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// ==========================================================================
// SeqAn - The Library for Sequence Analysis
// ==========================================================================
// Copyright (c) 2006-2026, Knut Reinert, FU Berlin
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// * Neither the name of Knut Reinert or the FU Berlin nor the names of
// its contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL KNUT REINERT OR THE FU BERLIN BE LIABLE
// FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
// SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
// CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
// LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
// OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
// DAMAGE.
//
// ==========================================================================
// Author: Tobias Raussch <rausch@embl.de>
// ==========================================================================
// Implementation of Bellman-Ford algorithm.
// ==========================================================================
#ifndef INCLUDE_SEQAN_GRAPH_ALGORITHMS_BELLMAN_FORD_H_
#define INCLUDE_SEQAN_GRAPH_ALGORITHMS_BELLMAN_FORD_H_
namespace seqan2 {
// ============================================================================
// Forwards
// ============================================================================
// ============================================================================
// Tags, Classes, Enums
// ============================================================================
// ============================================================================
// Metafunctions
// ============================================================================
// ============================================================================
// Functions
// ============================================================================
// ----------------------------------------------------------------------------
// Function bellmanFordAlgorithm()
// ----------------------------------------------------------------------------
/*!
* @fn bellmanFordAlgorithm
*
* @headerfile <seqan/graph_algorithms.h>
*
* @brief Computes shortest paths from a single source in a directed graph.
*
* @signature bool bellmanFordAlgorithm(g, source, weight, predecessor, distance)
*
* @param[out] predecessor A property map. A property map that represents predecessor relationships among vertices.
* It determines a shortest-paths tree.
* @param[out] distance A property map.Indicates for each vertex the distance from the source.
* @param[in] g A directed graph. Types: Directed Graph
* @param[in] source A source vertex. Types: VertexDescriptor
* @param[in] weight A weight map.A property map with edge weights. Edge weights may be negative.
*
* @return bool true if the graph has no negative weight cycles, false otherwise.
*
* Edge weights may be negative in the Bellman-Ford algorithm. The out parameters are only valid if the algorithm
* returns true.
*
* @section Example
*
* @include demos/dox/graph_algorithms/bellman_ford_algorithm.cpp
*
* @include demos/dox/graph_algorithms/bellman_ford_algorithm.cpp.stdout
*
* @see dagShortestPath
* @see dijkstra
*/
template <typename TSpec, typename TVertexDescriptor, typename TWeightMap, typename TPredecessorMap, typename TDistanceMap>
bool bellmanFordAlgorithm(TPredecessorMap & predecessor,
TDistanceMap & distance,
Graph<TSpec> const & g,
TVertexDescriptor const source,
TWeightMap const & weight)
{
typedef typename Size<Graph<TSpec> >::Type TSize;
// Initialization
typedef typename Iterator<Graph<TSpec>, VertexIterator>::Type TVertexIterator;
typedef typename Iterator<Graph<TSpec>, OutEdgeIterator>::Type TOutEdgeIterator;
resizeVertexMap(predecessor, g);
resizeVertexMap(distance, g);
_initializeSingleSource(predecessor, distance, g, source, weight);
// Run Bellman-Ford
for(TSize i=0; i<numVertices(g) - 1; ++i) {
TVertexIterator it(g);
for(;!atEnd(it);goNext(it)) {
TVertexDescriptor u = getValue(it);
TOutEdgeIterator itout(g, u);
for(;!atEnd(itout);++itout) {
_relax(g,weight,predecessor, distance, u, getValue(itout));
}
}
}
TVertexIterator it(g);
for(;!atEnd(it);goNext(it)) {
TVertexDescriptor u = getValue(it);
TOutEdgeIterator itout(g, u);
for(;!atEnd(itout);++itout) {
TVertexDescriptor v = targetVertex(g, getValue(itout));
if (getProperty(distance, v) > getProperty(distance,u) + getProperty(weight,getValue(itout))) {
return false;
}
}
}
return true;
}
} // namespace seqan2
#endif // #ifndef INCLUDE_SEQAN_GRAPH_ALGORITHMS_BELLMAN_FORD_H_
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