Exemple #1
0
        /// <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);
        }
Exemple #2
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        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);
            }
        }
Exemple #3
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        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));
        }
Exemple #4
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        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);
        }