/// <summary>
///
/// </summary>
/// <param name="startvertex"></param>
/// <param name="currentvertex"></param>
/// <param name="graph"></param>
/// <param name="blockedset"></param>
/// <param name="blockedmap"></param>
/// <param name="stack"></param>
/// <param name="allcycles"></param>
/// <returns></returns>
private bool GetComponentCycles(int startvertex, int currentvertex, IDigraph graph, HashSet <int> blockedset, Dictionary <int, HashSet <int> > blockedmap, Stack <int> stack, List <List <int> > allcycles)
{
bool hascycle = false;
stack.Push(currentvertex);
blockedset.Add(currentvertex);
if (graph.GetDegreeOut(currentvertex) > 0)
{
foreach (int neighbor in graph.GetVertexNeighborsOut(currentvertex))
{
if (neighbor == startvertex)
{
List <int> cycle = new List <int>();
stack.Push(startvertex);
cycle.AddRange(stack);
cycle.Reverse();
stack.Pop();
allcycles.Add(cycle);
hascycle = true;
}
else if (!blockedset.Contains(neighbor))
{
bool gotcycle = GetComponentCycles(startvertex, neighbor, graph, blockedset, blockedmap, stack, allcycles);
if (gotcycle == true)
{
hascycle = true;
}
}
}
if (hascycle == true)
{
UnBlock(currentvertex, blockedset, blockedmap);
}
else
{
foreach (int neighbor in graph.GetVertexNeighborsOut(currentvertex))
{
HashSet <int> bset = GetBlockedSet(neighbor, blockedmap);
bset.Add(currentvertex);
}
}
stack.Pop();
return(hascycle);
}
return(hascycle);
}
/// <summary>
/// Creates graph consisting of strongly connected components only and then returns the
/// minimum vertex among all the strongly connected components graph, ignores single vertex graph since it can't have a cycle
/// potentially can return null.
/// </summary>
/// <param name="sccs"></param>
/// <param name="graph"></param>
/// <returns></returns>
private Nullable <int> LeastIndexSCC(List <HashSet <int> > sccs, IDigraph graph)
{
int min = int.MaxValue;
Nullable <int> minvertex = null;
HashSet <int> minscc = null;
foreach (HashSet <int> component in sccs)
{
if (component.Count == 1)
{
continue;
}
foreach (int vertex in component)
{
if (vertex < min)
{
min = vertex;
minvertex = vertex;
minscc = component;
}
}
}
if (minvertex == null)
{
return(null);
}
IDigraph graphscc = new Digraph(graph.VertexCount);
for (int i = 0; i < graph.VertexCount; i++)
{
graphscc.AddVertex();
}
for (int i = 0; i < graph.VertexCount; i++)
{
if (minscc.Contains(i))
{
if (graph.GetDegreeOut(i) > 0)
{
foreach (int neighbor in graph.GetVertexNeighborsOut(i))
{
if (minscc.Contains(neighbor))
{
graphscc.AddEdge(i, neighbor);
}
}
}
}
}
Nullable <int> potentialminvertex = null;
if (graphscc.GetDegreeOut(min) > 0 || graphscc.GetDegreeIn(min) > 0)
{
potentialminvertex = minvertex;
}
return(potentialminvertex);
}
/// <summary>
/// (DIRECTED GRAPH) -Get all strongly connected components of a directed graph.
/// Based on Kosaraju's Algorithm:
/// https://en.wikipedia.org/wiki/Strongly_connected_component
/// https://en.wikipedia.org/wiki/Kosaraju%27s_algorithm
/// </summary>
/// <param name="graph"></param>
/// <returns></returns>
public List <HashSet <int> > GetSCC_DirectedGraph(IDigraph graph)
{
//stack contains vertices by finish time(reverse order)
Stack <int> stack = new Stack <int>();
//hashset contains visited vertices
HashSet <int> visited = new HashSet <int>();
//List contains all vertices
List <int> vertices = new List <int>();
//List of hashsets of vertices representing cycles
List <HashSet <int> > connectedcomponents = new List <HashSet <int> >();
//get all connected vertices
//add all vertices with edges to unvisited list
for (int i = 0; i < graph.VertexCount; i++)
{
List <int> neighborsout = (List <int>)graph.GetVertexNeighborsOut(i);
List <int> neighborsin = (List <int>)graph.GetVertexNeighborsIn(i);
if (neighborsout.Count > 0 || neighborsin.Count > 0)
{
vertices.Add(i);
}
}
foreach (int vertex in vertices)
{
if (visited.Contains(vertex))
{
continue;
}
DFSUtil(vertex, visited, stack, graph);
}
//reverse the graph
IDigraph reversegraph = ReverseGraph(graph);
//empty visited hashset
visited.Clear();
while (stack.Count > 0)
{
//get + remove vertex int at top of the stack
int vertex = stack.Pop();
if (visited.Contains(vertex))
{
continue;
}
HashSet <int> componentset = new HashSet <int>();
DFSUtilReverseGraph(vertex, visited, componentset, reversegraph);
connectedcomponents.Add(componentset);
}
return(connectedcomponents);
}
/// <summary>
/// Depth first search by vertex finish time in decreasing order on the reversed graph
/// </summary>
/// <param name="vertex"></param>
/// <param name="visited"></param>
/// <param name="set"></param>
/// <param name="reversegraph"></param>
private void DFSUtilReverseGraph(int vertex, HashSet <int> visited, HashSet <int> componentset, IDigraph reversegraph)
{
visited.Add(vertex);
componentset.Add(vertex);
foreach (int neighbor in reversegraph.GetVertexNeighborsOut(vertex))
{
if (visited.Contains(neighbor))
{
continue;
}
DFSUtilReverseGraph(neighbor, visited, componentset, reversegraph);
}
}
/// <summary>
/// Depth first search populates the stack with vertices ordered by finish time (vertex finishing last at top)
/// </summary>
/// <param name="vertex"></param>
/// <param name="visited"></param>
/// <param name="stack"></param>
/// <param name="graph"></param>
private void DFSUtil(int vertex, HashSet <int> visited, Stack <int> stack, IDigraph graph)
{
visited.Add(vertex);
foreach (int neighbor in graph.GetVertexNeighborsOut(vertex))
{
if (visited.Contains(neighbor))
{
continue;
}
DFSUtil(neighbor, visited, stack, graph);
}
stack.Push(vertex);
}
/// <summary>
/// (DIRECTED GRAPH) -Create a subgraph of an input graph between a start and end vertex (includes start and end vertex)
/// </summary>
/// <param name="startindex"></param>
/// <param name="endvertex"></param>
/// <param name="graph"></param>
/// <returns></returns>
public IDigraph CreateSubGraph(int startindex, int endvertex, IDigraph graph)
{
IDigraph subgraph = new Digraph(graph.VertexCount);
for (int i = 0; i < graph.VertexCount; i++)
{
subgraph.AddVertex();
}
for (int i = startindex; i <= endvertex; i++)
{
List <int> neighbors = (List <int>)graph.GetVertexNeighborsOut(i);
foreach (int neighbor in neighbors)
{
if (neighbor >= startindex && neighbor <= endvertex)
{
subgraph.AddEdge(i, neighbor);
}
}
}
return(subgraph);
}
/// <summary>
/// (DIRECTED GRAPH) -Create a copy of the directed graph that is reversed
/// </summary>
/// <param name="graph"></param>
/// <returns></returns>
public IDigraph ReverseGraph(IDigraph graph)
{
IDigraph reversegraph = new Digraph(graph.VertexCount);
for (int i = 0; i < graph.VertexCount; i++)
{
reversegraph.AddVertex();
}
for (int i = 0; i < graph.VertexCount; i++)
{
List <int> vertexneighbors = (List <int>)graph.GetVertexNeighborsOut(i);
//for each vertex that is connected, create a reverse edge with its neighbors
if (vertexneighbors.Count > 0)
{
foreach (int neighbor in vertexneighbors)
{
reversegraph.AddEdge(neighbor, i);
}
}
}
return(reversegraph);
}
