// there is path from start to end in the residual network.
private bool HasAugmentingPath(FlowWeightedGraph <V> graph, V startVertex, V endVertex)
{
Queue <V> queue = new Queue <V>();
queue.Enqueue(startVertex);
marked[startVertex.GetHashCode()] = true;
while (queue.Count != 0)
{
var first = queue.Dequeue();
foreach (var edge in graph.Adjacency(first))
{
var other = edge.Other(first);
if (edge.ResidualCapacityToVertex(other) > 0 && !marked[other.GetHashCode()])
{
edgeTo[other.GetHashCode()] = edge;
marked[other.GetHashCode()] = true;
queue.Enqueue(other);
}
}
}
return(marked[endVertex.GetHashCode()]);
}
public void FordFulkerson(FlowWeightedGraph <V> graph, V startVertex, V endVertex)
{
value = 0.0;
// visit the graph and find a path from s to t, fill edgeto and marked arrays
// this terminates when there is no augmenting path ( all full forward edges and empty backward edges)
while (HasAugmentingPath(graph, startVertex, endVertex))
{
double bottle = Double.PositiveInfinity;
V begin = endVertex;
for (; begin.CompareTo(startVertex) != 0; begin = edgeTo[begin.GetHashCode()].Other(begin))
{
// minimum of the unused capacity in forward edge or available flow in backward edge
bottle = Math.Min(bottle, edgeTo[begin.GetHashCode()].ResidualCapacityToVertex(begin));
}
// now go thru the edge and add the residual capacity to augment the flow
begin = endVertex;
for (; begin.CompareTo(startVertex) != 0; begin = edgeTo[begin.GetHashCode()].Other(begin))
{
edgeTo[begin.GetHashCode()].AddResidualFlowToVertex(begin, bottle);
}
value += bottle;
}
}
