fn() bellmanFordAlgorithmComputes shortest paths from a single source in a directed graph.
Computes shortest paths from a single source in a directed graph.
Defined in | <seqan/graph_algorithms.h> |
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Signature |
bool bellmanFordAlgorithm(g, source, weight, predecessor, distance)
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Parameters
predecessor
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A property map. A property map that represents predecessor relationships among vertices. It determines a shortest-paths tree. |
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distance
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A property map.Indicates for each vertex the distance from the source. |
g
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A directed graph. Types: Directed Graph |
source
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A source vertex. Types: VertexDescriptor |
weight
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A weight map.A property map with edge weights. Edge weights may be negative. |
Return Values
bool |
true if the graph has no negative weight cycles, false otherwise. |
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Detailed Description
Edge weights may be negative in the Bellman-Ford algorithm. The out parameters are only valid if the algorithm returns true.
Example
#include <iostream> #include <seqan/graph_algorithms.h> using namespace seqan; int main() { typedef Graph<Directed<> > TGraph; typedef VertexDescriptor<TGraph>::Type TVertexDescriptor; typedef Size<TGraph>::Type TSize; // Create graph with 10 directed edges (0,1), (0,3), ... TSize numEdges = 10; TVertexDescriptor edges[] = {0, 1, 0, 3, 1, 2, 1, 3, 2, 4, 3, 1, 3, 2, 3, 4, 4, 0, 4, 2}; TGraph g; addEdges(g, edges, numEdges); // Print graph. std::cout << g << "\n"; // Create external edge property map and assign to graph. unsigned weights[] = {10, 5, 1, 2, 4, 3, 9, 2, 7, 6}; String<unsigned> weightMap; assignEdgeMap(weightMap, g, weights); // Run Bellman-Ford algorithm from vertex 0. NB: Ford-Fulkerson also // detects negative cycles. String<unsigned int> predMap; String<unsigned int> distMap; bool noNegativeCycle = bellmanFordAlgorithm(predMap, distMap, g, 0, weightMap); // Print result to stdout. std::cout << "Single-Source Shortest Paths: " << "\n" << "Graph without negative cycles? " << noNegativeCycle << "\n"; typedef Iterator<TGraph, VertexIterator>::Type TVertexIterator; TVertexIterator it(g); while (!atEnd(it)) { std::cout << "Path from 0 to " << getValue(it) << ": "; _printPath(g, predMap, (TVertexDescriptor) 0, getValue(it)); std::cout << " (Distance: " << getProperty(distMap, getValue(it)) << ")\n"; goNext(it); } return 0; }
Adjacency list: 0 -> 3,1, 1 -> 3,2, 2 -> 4, 3 -> 4,2,1, 4 -> 2,0, Edge list: Source: 0,Target: 3 (Id: 1) Source: 0,Target: 1 (Id: 0) Source: 1,Target: 3 (Id: 3) Source: 1,Target: 2 (Id: 2) Source: 2,Target: 4 (Id: 4) Source: 3,Target: 4 (Id: 7) Source: 3,Target: 2 (Id: 6) Source: 3,Target: 1 (Id: 5) Source: 4,Target: 2 (Id: 9) Source: 4,Target: 0 (Id: 8) Single-Source Shortest Paths: Graph without negative cycles? 1 Path from 0 to 0: 0 (Distance: 0) Path from 0 to 1: 0,3,1 (Distance: 8) Path from 0 to 2: 0,3,1,2 (Distance: 9) Path from 0 to 3: 0,3 (Distance: 5) Path from 0 to 4: 0,3,4 (Distance: 7)
Data Races
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