/// <summary>
/// Computes the number of eulerian trail in the graph. If negative,
/// there is an eulerian circuit.
/// </summary>
/// <param name="g"></param>
/// <returns>number of eulerian trails</returns>
public static int ComputeEulerianPathCount(IVertexAndEdgeListGraph g)
{
if (g == null)
{
throw new ArgumentNullException("g");
}
int odd = AlgoUtility.OddVertices(g).Count;
if (odd == 0)
{
return(-1);
}
if (odd % 2 != 0)
{
return(0);
}
else if (odd == 0)
{
return(1);
}
else
{
return(odd / 2);
}
}
/// <summary>
/// Adds temporary edges to the graph to make all vertex even.
/// </summary>
/// <param name="g"></param>
/// <returns></returns>
public EdgeCollection AddTemporaryEdges(IMutableVertexAndEdgeListGraph g)
{
if (g == null)
{
throw new ArgumentNullException("g");
}
// first gather odd edges.
VertexCollection oddVertices = AlgoUtility.OddVertices(g);
// check that there are an even number of them
if (oddVertices.Count % 2 != 0)
{
throw new Exception("number of odd vertices in not even!");
}
// add temporary edges to create even edges:
EdgeCollection ec = new EdgeCollection();
bool found, foundbe, foundadjacent;
while (oddVertices.Count > 0)
{
IVertex u = oddVertices[0];
// find adjacent odd vertex.
found = false;
foundadjacent = false;
foreach (IEdge e in g.OutEdges(u))
{
IVertex v = e.Target;
if (v != u && oddVertices.Contains(v))
{
foundadjacent = true;
// check that v does not have an out-edge towards u
foundbe = false;
foreach (IEdge be in g.OutEdges(v))
{
if (be.Target == u)
{
foundbe = true;
break;
}
}
if (foundbe)
{
continue;
}
// add temporary edge
IEdge tempEdge = g.AddEdge(v, u);
// add to collection
ec.Add(tempEdge);
// remove u,v from oddVertices
oddVertices.Remove(u);
oddVertices.Remove(v);
// set u to null
found = true;
break;
}
}
if (!foundadjacent)
{
// pick another vertex
if (oddVertices.Count < 2)
{
throw new Exception("Eulerian trail failure");
}
IVertex v = oddVertices[1];
IEdge tempEdge = g.AddEdge(u, v);
// add to collection
ec.Add(tempEdge);
// remove u,v from oddVertices
oddVertices.Remove(u);
oddVertices.Remove(v);
// set u to null
found = true;
}
if (!found)
{
oddVertices.Remove(u);
oddVertices.Add(u);
}
}
temporaryEdges = ec;
return(ec);
}