/// <summary>
/// Creates graph consisting of strongly connected components only and then returns the
/// minimum vertex among all the strongly connected components graph, ignores single vertex graph since it can't have a cycle
/// potentially can return null.
/// </summary>
/// <param name="sccs"></param>
/// <param name="graph"></param>
/// <returns></returns>
private Nullable <int> LeastIndexSCC(List <HashSet <int> > sccs, IDigraph graph)
{
int min = int.MaxValue;
Nullable <int> minvertex = null;
HashSet <int> minscc = null;
foreach (HashSet <int> component in sccs)
{
if (component.Count == 1)
{
continue;
}
foreach (int vertex in component)
{
if (vertex < min)
{
min = vertex;
minvertex = vertex;
minscc = component;
}
}
}
if (minvertex == null)
{
return(null);
}
IDigraph graphscc = new Digraph(graph.VertexCount);
for (int i = 0; i < graph.VertexCount; i++)
{
graphscc.AddVertex();
}
for (int i = 0; i < graph.VertexCount; i++)
{
if (minscc.Contains(i))
{
if (graph.GetDegreeOut(i) > 0)
{
foreach (int neighbor in graph.GetVertexNeighborsOut(i))
{
if (minscc.Contains(neighbor))
{
graphscc.AddEdge(i, neighbor);
}
}
}
}
}
Nullable <int> potentialminvertex = null;
if (graphscc.GetDegreeOut(min) > 0 || graphscc.GetDegreeIn(min) > 0)
{
potentialminvertex = minvertex;
}
return(potentialminvertex);
}
/// <summary>
/// (DIRECTED GRAPH) -Create a subgraph of an input graph between a start and end vertex (includes start and end vertex)
/// </summary>
/// <param name="startindex"></param>
/// <param name="endvertex"></param>
/// <param name="graph"></param>
/// <returns></returns>
public IDigraph CreateSubGraph(int startindex, int endvertex, IDigraph graph)
{
IDigraph subgraph = new Digraph(graph.VertexCount);
for (int i = 0; i < graph.VertexCount; i++)
{
subgraph.AddVertex();
}
for (int i = startindex; i <= endvertex; i++)
{
List <int> neighbors = (List <int>)graph.GetVertexNeighborsOut(i);
foreach (int neighbor in neighbors)
{
if (neighbor >= startindex && neighbor <= endvertex)
{
subgraph.AddEdge(i, neighbor);
}
}
}
return(subgraph);
}
/// <summary>
/// (DIRECTED GRAPH) -Create a copy of the directed graph that is reversed
/// </summary>
/// <param name="graph"></param>
/// <returns></returns>
public IDigraph ReverseGraph(IDigraph graph)
{
IDigraph reversegraph = new Digraph(graph.VertexCount);
for (int i = 0; i < graph.VertexCount; i++)
{
reversegraph.AddVertex();
}
for (int i = 0; i < graph.VertexCount; i++)
{
List <int> vertexneighbors = (List <int>)graph.GetVertexNeighborsOut(i);
//for each vertex that is connected, create a reverse edge with its neighbors
if (vertexneighbors.Count > 0)
{
foreach (int neighbor in vertexneighbors)
{
reversegraph.AddEdge(neighbor, i);
}
}
}
return(reversegraph);
}