FindAllPairShortestPaths(WeightedDiGraph <T, W> graph)
{
var workGraph = graph.Clone();
//add an extra vertex with zero weight edge to all nodes
var randomVetex = operators.RandomVertex();
if (workGraph.Vertices.ContainsKey(randomVetex))
{
throw new Exception("Random Vertex is not unique for given graph.");
}
workGraph.AddVertex(randomVetex);
foreach (var vertex in workGraph.Vertices)
{
workGraph.AddEdge(randomVetex, vertex.Key, operators.DefaultValue);
}
//now compute shortest path from random vertex to all other vertices
var bellmanFordSp = new BellmanFordShortestPath <T, W>(operators);
var bellFordResult = new Dictionary <T, W>();
foreach (var vertex in workGraph.Vertices)
{
var result = bellmanFordSp.FindShortestPath(workGraph, randomVetex, vertex.Key);
bellFordResult.Add(vertex.Key, result.Length);
}
//adjust edges so that all edge values are now +ive
foreach (var vertex in workGraph.Vertices)
{
foreach (var edge in vertex.Value.OutEdges.ToList())
{
vertex.Value.OutEdges[edge.Key] = operators.Substract(
operators.Sum(bellFordResult[vertex.Key], edge.Value),
bellFordResult[edge.Key.Value]);
}
}
workGraph.RemoveVertex(randomVetex);
//now run dijikstra for all pairs of vertices
//trace path
var dijikstras = new DijikstraShortestPath <T, W>(operators);
var finalResult = new List <AllPairShortestPathResult <T, W> >();
foreach (var vertexA in workGraph.Vertices)
{
foreach (var vertexB in workGraph.Vertices)
{
var source = vertexA.Key;
var dest = vertexB.Key;
var sp = dijikstras.FindShortestPath(workGraph, source, dest);
//no path exists
if (sp.Length.Equals(operators.MaxValue))
{
continue;
}
var distance = sp.Length;
var path = sp.Path;
finalResult.Add(new AllPairShortestPathResult <T, W>(source, dest, distance, path));
}
}
return(finalResult);
}
FindAllPairShortestPaths(IDiGraph <T> graph)
{
if (this.@operator == null)
{
throw new ArgumentException("Provide an operator implementation for generic type W during initialization.");
}
if (!graph.IsWeightedGraph)
{
if ([email protected]() != typeof(int))
{
throw new ArgumentException("Edges of unweighted graphs are assigned an imaginary weight of one (1)." +
"Provide an appropriate IJohnsonsShortestPathOperators<T, int> operator implementation during initialization.");
}
}
var workGraph = clone(graph);
//add an extra vertex with zero weight edge to all nodes
var randomVetex = @operator.RandomVertex();
if (workGraph.Vertices.ContainsKey(randomVetex))
{
throw new Exception("Random Vertex is not unique for given graph.");
}
workGraph.AddVertex(randomVetex);
foreach (var vertex in workGraph.Vertices)
{
workGraph.AddEdge(randomVetex, vertex.Key, @operator.DefaultValue);
}
//now compute shortest path from random vertex to all other vertices
var bellmanFordSp = new BellmanFordShortestPath <T, W>(@operator);
var bellFordResult = new Dictionary <T, W>();
foreach (var vertex in workGraph.Vertices)
{
var result = bellmanFordSp.FindShortestPath(workGraph, randomVetex, vertex.Key);
bellFordResult.Add(vertex.Key, result.Length);
}
//adjust edges so that all edge values are now +ive
foreach (var vertex in workGraph.Vertices)
{
foreach (var edge in vertex.Value.OutEdges.ToList())
{
vertex.Value.OutEdges[edge.Key] = @operator.Substract(
@operator.Sum(bellFordResult[vertex.Key], edge.Value),
bellFordResult[edge.Key.Key]);
}
}
workGraph.RemoveVertex(randomVetex);
//now run dijikstra for all pairs of vertices
//trace path
var dijikstras = new DijikstraShortestPath <T, W>(@operator);
var finalResult = new List <AllPairShortestPathResult <T, W> >();
foreach (var vertexA in workGraph.Vertices)
{
foreach (var vertexB in workGraph.Vertices)
{
var source = vertexA.Key;
var dest = vertexB.Key;
var sp = dijikstras.FindShortestPath(workGraph, source, dest);
//no path exists
if (sp.Length.Equals(@operator.MaxValue))
{
continue;
}
var distance = sp.Length;
var path = sp.Path;
finalResult.Add(new AllPairShortestPathResult <T, W>(source, dest, distance, path));
}
}
return(finalResult);
}
