/// <summary>
/// Find all possible paths between two vertices.
/// </summary>
/// <typeparam name="V"></typeparam>
/// <typeparam name="E"></typeparam>
/// <param name="graph"></param>
/// <param name="start"></param>
/// <param name="destination"></param>
/// <param name="vertexComparer"></param>
/// <returns></returns>
public static IEnumerable <IReadOnlyList <V> > FindAllPaths <V, E>(this IDirectedGraph <V, E> graph, V start, V destination,
IEqualityComparer <V> vertexComparer = null)
{
using (Trace.Entering())
{
vertexComparer = vertexComparer ?? EqualityComparer <V> .Default;
HashSet <V> used = new HashSet <V>(vertexComparer);
used.Add(start);
List <V> localPath = new List <V>();
IEnumerable <IReadOnlyList <V> > result = graph.FindAllPathsInternal(start, destination, localPath, used, vertexComparer);
return(result);
}
}
private static IEnumerable <List <V> > FindAllPathsInternal <V, E>(this IDirectedGraph <V, E> graph,
V start, V destination,
List <V> localPath,
HashSet <V> alreadyUsed,
IEqualityComparer <V> vertexComparer)
{
using (Trace.Entering())
{
localPath.Add(start);
var toGo = graph.GetEdgesGoingFrom(start)
.Select(x => x.To)
.ToHashSet(vertexComparer);
foreach (var to in toGo)
{
if (vertexComparer.Equals(to, destination))
{
localPath.Add(to);
// Provide the whole path.
List <V> result = localPath.ToList();
localPath.RemoveAt(localPath.Count - 1);
yield return(result);
// If the self-reference is not included yet.
if (!vertexComparer.Equals(start, to))
{
List <V> pathWithSelfreferencingDestination = null;
bool selfReferencingDestination = graph.GetEdges(destination, destination).Any();
if (selfReferencingDestination)
{
pathWithSelfreferencingDestination = result.ToList();
pathWithSelfreferencingDestination.Add(destination);
yield return(pathWithSelfreferencingDestination);
}
// If an edge to itself exists then include it to the result.
if (toGo.Contains(start))
{
var pathWithSelfReference = result.ToList();
pathWithSelfReference.Insert(result.Count - 1, start);
yield return(pathWithSelfReference);
if (selfReferencingDestination)
{
var pathWithBothSelfReferences = pathWithSelfReference.ToList();
pathWithBothSelfReferences.Add(destination);
yield return(pathWithBothSelfReferences);
}
}
}
}
else if (alreadyUsed.Add(to))
{
IEnumerable <List <V> > foundPaths = graph.FindAllPathsInternal(to, destination, localPath, alreadyUsed, vertexComparer);
foreach (var path in foundPaths)
{
// Return the path.
yield return(path);
}
alreadyUsed.Add(start);
}
}
localPath.RemoveAt(localPath.Count - 1);
}
}
