fn() floydWarshallAlgorithmFinds shortest paths between all pairs of vertices in a graph.
Finds shortest paths between all pairs of vertices in a graph.
Defined in | <seqan/graph_algorithms.h> |
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Signature |
void floydWarshallAlgorithm(g, weight, distance, predecessor);
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Parameters
predecessor
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A matrix with predecessors. Entry (i,j) in this matrix indicates the predecessor of j on a shortest path from vertex i to vertex j. You can use _printAllPairsShortestPath(g, predecessor, i, j) to print the shortest path from i to j. Types: Matrix |
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distance
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A matrix with distances.Entry (i,j) in this matrix indicates the distance from vertex i to vertex j. Types: Matrix |
weight
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A weight map. A property map with edge weights. Edge weights may be negative. |
g
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A directed graph. Types: Directed Graph |
Detailed Description
The graph must be free of negative-weight cycles.
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 9 directed edges (0,1), (0,2) TSize numEdges = 9; TVertexDescriptor edges[] = {0, 1, 0, 2, 0, 4, 1, 3, 1, 4, 2, 1, 3, 0, 3, 2, 4, 3}; TGraph g; addEdges(g, edges, numEdges); // Print graph. std::cout << g << "\n"; // Fill external property map with edge weights and assign to graph. int weights[] = {3, 8, -4, 1, 7, 4, 2, -5, 6}; String<int> weightMap; assignEdgeMap(weightMap, g, weights); // Run Floyd-Warshall algorithm. String<int> distMat; String<TVertexDescriptor> predMat; floydWarshallAlgorithm(distMat, predMat, g, weightMap); // Print result to stdout. unsigned int len = static_cast<unsigned>(std::sqrt((double)length(distMat))); for (TSize row = 0; row < len; ++row) for (TSize col = 0; col < len; ++col) { std::cout << row << "," << col << " (Distance=" << getValue(distMat, row * len + col) << "): "; _printAllPairsShortestPath(g, predMat, row, col); std::cout << std::endl; } return 0; }
Adjacency list: 0 -> 4,2,1, 1 -> 4,3, 2 -> 1, 3 -> 2,0, 4 -> 3, Edge list: Source: 0,Target: 4 (Id: 2) Source: 0,Target: 2 (Id: 1) Source: 0,Target: 1 (Id: 0) Source: 1,Target: 4 (Id: 4) Source: 1,Target: 3 (Id: 3) Source: 2,Target: 1 (Id: 5) Source: 3,Target: 2 (Id: 7) Source: 3,Target: 0 (Id: 6) Source: 4,Target: 3 (Id: 8) 0,0 (Distance=0): 0 0,1 (Distance=1): 0,4,3,2,1 0,2 (Distance=-3): 0,4,3,2 0,3 (Distance=2): 0,4,3 0,4 (Distance=-4): 0,4 1,0 (Distance=3): 1,3,0 1,1 (Distance=0): 1 1,2 (Distance=-4): 1,3,2 1,3 (Distance=1): 1,3 1,4 (Distance=-1): 1,3,0,4 2,0 (Distance=7): 2,1,3,0 2,1 (Distance=4): 2,1 2,2 (Distance=0): 2 2,3 (Distance=5): 2,1,3 2,4 (Distance=3): 2,1,3,0,4 3,0 (Distance=2): 3,0 3,1 (Distance=-1): 3,2,1 3,2 (Distance=-5): 3,2 3,3 (Distance=0): 3 3,4 (Distance=-2): 3,0,4 4,0 (Distance=8): 4,3,0 4,1 (Distance=5): 4,3,2,1 4,2 (Distance=1): 4,3,2 4,3 (Distance=6): 4,3 4,4 (Distance=0): 4
Data Races
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