possible selection can be described by
one of the N-digit binary numbers from 0 to 2^N-1.
</p>
<p>
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.
</p>
<p>
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.
</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</b> is available in
<a href = "../../c_src/subset_sum/subset_sum.html">a C version</a> and
<a href = "../../cpp_src/subset_sum/subset_sum.html">a C++ version</a> and
<a href = "../../f_src/subset_sum/subset_sum.html">a FORTRAN90 version</a> and
<a href = "../../f77_src/subset_sum/subset_sum.html">a FORTRAN77 version</a> and
<a href = "../../m_src/subset_sum/subset_sum.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/change_making/change_making.html">
CHANGE_MAKING</a>,
a C++ library which
considers the change making problem,
in which a given sum is to be formed using coins of various denominations.
</p>
<p>
<a href = "../../cpp_src/combo/combo.html">
COMBO</a>,
a C++ library which
includes many combinatorial routines.
</p>
<p>
<a href = "../../cpp_src/knapsack_01/knapsack_01.html">
KNAPSACK_01</a>,
a C++ library which
uses brute force to solve small versions of the 0/1 knapsack problem;
</p>
<p>
<a href = "../../cpp_src/partition_problem/partition_problem.html">
PARTITION_PROBLEM</a>,
a C++ library which
seeks solutions of the partition problem, splitting a set of integers into
two subsets with equal sum.
</p>
<p>
<a href = "../../cpp_src/satisfy/satisfy.html">
SATISFY</a>,
a C++ program which
demonstrates, for a particular circuit, an exhaustive search
for solutions of the circuit satisfiability problem.
</p>
<p>
<a href = "../../datasets/subset_sum/subset_sum.html">
SUBSET_SUM</a>,
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.
</p>
<p>
<a href = "../../cpp_src/tsp_brute/tsp_brute.html">
TSP_BRUTE</a>,
a C++ program which
reads a file of city-to-city distances and solves the
traveling salesperson problem, using brute force.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Donald Kreher, Douglas Simpson,<br>
Combinatorial Algorithms,<br>
CRC Press, 1998,<br>
ISBN: 0-8493-3988-X,<br>
LC: QA164.K73.
</li>
<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>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "subset_sum.cpp">subset_sum.cpp</a>, the source code.
</li>
<li>
<a href = "subset_sum.hpp">subset_sum.hpp</a>, the include file.
</li>
<li>
<a href = "subset_sum.sh">subset_sum.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_prb.cpp">subset_sum_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "subset_sum_prb.sh">subset_sum_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "subset_sum_prb_output.txt">subset_sum_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the minimum of two I4's.
</li>
<li>
<b>I4_POWER</b> returns the value of I^J.
</li>
<li>
<b>I4_TO_DIGITS_BINARY</b> produces the binary digits of an I4.
</li>
<li>
<b>I4VEC_COPY_NEW</b> copies an I4VEC to a "new" I4VEC.
</li>
<li>
<b>I4VEC_DOT_PRODUCT</b> computes the dot product of two I4VEC's.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>SUBSET_SUM_COUNT</b> counts solutions to the subset sum problem in a range.
</li>
<li>
<b>SUBSET_SUM</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 19 December 2011.
</i>
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