private static int BreadthFirstSearch(
IWeightedGraph graph,
Vertex source,
Vertex target,
IWeightedGraph legalFlows,
out IDictionary<Vertex, Vertex> path)
{
path = new Dictionary<Vertex, Vertex>();
IDictionary<Vertex, int> pathCapacity = new Dictionary<Vertex, int>();
path[source] = null; // make sure source is not rediscovered
pathCapacity[source] = int.MaxValue;
Queue<Vertex> queue = new Queue<Vertex>();
queue.Enqueue(source);
while(queue.Count > 0)
{
Vertex u = queue.Dequeue();
foreach (Vertex v in graph.Neighbors(u))
{
// if there is available capacity between u and v,
// ... and v is not seen before in search
if (graph.GetCapacity(u, v) - legalFlows.GetCapacity(u, v) > 0 &&
path.ContainsKey(v) == false)
{
path[v] = u;
pathCapacity[v] = Math.Min(
pathCapacity[u],
graph.GetCapacity(u, v) - legalFlows.GetCapacity(u ,v));
if (!v.Equals(target)) queue.Enqueue(v);
else return pathCapacity[target];
}
}
}
return 0;
}
