public static IEnumerable <int> TopologicalSorting(GraphAdjacentLists <int> graph)
{
if (graph.DirectedGraph == GraphAdjacentLists <int> .DirectedGraphEnum.Undirected)
{
return(Enumerable.Empty <int>());
}
var traversedNodesStack = new Stack <int>();
var traversedNodes = new List <int>();
foreach (var node in graph.Vertices)
{
traversedNodesStack.Clear();
foreach (var traversedNode in DFSGraphNodesRecursive(graph, node))
{
traversedNodesStack.Push(traversedNode.Item1);
}
if (traversedNodesStack.Count() == graph.Vertices.Count())
{
break;
}
}
foreach (var traversedNode in traversedNodesStack)
{
traversedNodes.Add(traversedNode);
}
return(traversedNodes);
}
private static IEnumerable <int> TraverseGraphRecursive(GraphAdjacentLists <int> graph,
Queue <int> toBeTraversedNodes, HashSet <int> traversedNodes)
{
if (toBeTraversedNodes.Empty())
{
return(Enumerable.Empty <int>());
}
var returnValue = new List <int>();
var newToBeTraversedNodes = new Queue <int>();
while (!toBeTraversedNodes.Empty())
{
var currentNode = toBeTraversedNodes.Dequeue();
if (traversedNodes.Contains(currentNode))
{
continue;
}
traversedNodes.Add(currentNode);
returnValue.Add(currentNode);
foreach (var node in graph.GetAdjacentVertices(currentNode))
{
newToBeTraversedNodes.Enqueue(node);
}
}
return(returnValue.Concat(TraverseGraphRecursive(graph, newToBeTraversedNodes, traversedNodes)));
}
public static IEnumerable <GraphComponent <int> > BFSGraphIterative(GraphAdjacentLists <int> graph, int startNode)
{
var discoveredNodesQueue = new Queue <Tuple <int?, int> >();
var discoveredNodes = new HashSet <int>();
var processedNodesQueue = new Queue <int>();
var processedNodes = new HashSet <int>();
discoveredNodesQueue.Enqueue(new Tuple <int?, int>(null, startNode));
discoveredNodes.Add(startNode);
while (discoveredNodesQueue.Empty())
{
var currentNodeInfo = discoveredNodesQueue.Dequeue();
var currentNodeParent = currentNodeInfo.Item1;
var currentNode = currentNodeInfo.Item2;
yield return(new GraphComponent <int>
{
Type = GraphComponent <int> .TypeEnum.Node,
ParentNode = currentNodeParent,
NodeValue = currentNode,
NodeIsProcessed = false
});
foreach (var node in graph.GetAdjacentVertices(currentNode))
{
if (!processedNodes.Contains(node) ||
graph.DirectedGraph == GraphAdjacentLists <int> .DirectedGraphEnum.Directed)
{
yield return(new GraphComponent <int>
{
Type = GraphComponent <int> .TypeEnum.Edge,
EdgeStart = currentNode,
EdgeEnd = node
});
}
if (!discoveredNodes.Contains(node))
{
discoveredNodesQueue.Enqueue(new Tuple <int?, int>(currentNode, node));
}
}
processedNodes.Add(currentNode);
processedNodesQueue.Enqueue(currentNode);
yield return(new GraphComponent <int>
{
Type = GraphComponent <int> .TypeEnum.Node,
NodeValue = currentNode,
NodeIsProcessed = true
});
}
}
public static IEnumerable <int> TraverseGraphRecursive(GraphAdjacentLists <int> graph)
{
if (!graph.FirstVertex.HasValue)
{
return(Enumerable.Empty <int>());
}
var toBeTraversedNodes = new Queue <int>();
toBeTraversedNodes.Enqueue(graph.FirstVertex.Value);
return(TraverseGraphRecursive(graph, toBeTraversedNodes, new HashSet <int>()));
}
public static IEnumerable <Tuple <int, int, int> > DFSGraphNodesRecursive(GraphAdjacentLists <int> graph, int startNode,
HashSet <int> discoveredNodes = null, HashSet <int> processedNodes = null, int?timer = null)
{
if (!graph.HasVertex(startNode))
{
yield break;
}
var currentNode = startNode;
if (discoveredNodes == null)
{
discoveredNodes = new HashSet <int>();
}
if (processedNodes == null)
{
processedNodes = new HashSet <int>();
}
if (!timer.HasValue)
{
timer = 0;
}
discoveredNodes.Add(currentNode);
var entryTime = timer.Value;
++timer;
foreach (var node in graph.GetAdjacentVertices(currentNode))
{
if (discoveredNodes.Contains(node))
{
continue;
}
foreach (var subNode in DFSGraphNodesRecursive(graph, node, discoveredNodes, processedNodes, timer))
{
yield return(subNode);
}
}
processedNodes.Add(currentNode);
++timer;
var exitTime = timer.Value;
yield return(new Tuple <int, int, int>(startNode, entryTime, exitTime));
}
public static IEnumerable <int> TraverseGraphIterative(GraphAdjacentLists <int> graph, int?vertex = null)
{
if (!graph.FirstVertex.HasValue)
{
return(Enumerable.Empty <int>());
}
if (!vertex.HasValue)
{
vertex = graph.FirstVertex;
}
var returnValue = new List <int>();
var traversedNodes = new HashSet <int>();
var toBeTraversedNodes = new Queue <int>();
toBeTraversedNodes.Enqueue(vertex.Value);
while (!toBeTraversedNodes.Empty())
{
var currentNode = toBeTraversedNodes.Dequeue();
if (traversedNodes.Contains(currentNode))
{
continue;
}
traversedNodes.Add(currentNode);
returnValue.Add(currentNode);
foreach (var node in graph.GetAdjacentVertices(currentNode))
{
toBeTraversedNodes.Enqueue(node);
}
}
return(returnValue);
}
public static int GetConnectedComponentsCount(GraphAdjacentLists <int> graph)
{
var componentId = 0;
var vertexToComponentTable = new Dictionary <int, int>();
foreach (var vertex in graph.Vertices)
{
if (vertexToComponentTable.ContainsKey(vertex))
{
continue;
}
++componentId;
var traversedNodes = TraverseGraphIterative(graph, vertex);
foreach (var traversedNode in traversedNodes)
{
if (!vertexToComponentTable.ContainsKey(traversedNode))
{
vertexToComponentTable[traversedNode] = componentId;
}
}
}
return(componentId);
}
public static (IEnumerable <int>, IEnumerable <string>) TraverseGraphWithEdgesIterative(GraphAdjacentLists <int> graph)
{
if (!graph.FirstVertex.HasValue)
{
return(Enumerable.Empty <int>(), Enumerable.Empty <string>());
}
var processedNodes = new HashSet <int>();
var traversedEdges = new HashSet <Tuple <int, int> >();
var toBeTraversedNodes = new Queue <int>();
toBeTraversedNodes.Enqueue(graph.FirstVertex.Value);
while (!toBeTraversedNodes.Empty())
{
var currentNode = toBeTraversedNodes.Dequeue();
processedNodes.Add(currentNode);
foreach (var node in graph.GetAdjacentVertices(currentNode))
{
if (graph.DirectedGraph == GraphAdjacentLists <int> .DirectedGraphEnum.Directed ||
!processedNodes.Contains(node))
{
traversedEdges.Add(new Tuple <int, int>(currentNode, node));
}
if (!processedNodes.Contains(node))
{
toBeTraversedNodes.Enqueue(node);
}
}
}
return(processedNodes, traversedEdges.Select(x => x.Item1 + "-" + x.Item2));
}
public static bool DFSGraphHasCycles(GraphAdjacentLists <int> graph)
{
return(DFSGraphEdgesRecursive(graph, graph.Vertices.First()).Any(edge => edge.Contains("back")));
}
public static IEnumerable <string> DFSGraphEdgesRecursive(GraphAdjacentLists <int> graph, int startNode,
HashSet <int> discoveredNodes = null, HashSet <int> processedNodes = null,
Dictionary <int, int> parentNodes = null, int parentNode = -1)
{
if (!graph.HasVertex(startNode))
{
yield break;
}
var currentNode = startNode;
if (discoveredNodes == null)
{
discoveredNodes = new HashSet <int>();
}
if (processedNodes == null)
{
processedNodes = new HashSet <int>();
}
if (parentNodes == null)
{
parentNodes = new Dictionary <int, int>();
}
parentNodes[currentNode] = parentNode;
discoveredNodes.Add(currentNode);
foreach (var node in graph.GetAdjacentVertices(currentNode))
{
if (processedNodes.Contains(node))
{
if (graph.DirectedGraph == GraphAdjacentLists <int> .DirectedGraphEnum.Directed)
{
yield return("back edge: " + currentNode + "-" + node);
}
else
{
continue;
}
}
else if (discoveredNodes.Contains(node))
{
if (parentNode == node)
{
continue;
}
else
{
yield return("back edge: " + currentNode + "-" + node);
}
}
else if (!discoveredNodes.Contains(node))
{
parentNodes[node] = currentNode;
yield return("tree edge: " + currentNode + "-" + node);
foreach (var subEdge in DFSGraphEdgesRecursive(graph, node, discoveredNodes, processedNodes, parentNodes, currentNode))
{
yield return(subEdge);
}
}
}
processedNodes.Add(currentNode);
}