void FillMaximalMatching(BipartiteGraphMatching <T> matching)
{
GetMaximalMatchingFSet fSet = new GetMaximalMatchingFSet(Data.VSize);
do
{
fSet.Clear();
var freeUVertexList = Data.GetUVertexList().Where(x => !IsMatchedVertex(x));
foreach (var uVertex in freeUVertexList)
{
Color bfsColor = Color.CreateColor();
DoBFSearch(uVertex, (x, y) =>
IsMatchedEdge(x, y) ? Data.IsVVertex(x) : Data.IsUVertex(x)
, (x, y) =>
Data.UpdateEdgeData(x, y, edgeData => edgeData.WithColor(bfsColor))
, x => {
if (Data.IsVVertex(x) && !IsMatchedVertex(x))
{
if (IsInFSet(x))
{
fSet.UpdateItem(x.GetData <GetMaximalMatchingVertexInFSetData>().ItemIndex, new GetMaximalMatchingFSetItem(x, bfsColor));
}
else
{
int itemIndex = fSet.AddItem(new GetMaximalMatchingFSetItem(x, bfsColor));
x.Data = new GetMaximalMatchingVertexInFSetData(itemIndex);
}
return(false);
}
return(true);
});
}
foreach (var fSetItem in fSet)
{
DoDFSearch(fSetItem.Vertex, (x, y) => Data.GetEdgeData(x, y).Color == fSetItem.BfsColor
, (x, y) => {
var uVertex = matching.Data.GetUVertex(Data.GetUVertex(x, y).Handle);
var vVertex = matching.Data.GetVVertex(Data.GetVVertex(x, y).Handle);
if (IsMatchedEdge(x, y))
{
Data.GetEdgeData(x, y).WithData(null);
matching.DeleteEdge(uVertex, vVertex);
}
else
{
Data.UpdateEdgeData(x, y, edgeData => edgeData.WithData(new GetMaximalMatchingMatchedData()));
matching.CreateEdge(uVertex, vVertex);
}
}, x => {
bool stopSearch = Data.IsUVertex(x) && !IsMatchedVertex(x);
x.Data = new GetMaximalMatchingMatchedData();
return(stopSearch ? false : true);
});
}
}while(fSet.Size != 0);
ClearData(true, true);
}
BipartiteGraphMatching <T> GetMaximalMatchingCore()
{
BipartiteGraphMatching <T> matching = Clone <BipartiteGraphMatching <T> >(false);
if (Size != 0)
{
FillMaximalMatching(matching);
}
return(matching);
}
public BipartiteGraphMatching <T> GetAssignmentMatching()
{
if (Data.USize != Data.VSize || Properties.IsNegativeWeighted || !IsComplete())
{
throw new InvalidOperationException();
}
BipartiteGraphMatching <T> graph = Clone <BipartiteGraphMatching <T> >(false);
Func <int, int, double, EdgeData, EdgeData> func1 = (row, column, minVal, x) => {
var edgeData = x.WithWeight(x.Weight - minVal);
if (MathUtils.AreEqual(edgeData.Weight, 0))
{
graph.EnsureEdge(column, row, x.Weight);
}
return(edgeData);
};
Func <int, int, double, EdgeData, EdgeData> func2 = (row, column, minVal, x) => {
var edgeData = x.WithWeight(x.Weight + minVal);
if (!MathUtils.AreEqual(edgeData.Weight, 0))
{
graph.EnsureNoEdge(column, row);
}
return(edgeData);
};
RectMatrix <EdgeData, Color> matrix = Data.Matrix.Clone();
int rowCount = matrix.Size.RowCount;
for (int n = 0; n < rowCount; n++)
{
double minVal = matrix.GetRowItemList(n).Select(x => x.Weight).Min();
matrix.TranslateRow(n, func1, minVal);
}
if (graph.IsPerfect())
{
return(graph);
}
int columnCount = matrix.Size.ColumnCount;
for (int n = 0; n < columnCount; n++)
{
double minVal = matrix.GetColumnItemList(n).Select(x => x.Weight).Min();
matrix.TranslateColumn(n, func1, minVal);
}
if (graph.IsPerfect())
{
return(graph);
}
while (true)
{
var matching = graph.GetMaximalMatchingCore();
if (matching.IsPerfect())
{
return(CloneWithEdges(matching));
}
Color color1 = Color.CreateColor();
matching.Data.GetVVertexList()
.Where(x => x.Degree != 0)
.ForEach(x => matrix.RowAttributes[x.Handle] = color1);
Color color2 = Color.CreateColor();
matrix.TranslateRowAttributes((row, rowColor) => rowColor != color1, x => color2);
matrix.ForEach((row, column, rowColor, columnColor, x) => rowColor == color2 && MathUtils.AreEqual(x.Weight, 0), (row, column, x) => {
matrix.ColumnAttributes[column] = color2;
for (int n = 0; n < matrix.Size.RowCount; n++)
{
if (matching.AreVerticesAdjacent(column, n))
{
matrix.RowAttributes[n] = color2;
}
}
});
Color color3 = Color.CreateColor();
matrix.TranslateColumnAttributes((column, columnColor) => columnColor == color2, x => color3);
matrix.TranslateRowAttributes((row, rowColor) => rowColor != color2, x => color3);
double minValue = matrix.GetItems((row, column, rowColor, columnColor, x) => rowColor != color3 && columnColor != color3).Select(x => x.Weight).Min();
matrix.Translate((row, column, rowColor, columnColor, x) => rowColor != color3 && columnColor != color3, func1, minValue);
matrix.Translate((row, column, rowColor, columnColor, x) => rowColor == color3 && columnColor == color3, func2, minValue);
}
}
