public Edmonds_Karp(WeightGraph weightGraph, int s, int t)
{
_weightGraph = weightGraph;
_s = s;
_t = t;
if (!weightGraph.Directed)
{
throw new Exception("directed graph can be supported");
}
if (_weightGraph.V < 2)
{
throw new Exception("vertex must be more than 2");
}
_weightGraph.ValidateNumber(s);
_weightGraph.ValidateNumber(t);
if (s == t)
{
throw new Exception("source point and sink point can't be same");
}
_residualQuantityGraph = new WeightGraph(_weightGraph.V, true);
for (int v = 0; v < _weightGraph.V; v++)
{
foreach (var w in _weightGraph.GetAllContiguousEdge(v))
{
int weight = _weightGraph.GetWeight(v, w);
_residualQuantityGraph.AddEdge(v, w, weight);
_residualQuantityGraph.AddEdge(w, v, 0);
}
}
while (true)
{
List <int> path = GetArgumentingPath();
if (path.Count == 0)
{
break;
}
int f = int.MaxValue;
for (int i = 1; i < path.Count; i++)
{
int v = path[i - 1];
int w = path[i];
f = Math.Min(f, _residualQuantityGraph.GetWeight(v, w));
}
MaxFlow += f;
for (int i = 1; i < path.Count; i++)
{
int v = path[i - 1];
int w = path[i];
int weight = _residualQuantityGraph.GetWeight(v, w);
int residualQuantity = _residualQuantityGraph.GetWeight(w, v);
_residualQuantityGraph.SetWeight(v, w, weight - f);
_residualQuantityGraph.SetWeight(w, v, residualQuantity + f);
}
}
}
public BinaryPartGraphMatch(IAdjacency iAdjacency)
{
_iAdjacency = iAdjacency;
BinaryPartitionDetection binaryPartitionDetection = new BinaryPartitionDetection(iAdjacency);
if (!binaryPartitionDetection.IsBinaryPartition)
{
throw new Exception("you must use two partite graph");
}
int[] colors = binaryPartitionDetection.Colors;
WeightGraph weightGraph = new WeightGraph(iAdjacency.V + 2, true);
for (int v = 0; v < iAdjacency.V; v++)
{
if (colors[v] == 0)
{
weightGraph.AddEdge(iAdjacency.V, v, 1);
}
if (colors[v] == 1)
{
weightGraph.AddEdge(v, iAdjacency.V + 1, 1);
}
foreach (var w in iAdjacency.GetAllContiguousEdge(v))
{
if (colors[v] == 0)
{
weightGraph.AddEdge(v, w, 1);
}
else if (colors[v] == 1)
{
weightGraph.AddEdge(w, v, 1);
}
}
}
Edmonds_Karp edmondsKarp = new Edmonds_Karp(weightGraph, iAdjacency.V, iAdjacency.V + 1);
MaxMatch = edmondsKarp.MaxFlow;
IsPerfectMatch = MaxMatch * 2 == iAdjacency.V;
}
