/// <summary>
/// We cannot use the same method as we used for undirected graphs
/// We can use Kosaraju’s DFS based simple algorithm with 2 DFS passes
/// Steps are as follows:
/// 1. Initialize all vertices' isvisited as false
/// 2. Do DFS on an arbitarily selected vertex v. If all the vertices is not visited return false
/// 3. Initialize all vertices' isvisited as false
/// 4. Reverse all the edges of the graph
/// 5. Do DFS on the same vertex v. If all the vertices are not visited return false.
/// Return true
///
///
/// The running time here is O(V+E)
/// </summary>
/// <param name="udg"></param>
/// <returns></returns>
public bool IsDirectedGraphStronglyConnected(DirectedGraphWithVertexDictionary dg)
{
if (dg.AllVertices.Values.Count == 0)
{
// error condition
throw new ArgumentException("The graph is empty");
}
// 1. Initialize all vertices' isvisited as false
foreach (GraphVertex vertex in dg.AllVertices.Values)
{
vertex.IsVisited = false;
}
// select the arbitrary vertex
GraphVertex arbVertex = dg.AllVertices.Values.ElementAt(0);
//2. Do DFS on an arbitarily selected vertex v. If all the vertices is not visited return false
DFS(arbVertex);
foreach (GraphVertex vertex in dg.AllVertices.Values)
{
if (!vertex.IsVisited)
{
return(false);
}
}
//3.Initialize all vertices' isvisited as false
foreach (GraphVertex vertex in dg.AllVertices.Values)
{
vertex.IsVisited = false;
}
//4. Reverse all the edges of the graph
dg = dg.ReverseDirectedGraphWithVertexDictionary();
// 5. Do DFS on the same vertex v. If all the vertices are not visited return false.
DFS(dg.AllVertices[arbVertex.Data]);
foreach (GraphVertex vertex in dg.AllVertices.Values)
{
if (!vertex.IsVisited)
{
return(false);
}
}
return(true);
}
public SnakeAndLadder(int sAndLBoardLength, List <GraphEdge> snakesAndLadders)
{
Board = new DirectedGraphWithVertexDictionary();
for (int i = 1; i <= sAndLBoardLength; i++)
{
for (int j = 1; j <= 6 && i + j <= sAndLBoardLength; j++) // This represents the different outcomes of the dice throw
{
// i+j<= sAndLBoardLength handles the overflow(from the board) corner case
Board.AddEdge(i, i + j);
}
}
foreach (GraphEdge edge in snakesAndLadders)
{
Board.MergeVertex(edge.StartEdgeId, edge.EndEdgeId);
}
}
public static void TestStronglyConnectedGraph()
{
StronglyConnectedGraph scg = new StronglyConnectedGraph();
UndirectedGraph notStronglyConnected = GraphProbHelper.CreateUndirectedGraphNotStronglyConnected();
Console.WriteLine("The graph is strongly connected. Expected: False, Actual: {0}", scg.IsUndirectedGraphStronglyConnected(notStronglyConnected));
UndirectedGraph stronglyConnected = GraphProbHelper.CreateUndirectedGraphStronglyConnected();
Console.WriteLine("The graph is strongly connected. Expected: True, Actual: {0}", scg.IsUndirectedGraphStronglyConnected(stronglyConnected));
DirectedGraphWithVertexDictionary dg = GraphProbHelper.CreateDirectedGraphWithVertexDictStronglyConnected();
Console.WriteLine("The graph is strongly connected. Expected: True, Actual: {0}", scg.IsDirectedGraphStronglyConnected(dg));
dg = GraphProbHelper.CreateDirectedGraphWithVertexDictNotStronglyConnected();
Console.WriteLine("The graph is strongly connected. Expected: False, Actual: {0}", scg.IsDirectedGraphStronglyConnected(dg));
}
public static DirectedGraphWithVertexDictionary ReverseDirectedGraphWithVertexDictionary(this DirectedGraphWithVertexDictionary dg)
{
// Add all edges to this dictionary where for an edge u->v add it as dict[v].Add(u)
Dictionary <GraphVertex, List <GraphVertex> > allVertices = new Dictionary <GraphVertex, List <GraphVertex> >();
foreach (GraphVertex vertex in dg.AllVertices.Values)
{
if (vertex.NeighbourVertices != null)
{
foreach (GraphVertex neighbour in vertex.NeighbourVertices)
{
if (!allVertices.ContainsKey(neighbour))
{
allVertices.Add(neighbour, new List <GraphVertex> {
vertex
});
}
else
{
allVertices[neighbour].Add(vertex);
}
}
}
}
// Make the changes to all the vertices in the directed graph
foreach (GraphVertex vertex in dg.AllVertices.Values)
{
if (allVertices.ContainsKey(vertex))
{
vertex.NeighbourVertices = allVertices[vertex];
}
else
{
vertex.NeighbourVertices = null;
}
}
return(dg);
}
