private List <Edge> FindAugmentingPath(UndirectedGraph graph, List <Edge> currentMatching)
{
Dictionary <int, UndirectedGraph> forest = new Dictionary <int, UndirectedGraph>();
List <int> unmarkedV = new List <int>(Enumerable.Range(0, graph.VerticeCount()));
List <Edge> unmarkedE = graph.Edges.Except(currentMatching, new EdgeComparer()).ToList();
List <int> exposedV = GetExposedV(graph, currentMatching);
foreach (int v in exposedV)
{
forest[v] = new UndirectedGraph(graph.VerticeCount());
}
while (GetEvenDistanceV(forest, unmarkedV) != -1)
{
int targetV = GetEvenDistanceV(forest, unmarkedV);
while (GetUnmarkedE(targetV, unmarkedE) != null)
{
Edge targetE = GetUnmarkedE(targetV, unmarkedE);
int secondV = targetE.V1 == targetV ? targetE.V2 : targetE.V1;
if (!InForest(forest, secondV))
{
//secondV is matched, so add its matched edge and targetE to forest[targetV]
int matchingV = GetMatchingV(currentMatching, secondV);
forest[GetVerticeRoot(forest, targetV)].AddEdge(targetE.V1, targetE.V2);
forest[GetVerticeRoot(forest, targetV)].AddEdge(secondV, matchingV);
}
else
{
if (!OddForestDistance(forest, secondV))
{
if (GetVerticeRoot(forest, targetV) != GetVerticeRoot(forest, secondV))
{
return(GetPathFromRoot(forest[GetVerticeRoot(forest, targetV)], GetVerticeRoot(forest, targetV), targetV).
Concat(new List <Edge>()
{
new Edge(targetV, secondV)
}).
Concat(GetPathToRoot(forest[GetVerticeRoot(forest, secondV)], GetVerticeRoot(forest, secondV), secondV)).ToList());
}
else
{
//Contract a blossom in G
List <Edge> blossom = GetBlossom(targetV, secondV, forest);
UndirectedGraph contractedGraph = Contract(graph, blossom, targetV);
List <Edge> newMatching = Contract(currentMatching, blossom, targetV);
List <Edge> path = FindAugmentingPath(contractedGraph, newMatching);
return(Lift(path, blossom, targetV, graph, currentMatching));
}
}
}
unmarkedE.Remove(targetE);
}
unmarkedV.Remove(targetV);
}
return(new List <Edge>());
}
private List <int> GetExposedV(UndirectedGraph graph, List <Edge> currentMatching)
{
List <int> exposedV = new List <int>(Enumerable.Range(0, graph.VerticeCount()));
foreach (Edge e in currentMatching)
{
exposedV.Remove(e.V1);
exposedV.Remove(e.V2);
}
return(exposedV);
}