/// <summary>
/// Recursive DFS subroutine used by Ford fulkerson's algorithm
/// </summary>
/// <param name="vertexId"></param>
/// <param name="endId"></param>
/// <param name="backtrack"></param>
/// <returns></returns>
private bool DFS(string vertexId, string endId, Dictionary <string, string> backtrack)
{
if (!string.IsNullOrEmpty(vertexId))
{
// Check Error condition
if (vertexId == endId)
{
//We have found a path
return(true);
}
else
{
GraphVertex currentVertex = Graph.AllVertices[vertexId];
foreach (GraphVertex neighbour in currentVertex.Neighbours)
{
string edgeId = currentVertex.Id + "#" + neighbour.Id;
if (!backtrack.ContainsKey(neighbour.Id) && Graph.EdgeWeights[edgeId] > 0)
{
backtrack[neighbour.Id] = currentVertex.Id;
if (DFS(neighbour.Id, endId, backtrack))
{
return(true);
}
}
}
}
}
return(false);
}
/// <summary>
/// Gets all the vertices that can be reached from the source
/// We can do BFS to get this.
/// </summary>
/// <param name="graph">graph object</param>
/// <param name="startId">id of the source vertex</param>
/// <returns></returns>
private Dictionary <GraphVertex, bool> GetAllVerticesThatCanBeReachedFromSrc(Graph graph, string startId)
{
Dictionary <GraphVertex, bool> setOfVerticesFromSource = new Dictionary <GraphVertex, bool>();
//Do a BFS to get all the vertices that can be reached from the source
Queue <GraphVertex> queue = new Queue <GraphVertex>();
GraphVertex source = graph.AllVertices[startId];
queue.Enqueue(source);
setOfVerticesFromSource[source] = true;
while (queue.Count > 0)
{
GraphVertex vertex = queue.Dequeue();
foreach (GraphVertex neighbour in vertex.Neighbours)
{
if (graph.EdgeWeights[vertex.Id + "#" + neighbour.Id] != 0 && !setOfVerticesFromSource.ContainsKey(neighbour))
{
// Edges with flow 0 should not be considered
// vertices in setOfVerticesFromSource keeps track of the visited vertices
setOfVerticesFromSource[neighbour] = true;
queue.Enqueue(neighbour);
}
}
}
return(setOfVerticesFromSource);
}
/// <summary>
/// Do the BFS and get the augmented path and return the current flow in that path
/// </summary>
/// <param name="graph">graph object</param>
/// <param name="startId">source in the graph</param>
/// <param name="endId">sink in the graph</param>
/// <returns>current flow in that path</returns>
public int BFS(Graph graph, string startId, string endId)
{
Dictionary <string, string> parentDict = new Dictionary <string, string>();
Queue <GraphVertex> queue = new Queue <GraphVertex>();
queue.Enqueue(graph.AllVertices[startId]);
parentDict[startId] = string.Empty;
while (queue.Count > 0)
{
GraphVertex vertex = queue.Dequeue();
if (vertex.Id == endId)
{
// found the augmented path and get the current flow
return(GetTheFlowInCurrentPath(graph, parentDict, startId, endId));
}
foreach (GraphVertex neighbour in vertex.Neighbours)
{
if (!parentDict.ContainsKey(neighbour.Id) && graph.EdgeWeights[vertex.Id + "#" + neighbour.Id] != 0)
{
// the neighbour should not have been visited and the weight of the edge should not be 0
queue.Enqueue(neighbour);
parentDict[neighbour.Id] = vertex.Id;
}
}
}
return(-1);
}
/// <summary>
/// Add a weighted directed edge
/// </summary>
/// <param name="startId"></param>
/// <param name="endId"></param>
/// <param name="weight"></param>
public void AddEdge(string startId, string endId, int weight)
{
if (!AllVertices.ContainsKey(startId))
{
AllVertices[startId] = new GraphVertex(startId);
}
if (!AllVertices.ContainsKey(endId))
{
AllVertices[endId] = new GraphVertex(endId);
}
AllVertices[startId].Neighbours.Add(AllVertices[endId]);
EdgeWeights[startId + "#" + endId] = weight;
}