/// <summary>
/// Augmentation of the flows
/// </summary>
/// <param name="path">The augmentation path found</param>
private void Augment(FlowPath path)
{
foreach (KeyValuePair <FlowArc, int> arcEntry in path.Arcs)
{
this.Flows[arcEntry.Key] += path.AdditionalCapacity * arcEntry.Value;
}
}
/// <summary>
/// Search of augmentating path
/// </summary>
/// <param name="source">Begining of the path</param>
/// <param name="target">End of the path</param>
/// <param name="visited">List of already visited nodes</param>
/// <returns>An augmentating path OR null if none is found</returns>
private FlowPath PathFinder(FlowNode source, FlowNode target, List <FlowNode> visited)
{
// adding source to list of visited nodes
visited.Add(source);
// trivial ending of recursion
if (source == target)
{
FlowPath path = new FlowPath();
path.AdditionalCapacity = float.MaxValue;
return(path);
}
// searching for ongoing path
foreach (FlowArc arc in this.Arcs)
{
double delta = 0.0;
FlowPath path = null;
int sens = 0;
// is it a positive path ?
if (arc.Start == source && this.Flows[arc] < arc.Capacity && !visited.Contains(arc.End))
{
// recursive call on pathfinder
path = this.PathFinder(arc.End, target, new List <FlowNode>(visited));
delta = arc.Capacity - this.Flows[arc];
sens = 1;
}
// is it a negative path ?
if (arc.End == source && this.Flows[arc] > 0 && !visited.Contains(arc.Start))
{
// recursive call on pathfinder
path = this.PathFinder(arc.Start, target, new List <FlowNode>(visited));
delta = this.Flows[arc];
sens = -1;
}
// if an ongoing path has been found then
if (null != path)
{
// updating arcs and capacitiy
path.Arcs.Add(arc, sens);
path.AdditionalCapacity = Math.Min(delta, path.AdditionalCapacity);
return(path);
}
}
// if no ongoing path found then return null
return(null);
}
/// <summary>
/// Implementation of the Ford-Fulkerson algorithm
/// in order to calculate maximum flow
/// </summary>
private void CalculateMaximumFlow()
{
this.ResetCapacity();
// search path
FlowPath path = this.PathFinder(this.Source, this.Target, new List <FlowNode>());
// if path exists then augmentation of flows
while (null != path)
{
/* Only for debugging
* MessageBox.Show(path.ToString()); */
this.Augment(path);
// search new path
path = this.PathFinder(this.Source, this.Target, new List <FlowNode>());
}
}