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<html>
<head>
<title>
BELLMAN_FORD - All-to-One Shortest Distances on Directed Graph
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
BELLMAN_FORD <br> All-to-One Shortest Distances on Directed Graph
</h1>
<hr>
<p>
<b>BELLMAN_FORD</b>,
a C++ library which
implements the Bellman-Ford algorithm for finding the shortest distance
from a given node to all other nodes in a directed graph whose
edges have been assigned real-valued lengths.
</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>BELLMAN_FORD</b> is available in
<a href = "../../c_src/bellman_ford/bellman_ford.html">a C version</a> and
<a href = "../../cpp_src/bellman_ford/bellman_ford.html">a C++ version</a> and
<a href = "../../f77_src/bellman_ford/bellman_ford.html">a FORTRAN77 version</a> and
<a href = "../../f_src/bellman_ford/bellman_ford.html">a FORTRAN90 version</a> and
<a href = "../../m_src/bellman_ford/bellman_ford.html">a MATLAB version</a> and
<a href = "../../py_src/bellman_ford/bellman_ford.html">a Python version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/dijkstra/dijkstra.html">
DIJKSTRA</a>,
a C++ library which
implements a simple version of Dijkstra's minimum distance algorithm
for graphs.
</p>
<p>
<a href = "../../cpp_src/floyd/floyd.html">
FLOYD</a>,
a C++ library which
implements Floyd's algorithm for finding the shortest distance
between pairs of nodes on a directed graph.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Richard Bellman,<br>
On a routing problem,<br>
Quarterly of Applied Mathematics,<br>
Volume 16, 1958, pages 87-90.
</li>
<li>
Lester Ford,<br>
Network Flow Theory,<br>
RAND Corporation Paper P-923, 1956.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "bellman_ford.cpp">bellman_ford.cpp</a>, the source code.
</li>
<li>
<a href = "bellman_ford.hpp">bellman_ford.hpp</a>, the include file.
</li>
<li>
<a href = "bellman_ford.sh">bellman_ford.sh</a>,
BASH commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "bellman_ford_prb.cpp">bellman_ford_prb.cpp</a>,
a sample calling program.
</li>
<li>
<a href = "bellman_ford_prb.sh">bellman_ford_prb.sh</a>,
BASH commands to compile and run the sample program.
</li>
<li>
<a href = "bellman_ford_prb_output.txt">bellman_ford_prb_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>BELLMAN_FORD</b> finds shortest paths from a given vertex of a weighted directed graph.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of an I4MAT, transposed.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</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 12 November 2014.
</i>
<!-- John Burkardt -->
</body>
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</html>