/// <summary>
/// Return true if the graph is (complete) bipartite
/// Time complexity: O(V + E)
/// </summary>
/// <param name="graph">graph</param>
/// <returns>(bool, bool) - the first item stands for bipartite and the second item stands for complete
/// (true, true) - complete bipartite graph
/// (true, false) - bipartite graph
/// (false, - ) - the graph is not (complete) bipartite</returns>
public static Tuple <bool, bool> IsBipartiteGraph(IGraphInterface graph)
{
// Variable
IVertexInterface vertex;
List <IVertexInterface> neighboursVertexList;
bool isFirstPartite, isBipartite = true;
HashSet <IVertexInterface> firstPartite = new HashSet <IVertexInterface>();
HashSet <IVertexInterface> secondPartite = new HashSet <IVertexInterface>();
Queue <IVertexInterface> vertexQueue = new Queue <IVertexInterface>();
vertex = graph.GetFirstVertex();
vertexQueue.Enqueue(vertex);
firstPartite.Add(vertex);
while (vertexQueue.Count != 0)
{
vertex = vertexQueue.Dequeue();
neighboursVertexList = graph.Neighbours(vertex);
if (firstPartite.Contains(vertex))
{
isFirstPartite = true;
}
else
{
isFirstPartite = false;
}
foreach (IVertexInterface neighbourVertex in neighboursVertexList)
{
if (!firstPartite.Contains(neighbourVertex) && !secondPartite.Contains(neighbourVertex))
{
if (isFirstPartite)
{
secondPartite.Add(neighbourVertex);
}
else
{
firstPartite.Add(neighbourVertex);
}
vertexQueue.Enqueue(neighbourVertex);
}
else
{
if ((firstPartite.Contains(neighbourVertex) && isFirstPartite) || (secondPartite.Contains(neighbourVertex) && !isFirstPartite))
{
isBipartite = false;
}
}
}
}
if (!isBipartite)
{
return(new Tuple <bool, bool>(false, false));
}
// Set bipartites
graph.GetGraphProperty().SetPartites(firstPartite.ToList(), secondPartite.ToList());
// Variable
int countFirstPartiteVertex = firstPartite.Count;
int countSecondPartiteVertex = secondPartite.Count;
// Is the graph a complete bipartite graph
foreach (Vertex firstPartiteVertex in firstPartite)
{
if (graph.CountNeighbours(firstPartiteVertex) != countSecondPartiteVertex)
{
return(new Tuple <bool, bool>(true, false));
}
}
foreach (Vertex secondPartiteVertex in secondPartite)
{
if (graph.CountNeighbours(secondPartiteVertex) != countFirstPartiteVertex)
{
return(new Tuple <bool, bool>(true, false));
}
}
return(new Tuple <bool, bool>(true, true));
}