private bool dfs(DiGraphVertex <T> current,
HashSet <T> visited, HashSet <T> visiting)
{
visiting.Add(current.Value);
foreach (var edge in current.OutEdges)
{
//if we encountered a visiting vertex again
//then their is a cycle
if (visiting.Contains(edge.Value))
{
return(true);
}
if (visited.Contains(edge.Value))
{
continue;
}
if (dfs(edge, visited, visiting))
{
return(true);
}
}
visiting.Remove(current.Value);
visited.Add(current.Value);
return(false);
}
/// <summary>
/// Do a depth first search to find Strongly Connected by keeping track of
/// discovery nodes and checking for back edges using low/discovery time maps
/// </summary>
/// <param name="currentVertex"></param>
/// <param name="result"></param>
/// <param name="discovery"></param>
/// <param name="discoveryTimeMap"></param>
/// <param name="lowTimeMap"></param>
/// <param name="parent"></param>
/// <param name="discoveryTime"></param>
/// <returns></returns>
private void DFS(DiGraphVertex <T> currentVertex,
List <List <T> > result,
Dictionary <T, int> discoveryTimeMap, Dictionary <T, int> lowTimeMap,
Stack <T> pathStack,
HashSet <T> pathStackMap, ref int discoveryTime)
{
discoveryTimeMap.Add(currentVertex.Value, discoveryTime);
lowTimeMap.Add(currentVertex.Value, discoveryTime);
pathStack.Push(currentVertex.Value);
pathStackMap.Add(currentVertex.Value);
foreach (var edge in currentVertex.OutEdges)
{
if (!discoveryTimeMap.ContainsKey(edge.Value))
{
discoveryTime++;
DFS(edge, result, discoveryTimeMap, lowTimeMap,
pathStack, pathStackMap, ref discoveryTime);
//propogate lowTime index of neighbour so that ancestors can see it in DFS
lowTimeMap[currentVertex.Value] =
Math.Min(lowTimeMap[currentVertex.Value], lowTimeMap[edge.Value]);
}
else
{
//ignore cross edges
//even if edge vertex was already visisted
//update this so that ancestors can see it
if (pathStackMap.Contains(edge.Value))
{
lowTimeMap[currentVertex.Value] =
Math.Min(lowTimeMap[currentVertex.Value],
discoveryTimeMap[edge.Value]);
}
}
}
//if low is high this means we reached head of the DFS tree with strong connectivity
//now print items in the stack
if (lowTimeMap[currentVertex.Value] == discoveryTimeMap[currentVertex.Value])
{
var strongConnected = new List <T>();
while (!pathStack.Peek().Equals(currentVertex.Value))
{
var vertex = pathStack.Pop();
strongConnected.Add(vertex);
pathStackMap.Remove(vertex);
}
//add current vertex
var finalVertex = pathStack.Pop();
strongConnected.Add(finalVertex);
pathStackMap.Remove(finalVertex);
result.Add(strongConnected);
}
}
/// <summary>
/// Do a depth first search
/// </summary>
/// <param name="vertex"></param>
/// <param name="visited"></param>
/// <param name="pathStack"></param>
private void dfs(DiGraphVertex <T> vertex,
HashSet <T> visited, Stack <T> pathStack)
{
visited.Add(vertex.Value);
foreach (var edge in vertex.OutEdges)
{
if (!visited.Contains(edge.Value))
{
dfs(edge, visited, pathStack);
}
}
//add vertex to stack after all edges are visited
pathStack.Push(vertex.Value);
}
/// <summary>
/// In step two we just add all reachable nodes to result (connected componant)
/// </summary>
/// <param name="currentVertex"></param>
/// <param name="visited"></param>
/// <param name="finishStack"></param>
/// <param name="result"></param>
/// <returns></returns>
private List <T> KosarajuStep2(DiGraphVertex <T> currentVertex,
HashSet <T> visited, Stack <T> finishStack,
List <T> result)
{
visited.Add(currentVertex.Value);
result.Add(currentVertex.Value);
foreach (var edge in currentVertex.OutEdges)
{
if (!visited.Contains(edge.Value))
{
KosarajuStep2(edge, visited, finishStack, result);
}
}
return(result);
}
/// <summary>
/// Just do a DFS keeping track on finish Stack of Vertices
/// </summary>
/// <param name="currentVertex"></param>
/// <param name="visited"></param>
/// <param name="finishStack"></param>
private void KosarajuStep1(DiGraphVertex <T> currentVertex,
HashSet <T> visited,
Stack <T> finishStack)
{
visited.Add(currentVertex.Value);
foreach (var edge in currentVertex.OutEdges)
{
if (!visited.Contains(edge.Value))
{
KosarajuStep1(edge, visited, finishStack);
}
}
//finished visiting, so add to stack
finishStack.Push(currentVertex.Value);
}
