public void CreateEmptyGraphAndAddVertices()
{
var graph = new UndirectedGraph();
Assert.AreEqual(0, graph.Vertices());
Assert.AreEqual(0, graph.Edges());
int vertex1id = graph.AddVertex();
int vertex2id = graph.AddVertex();
Assert.AreEqual(0, vertex1id);
Assert.AreEqual(1, vertex2id);
graph.AddEdge(0, 1);
Assert.AreEqual(2, graph.Vertices());
Assert.AreEqual(1, graph.Edges());
Assert.IsTrue(graph.AdjacentVertices(0).Contains(1));
Assert.IsTrue(graph.AdjacentVertices(1).Contains(0));
// add the same edge again
graph.AddEdge(0, 1);
Assert.AreEqual(2, graph.Vertices());
Assert.AreEqual(2, graph.Edges());
Assert.IsTrue(graph.AdjacentVertices(0).Contains(1));
Assert.IsTrue(graph.AdjacentVertices(1).Contains(0));
}
private List <UndirectedGraph <int, IEdge <int> > > FindComponents(UndirectedGraph <int, IEdge <int> > g)
{
List <UndirectedGraph <int, IEdge <int> > > components = new List <UndirectedGraph <int, IEdge <int> > >();
HashSet <int> vertices = g.Vertices.ToHashSet();
while (vertices.Count > 0)
{
UndirectedGraph <int, IEdge <int> > component = new UndirectedGraph <int, IEdge <int> >(false);
Queue <int> queue = new Queue <int>();
int v = vertices.First();
vertices.Remove(v);
queue.Enqueue(v);
component.AddVertex(v);
while (queue.Count > 0)
{
v = queue.Dequeue();
foreach (int n in g.AdjacentVertices(v))
{
if (vertices.Contains(n))
{
component.AddVertex(n);
queue.Enqueue(n);
vertices.Remove(n);
}
component.AddEdge(new Edge <int>(v, n));
}
}
components.Add(component);
}
return(components);
}
private bool TryColors(int vertex)
{
if (vertex == graph.VertexCount)
{
return(true);
}
var available = new SortedSet <GraphColor> {
GraphColor.White, GraphColor.Gray, GraphColor.Black
};
foreach (int v in graph.AdjacentVertices(vertex))
{
if (coloring[v] is not null)
{
available.Remove(coloring[v].Value);
}
}
var next = vertex + 1;
foreach (GraphColor c in available)
{
coloring[vertex] = c;
if (TryColors(next))
{
return(true);
}
}
coloring[vertex] = null;
return(false);
}
public void CreateGraphWithSelfLoops()
{
var graph = new UndirectedGraph(1);
Assert.AreEqual(1, graph.Vertices());
Assert.AreEqual(0, graph.Edges());
graph.AddEdge(0, 0);
Assert.AreEqual(1, graph.Edges());
Assert.IsTrue(graph.AdjacentVertices(0).Contains(0));
}
Triangulate(UndirectedGraph <int, IEdge <int> > tree, int root = 0)
{
Dictionary <(int source, int target), int> innerVerticesCount = new Dictionary <(int source, int target), int>();
UndirectedGraph <int, IEdge <int> > res = new UndirectedGraph <int, IEdge <int> >();
if (tree.IsVerticesEmpty)
{
return(res, innerVerticesCount);
}
if (!tree.ContainsVertex(root))
{
throw new ArgumentException("root");
}
// create counter-clockwise combinatorial embedding
// assumes vertices are numbered as in BFS
// so it's proper to add them to list in order they are stored internally
UndirectedGraph <int, IEdge <int> > G = tree.Clone();
Dictionary <int, List <int> > embedding = new Dictionary <int, List <int> >(); // TODO: what if graph vertices are only subgraph? this assumption may be wrong
foreach (int i in G.Vertices)
{
embedding.Add(i, new List <int>());
foreach (int v in G.AdjacentVertices(i))
{
embedding[i].Add(v);
}
}
foreach (int v in tree.Vertices)
{
int[] neighbors = new int[embedding[v].Count];
embedding[v].CopyTo(neighbors);
int prev = neighbors[0];
for (int i = 1; i < neighbors.Length; i++)
{
int curr = neighbors[i];
TryAddEdge(prev, curr, v, ref G, ref res, ref embedding, ref innerVerticesCount);
prev = curr;
}
if (neighbors.Length > 2)
{
TryAddEdge(prev, neighbors[0], v, ref G, ref res, ref embedding, ref innerVerticesCount);
}
}
return(res, innerVerticesCount);
}
private bool existsInGraph(List <TVertex> path)
{
if (path.Count > 1)
{
path.Add(path[0]); // make cycle, not simple path
}
for (int i = 0; i < path.Count() - 1; i++)
{
if (!graph.AdjacentVertices(path[i]).Contains(path[i + 1]))
{
return(false);
}
}
return(true);
}
public void AdjacentVertices()
{
var graph = new UndirectedGraph <int, Edge <int> >();
var edge12 = new Edge <int>(1, 2);
var edge13 = new Edge <int>(1, 3);
var edge13Bis = new Edge <int>(1, 3);
var edge14 = new Edge <int>(1, 4);
var edge24 = new Edge <int>(2, 4);
var edge31 = new Edge <int>(3, 1);
var edge33 = new Edge <int>(3, 3);
var edge51 = new Edge <int>(5, 1);
var edge65 = new Edge <int>(6, 5);
var edge66 = new Edge <int>(6, 6);
graph.AddVertex(7);
graph.AddVerticesAndEdgeRange(new[]
{
edge12, edge13, edge13Bis,
edge14, edge24, edge31, edge33,
edge51, edge65, edge66
});
CollectionAssert.AreEquivalent(
new[] { 2, 3, 4, 5 },
graph.AdjacentVertices(1));
CollectionAssert.AreEquivalent(
new[] { 1, 4 },
graph.AdjacentVertices(2));
CollectionAssert.AreEquivalent(
new[] { 1 },
graph.AdjacentVertices(3));
CollectionAssert.AreEquivalent(
new[] { 1, 2 },
graph.AdjacentVertices(4));
CollectionAssert.AreEquivalent(
new[] { 1, 6 },
graph.AdjacentVertices(5));
CollectionAssert.AreEquivalent(
new[] { 5 },
graph.AdjacentVertices(6));
CollectionAssert.IsEmpty(graph.AdjacentVertices(7));
}
private bool ExistsInGraph([NotNull, ItemNotNull] List <TVertex> path)
{
if (path.Count > 1)
{
path.Add(path[0]); // Make cycle, not simple path
}
for (int i = 0; i < path.Count - 1; i++)
{
if (!_graph.AdjacentVertices(path[i]).Contains(path[i + 1]))
{
return(false);
}
}
return(true);
}
public void CreateGraphWithPresetAmountOfVertices()
{
// a cube
var graph = new UndirectedGraph(4);
graph.AddEdge(0, 1);
graph.AddEdge(1, 2);
graph.AddEdge(2, 3);
graph.AddEdge(3, 0);
Assert.AreEqual(4, graph.Vertices());
Assert.AreEqual(4, graph.Edges());
Assert.IsTrue(graph.AdjacentVertices(0).Contains(1));
Assert.IsTrue(graph.AdjacentVertices(0).Contains(3));
Assert.IsTrue(graph.AdjacentVertices(1).Contains(0));
Assert.IsTrue(graph.AdjacentVertices(1).Contains(2));
Assert.IsTrue(graph.AdjacentVertices(2).Contains(1));
Assert.IsTrue(graph.AdjacentVertices(2).Contains(3));
Assert.IsTrue(graph.AdjacentVertices(3).Contains(2));
Assert.IsTrue(graph.AdjacentVertices(3).Contains(0));
}
List <List <string> > PathsToEnd(string from, List <List <string> > paths, List <string> path, bool checkCount = false)
{
var thisPath = path.ToList();
thisPath.Add(from);
var nodes = _graph.AdjacentVertices(from);
foreach (var node in nodes)
{
if (char.IsLower(node[0]) && thisPath.Contains(node))
{
if (!checkCount)
{
continue;
}
var maxCountReached = thisPath.Where(c => char.IsLower(c[0])).GroupBy(s => s).Any(g => g.Count() == 2);
if (node == "start" || node == "end" || maxCountReached)
{
continue;
}
}
if (node == "end")
{
var x = thisPath.ToList();
x.Add(node);
paths.Add(x);
continue;
}
PathsToEnd(node, paths, thisPath, checkCount);
}
return(paths);
}
public void AdjacentVertices_Throws()
{
var graph = new UndirectedGraph <int, Edge <int> >();
Assert.Throws <VertexNotFoundException>(() => graph.AdjacentVertices(10));
}
void GenerateLanes()
{
foreach (Node node in graph.Vertices)
{
IOrderedEnumerable <Node> orderedNodes = graph.Vertices.OrderBy(nodeToOrder => CartezianPosition.CalculateDistance(node.position, nodeToOrder.position));
IEnumerator <Node> enumeratorNodes = orderedNodes.GetEnumerator();
enumeratorNodes.MoveNext();
enumeratorNodes.MoveNext();
if (CartezianPosition.CalculateDistance(enumeratorNodes.Current.position, node.position) > galaxy.maxDistanceBetweenNodesToConnect)
{
Node reference = enumeratorNodes.Current;
Starlane newEdge = new Starlane(node, reference);
graph.AddEdge(newEdge);
edgeCosts.Add(newEdge, CartezianPosition.CalculateDistance(enumeratorNodes.Current.position, node.position));
//node.starlanes.Add(new Starlane(new CartezianLine(node.position,orderedNodes.ElementAt(1).position),node, orderedNodes.ElementAt(1)));
//orderedNodes.ElementAt(1).starlanes.Add(new Starlane(new CartezianLine(node.position, orderedNodes.ElementAt(1).position), orderedNodes.ElementAt(1), node));
//graph.AddEdge(new Starlane(new CartezianLine(node.position, orderedNodes.ElementAt(1).position), node, orderedNodes.ElementAt(1)));
//graph.AddEdge(new Starlane(new CartezianLine(node.position, orderedNodes.ElementAt(1).position), orderedNodes.ElementAt(1), node));
}
else
{
for (int j = 1; j < 6; j++)
{
if (graph.AdjacentEdges(node).Count() < galaxy.maxConnectionsPerNode && graph.AdjacentEdges(enumeratorNodes.Current).Count() < galaxy.maxConnectionsPerNode)
{
bool foundIntersection = false;
foreach (Node linkNode in graph.AdjacentVertices(enumeratorNodes.Current))
{
foreach (Node linkOfLinkNode in graph.AdjacentVertices(linkNode))
{
if (CartezianLine.LineSegmentsIntersect(new CartezianLine(node.position, enumeratorNodes.Current.position), new CartezianLine(linkNode.position, linkOfLinkNode.position)))
{
foundIntersection = true;
}
}
}
foreach (Node linkNode in graph.AdjacentVertices(node))
{
foreach (Node linkOfLinkNode in graph.AdjacentVertices(linkNode))
{
if (CartezianLine.LineSegmentsIntersect(new CartezianLine(node.position, enumeratorNodes.Current.position), new CartezianLine(linkNode.position, linkOfLinkNode.position)))
{
foundIntersection = true;
}
}
}
if (foundIntersection == false)
{
Node reference = enumeratorNodes.Current;
Starlane newEdge = new Starlane(node, reference);
graph.AddEdge(newEdge);
edgeCosts.Add(newEdge, CartezianPosition.CalculateDistance(enumeratorNodes.Current.position, node.position));
//node.starlanes.Add(new Starlane(new CartezianLine(node.position, orderedNodes.ElementAt(j).position), node, orderedNodes.ElementAt(j)));
//orderedNodes.ElementAt(j).starlanes.Add(new Starlane(new CartezianLine(node.position, orderedNodes.ElementAt(j).position), orderedNodes.ElementAt(j), node));
//graph.AddEdge(new Starlane(new CartezianLine(node.position, orderedNodes.ElementAt(j).position), node, orderedNodes.ElementAt(j)));
//graph.AddEdge(new Starlane(new CartezianLine(node.position, orderedNodes.ElementAt(j).position), orderedNodes.ElementAt(j), node));
}
}
enumeratorNodes.MoveNext();
}
}
}
}
Triangulate(UndirectedGraph <int, IEdge <int> > tree, int root = 0)
{
UndirectedGraph <int, IEdge <int> > res = new UndirectedGraph <int, IEdge <int> >();
Dictionary <(int source, int target), int> innerVerticesCount = new Dictionary <(int source, int target), int>();
if (tree.IsVerticesEmpty)
{
return(res, innerVerticesCount);
}
if (!tree.ContainsVertex(root))
{
throw new ArgumentException("root");
}
UndirectedGraph <int, IEdge <int> > G = tree.Clone();
// create counter-clockwise combinatorial embedding
// assumes vertices are numbered as in BFS
// so it's proper to add them to list in order they are stored internally
Dictionary <int, List <int> > embedding = new Dictionary <int, List <int> >();
for (int i = 0; i < G.VertexCount; i++)
{
embedding.Add(i, new List <int>());
foreach (int v in G.AdjacentVertices(i))
{
embedding[i].Add(v);
}
}
// BFS
Queue <int> q = new Queue <int>();
bool[] enqueued = new bool[G.VertexCount];
q.Enqueue(root);
enqueued[root] = true;
while (q.Count > 0)
{
int p = q.Dequeue();
int[] neighbors = new int[embedding[p].Count];
embedding[p].CopyTo(neighbors);
int first = neighbors[0];
if (!enqueued[first])
{
q.Enqueue(first);
enqueued[first] = true;
}
int prev = first;
int curr = -1;
for (int i = 1; i < neighbors.Length; i++)
{
curr = neighbors[i];
TryAddEdge(prev, curr, p, ref G, ref res, ref embedding, ref innerVerticesCount);
prev = curr;
if (!enqueued[curr])
{
q.Enqueue(curr);
enqueued[curr] = true;
}
}
if (neighbors.Length > 2)
{
TryAddEdge(curr, first, p, ref G, ref res, ref embedding, ref innerVerticesCount);
}
}
return(res, innerVerticesCount);
}
private bool DnCColoring(List <UndirectedGraph <int, IEdge <int> > > components, HashSet <int> s)
{
//Separator colored
if (s.Count == 0)
{
foreach (UndirectedGraph <int, IEdge <int> > component in components)
{
if (component.VertexCount < 15)
{
//Can't find separator for component - color using bruteforce
if (!DnCColoring(new List <UndirectedGraph <int, IEdge <int> > >(),
new HashSet <int>(component.Vertices)))
{
return(false);
}
}
else
{
HashSet <int> sPrim = PlanarSeparator.FindSeparator(component);
UndirectedGraph <int, IEdge <int> > componentCopy = component.Clone();
foreach (int vPrim in sPrim)
{
componentCopy.RemoveVertex(vPrim);
}
List <UndirectedGraph <int, IEdge <int> > > componentsPrim = FindComponents(componentCopy);
if (!DnCColoring(componentsPrim, sPrim))
{
return(false);
}
}
}
return(true);
}
//Separator still not colored
int v = s.First();
s.Remove(v);
foreach (GraphColor color in (GraphColor[])Enum.GetValues(typeof(GraphColor)))
{
if (!_availableColors[v].Contains(color))
{
continue;
}
//Color v with color
_coloring[v] = color;
bool moveToNextColor = false;
List <int> verticesWithTakenColor = new List <int>();
foreach (int n in _graph.AdjacentVertices(v))
{
if (_availableColors[n].Contains(color))
{
//Adjacent not colored vertex has no available color - invalid coloring
if (_availableColors[n].Count == 1)
{
//Reverse changes
foreach (int vertex in verticesWithTakenColor)
{
_availableColors[vertex].Add(color);
}
//Move to next v coloring
moveToNextColor = true;
break;
}
//Adjacent vertices cannot be colored with color
_availableColors[n].Remove(color);
verticesWithTakenColor.Add(n);
}
}
if (moveToNextColor)
{
continue;
}
if (DnCColoring(components, s))
{
return(true);
}
//Reverse changes
foreach (int vertex in verticesWithTakenColor)
{
_availableColors[vertex].Add(color);
}
}
s.Add(v);
return(false);
}
