/// <summary>
/// Trace back path from destination to source using parent map.
/// </summary>
private ShortestPathResult <T, W> tracePath(IDiGraph <T> graph,
Dictionary <T, T> parentMap, T source, T destination)
{
//trace the path
var pathStack = new Stack <T>();
pathStack.Push(destination);
var currentV = destination;
while (!Equals(currentV, default(T)) && !Equals(parentMap[currentV], default(T)))
{
pathStack.Push(parentMap[currentV]);
currentV = parentMap[currentV];
}
//return result
var resultPath = new List <T>();
var resultLength = @operator.DefaultValue;
while (pathStack.Count > 0)
{
resultPath.Add(pathStack.Pop());
}
for (var i = 0; i < resultPath.Count - 1; i++)
{
resultLength = @operator.Sum(resultLength,
graph.GetVertex(resultPath[i]).GetOutEdge(graph.GetVertex(resultPath[i + 1])).Weight <W>());
}
return(new ShortestPathResult <T, W>(resultPath, resultLength));
}
/// <summary>
/// Returns the vertices in Topologically Sorted Order.
/// </summary>
public List <T> GetTopSort(IDiGraph <T> graph)
{
var inEdgeMap = new Dictionary <T, int>();
var kahnQueue = new Queue <T>();
foreach (var vertex in graph.VerticesAsEnumberable)
{
inEdgeMap.Add(vertex.Key, vertex.InEdgeCount);
//init queue with vertices having not in edges
if (vertex.InEdgeCount == 0)
{
kahnQueue.Enqueue(vertex.Key);
}
}
//no vertices with zero number of in edges
if (kahnQueue.Count == 0)
{
throw new Exception("Graph has a cycle.");
}
var result = new List <T>();
int visitCount = 0;
//until queue is empty
while (kahnQueue.Count > 0)
{
//cannot exceed vertex number of iterations
if (visitCount > graph.VerticesCount)
{
throw new Exception("Graph has a cycle.");
}
//pick a neighbour
var nextPick = graph.GetVertex(kahnQueue.Dequeue());
//if in edge count is 0 then ready for result
if (inEdgeMap[nextPick.Key] == 0)
{
result.Add(nextPick.Key);
}
//decrement in edge count for neighbours
foreach (var edge in nextPick.OutEdges)
{
inEdgeMap[edge.TargetVertexKey]--;
kahnQueue.Enqueue(edge.TargetVertexKey);
}
visitCount++;
}
return(result);
}
public List <MinCutEdge <T> > ComputeMinCut(IDiGraph <T> graph,
T source, T sink)
{
if (this.@operator == null)
{
throw new ArgumentException("Provide an operator implementation for generic type W during initialization.");
}
if (!graph.IsWeightedGraph)
{
if ([email protected]() != typeof(int))
{
throw new ArgumentException("Edges of unweighted graphs are assigned an imaginary weight of one (1)." +
"Provide an appropriate IFlowOperators<int> operator implementation during initialization.");
}
}
var edmondsKarpMaxFlow = new EdmondKarpMaxFlow <T, W>(@operator);
var maxFlowResidualGraph = edmondsKarpMaxFlow
.computeMaxFlowAndReturnResidualGraph(graph, source, sink);
//according to Min Max theory
//the Min Cut can be obtained by Finding edges
//from Reachable Vertices from Source
//to unreachable vertices in residual graph
var reachableVertices = getReachable(maxFlowResidualGraph, source);
var result = new List <MinCutEdge <T> >();
foreach (var vertex in reachableVertices)
{
foreach (var edge in graph.GetVertex(vertex).OutEdges)
{
//if unreachable
if (!reachableVertices.Contains(edge.TargetVertexKey))
{
result.Add(new MinCutEdge <T>(vertex, edge.TargetVertexKey));
}
}
}
return(result);
}
/// <summary>
/// Find shortest distance to target.
/// </summary>
public ShortestPathResult <T, W> FindShortestPath(IDiGraph <T> graph,
T source, T destination)
{
//regular argument checks
if (graph == null || graph.GetVertex(source) == null ||
graph.GetVertex(destination) == null)
{
throw new ArgumentException("Empty Graph or invalid source/destination.");
}
if (this.@operator == null)
{
throw new ArgumentException("Provide an operator implementation for generic type W during initialization.");
}
if (!graph.IsWeightedGraph)
{
if ([email protected]() != typeof(int))
{
throw new ArgumentException("Edges of unweighted graphs are assigned an imaginary weight of one (1)." +
"Provide an appropriate IShortestPathOperators<int> operator implementation during initialization.");
}
}
var progress = new Dictionary <T, W>();
var parentMap = new Dictionary <T, T>();
foreach (var vertex in graph.VerticesAsEnumberable)
{
parentMap.Add(vertex.Key, default(T));
progress.Add(vertex.Key, @operator.MaxValue);
}
progress[source] = @operator.DefaultValue;
var iterations = graph.VerticesCount - 1;
var updated = true;
while (iterations > 0 && updated)
{
updated = false;
foreach (var vertex in graph.VerticesAsEnumberable)
{
//skip not discovered nodes
if (progress[vertex.Key].Equals(@operator.MaxValue))
{
continue;
}
foreach (var edge in vertex.OutEdges)
{
var currentDistance = progress[edge.TargetVertexKey];
var newDistance = @operator.Sum(progress[vertex.Key],
vertex.GetOutEdge(edge.TargetVertex).Weight <W>());
if (newDistance.CompareTo(currentDistance) < 0)
{
updated = true;
progress[edge.TargetVertexKey] = newDistance;
parentMap[edge.TargetVertexKey] = vertex.Key;
}
}
}
iterations--;
if (iterations < 0)
{
throw new Exception("Negative cycle exists in this graph.");
}
}
return(tracePath(graph, parentMap, source, destination));
}
