public GraphColor[] Find3Colorings(UndirectedGraph <int, IEdge <int> > graph)
{
//Initialize structures
_graph = graph.Clone();
_availableColors = new HashSet <GraphColor> [_graph.VertexCount];
for (int i = 0; i < _graph.VertexCount; i++)
{
_availableColors[i] = new HashSet <GraphColor>()
{
GraphColor.Black, GraphColor.Gray, GraphColor.White
}
}
;
_coloring = new GraphColor?[_graph.VertexCount];
//Get all components of G
List <UndirectedGraph <int, IEdge <int> > > G_components = FindComponents(_graph);
foreach (UndirectedGraph <int, IEdge <int> > component in G_components)
{
//Find separator S for component
HashSet <int> S = PlanarSeparator.FindSeparator(component);
////Split component into smaller components
foreach (int v in S)
{
component.RemoveVertex(v);
}
List <UndirectedGraph <int, IEdge <int> > > components = FindComponents(component);
//One of components cannot be colored => whole G cannot be colored
//Slow version
if (!DnCColoring(components, S))
{
return(null);
}
//Fast version
//if (!BruteForceColoring(new List<UndirectedGraph<int, IEdge<int>>>(), _graph.Vertices.ToHashSet()))
// return null;
}
return(_coloring.Select(c => c.Value).ToArray());
}
public GraphColor[] Find3Colorings(UndirectedGraph <int, IEdge <int> > graph)
{
//Initialize structures
_graph = graph.Clone();
_availableColors = new HashSet <GraphColor> [_graph.VertexCount];
for (int i = 0; i < _graph.VertexCount; i++)
{
_availableColors[i] = new HashSet <GraphColor>()
{
GraphColor.Black, GraphColor.Gray, GraphColor.White
}
}
;
_coloring = new GraphColor?[_graph.VertexCount];
//Get all components of G
(List <UndirectedGraph <int, IEdge <int> > > list, Dictionary <int, int> dict)G_components = FindComponents(_graph);
foreach (UndirectedGraph <int, IEdge <int> > component in G_components.list)
{
//Find separator S for component
HashSet <int> S = PlanarSeparator.FindSeparator(component);
////Split component into smaller components
foreach (int v in S)
{
component.RemoveVertex(v);
}
(List <UndirectedGraph <int, IEdge <int> > >, Dictionary <int, int>)components = FindComponents(component);
//One of components cannot be colored => whole G cannot be colored
if (!DnCColoring(components, S).isColorable)
{
return(null);
}
}
return(_coloring.Select(c => c.Value).ToArray());
}
private bool DnCColoring(List <UndirectedGraph <int, IEdge <int> > > components, HashSet <int> s)
{
//Separator colored
if (s.Count == 0)
{
foreach (UndirectedGraph <int, IEdge <int> > component in components)
{
if (component.VertexCount < 15)
{
//Can't find separator for component - color using bruteforce
if (!DnCColoring(new List <UndirectedGraph <int, IEdge <int> > >(),
new HashSet <int>(component.Vertices)))
{
return(false);
}
}
else
{
HashSet <int> sPrim = PlanarSeparator.FindSeparator(component);
UndirectedGraph <int, IEdge <int> > componentCopy = component.Clone();
foreach (int vPrim in sPrim)
{
componentCopy.RemoveVertex(vPrim);
}
List <UndirectedGraph <int, IEdge <int> > > componentsPrim = FindComponents(componentCopy);
if (!DnCColoring(componentsPrim, sPrim))
{
return(false);
}
}
}
return(true);
}
//Separator still not colored
int v = s.First();
s.Remove(v);
foreach (GraphColor color in (GraphColor[])Enum.GetValues(typeof(GraphColor)))
{
if (!_availableColors[v].Contains(color))
{
continue;
}
//Color v with color
_coloring[v] = color;
bool moveToNextColor = false;
List <int> verticesWithTakenColor = new List <int>();
foreach (int n in _graph.AdjacentVertices(v))
{
if (_availableColors[n].Contains(color))
{
//Adjacent not colored vertex has no available color - invalid coloring
if (_availableColors[n].Count == 1)
{
//Reverse changes
foreach (int vertex in verticesWithTakenColor)
{
_availableColors[vertex].Add(color);
}
//Move to next v coloring
moveToNextColor = true;
break;
}
//Adjacent vertices cannot be colored with color
_availableColors[n].Remove(color);
verticesWithTakenColor.Add(n);
}
}
if (moveToNextColor)
{
continue;
}
if (DnCColoring(components, s))
{
return(true);
}
//Reverse changes
foreach (int vertex in verticesWithTakenColor)
{
_availableColors[vertex].Add(color);
}
}
s.Add(v);
return(false);
}
