public static List <Graphs.Vector> GetSpringsLayout(this Choosability.Graph g, int randomSeed)
{
var satsumaGraph = g.CreateSatsumaGraph();
var layout = new ForceDirectedLayout(satsumaGraph, null, randomSeed);
layout.Run();
var minX = double.MaxValue;
var minY = double.MaxValue;
var maxX = double.MinValue;
var maxY = double.MinValue;
foreach (var p in layout.NodePositions)
{
minX = Math.Min(minX, p.Value.X);
minY = Math.Min(minY, p.Value.Y);
maxX = Math.Max(maxX, p.Value.X);
maxY = Math.Max(maxY, p.Value.Y);
}
var width = maxX - minX;
var height = maxY - minY;
return(satsumaGraph.Nodes().Select(n => new Graphs.Vector(0.1 + 0.7 * (layout.NodePositions[n].X - minX) / width, 0.1 + 0.7 * (layout.NodePositions[n].Y - minY) / height)).ToList());
}
public static void WriteProof()
{
// var uiG = GraphsCore.CompactSerializer.Deserialize("webgraph:7qM`$!.4bH!!!R&a9[/.`!KrS!Aa_K%n$+I!*C1-pbPd:TFX<n1&s-S7JJ\\_\"eHt>8?!.J7JQ4#6hiD:#64`)!<=YO!!!'6/-5ne/-I40\"U#Ji#\"0\"-!!!\"L\"p\"]T!<<"); //small tree aka fig1 left
// var uiG = GraphsCore.CompactSerializer.Deserialize("webgraph:7oB<e!-S>B!!#8TJd$*0\\-lgI!AXY2';,k%#;Z?^)[2gP(C-Of'0ujY!!N?&!.ZPL!<E0O!=+(&I\"$HlIKBKg/-?eA!uhdS2\\:FcIXV"); // fig1 middle
// var uiG = GraphsCore.CompactSerializer.Deserialize("webgraph:7qDZ#!2KSp!!#7s_?WaT\\-lgI!Aa^d)5%L-#>?-AShqSoSn&^p'0ujY!)+Du>Qb&\"e2/>6>R(6/!<E0O!=+(&I\"$HlIK0Hg/-6b%!s0Al\"<.mU.hDa^!.Y84&:T\"UIK"); // fig1 right
// var uiG = GraphsCore.CompactSerializer.Deserialize("webgraph:8!X,T!$D:B!!&)lOptM4\\-lgI!Aa^@+,/T#,DG#?+.s-1#;Q9])[2f],6a[K$V?KmJ;)mR%u&ns'8>>R$O*,X'*Xu#%gAPD(XNCQ#;Z>g!!*'#!6>-?Uf-F^IXZZnI\"$MF!ZK,^!?0#^$P3Il&-`@Xa9[/)$6$tl\"rbPjHP\"$p#ljsUL^OUs(<CrPIXV"); // big tree
var uiG = GraphsCore.CompactSerializer.Deserialize("webgraph:7RI.U!'1)[!!@T`X:8\\?!AXXc)8lhl!!+kU9HC2DA,lWc!!3-$!!*'N!=+(&I\"$HlIK9KN!%\\-UIXZZnI\"$M"); // val
var potSize = uiG.Vertices.Max(v => int.Parse(v.Label));
var g = new Choosability.Graph(uiG.GetEdgeWeights());
var template = new Template(g.Vertices.Select(v => potSize + g.Degree(v) - uiG.Vertices[v].Label.TryParseInt().Value).ToList());
var mind = new Choosability.FixerBreaker.KnowledgeEngine.Slim.Super.SuperSlimMind(g, proofFindingMode: true);
mind.MaxPot = potSize;
// mind.MissingEdgeIndex = 0;
// mind.OnlyConsiderNearlyColorableBoards = true;
int j = 0;
var win = mind.Analyze(template);
if (win)
{
var pb = new MaximumDegreeThreeProofBuilder(mind);
var proof = pb.WriteProof();
}
}
AlgorithmBlob(TabCanvas tabCanvas)
{
UIGraph = tabCanvas.GraphCanvas.Graph;
AlgorithmGraph = new Choosability.Graph(UIGraph.GetEdgeWeights());
BitGraph = new BitLevelGeneration.BitGraph_long(UIGraph.GetEdgeWeights());
SelectedVertices = UIGraph.Vertices.Select((v, i) => v.IsSelected ? i : -1).Where(x => x >= 0).ToList();
SelectedEdges = UIGraph.Edges.Where(e => e.IsSelected).Select(e => new Tuple <int, int>(UIGraph.Vertices.IndexOf(e.V1), UIGraph.Vertices.IndexOf(e.V2))).ToList();
EdgeIndexLookup = new Dictionary <Tuple <int, int>, int>();
int k = 0;
for (int i = 0; i < AlgorithmGraph.N; i++)
{
for (int j = i + 1; j < AlgorithmGraph.N; j++)
{
if (AlgorithmGraph[i, j])
{
EdgeIndexLookup[new Tuple <int, int>(i, j)] = k;
EdgeIndexLookup[new Tuple <int, int>(j, i)] = k;
k++;
}
}
}
SelectedEdgeIndices = SelectedEdges.Select(tuple => EdgeIndexLookup[tuple]).ToList();
}
static void DoEdgeAlls(Graphs.Graph uiG, int potSize, Choosability.Graph G, Template template, int i)
{
var mind = new Choosability.FixerBreaker.KnowledgeEngine.Slim.Super.SuperSlimMind(G);
mind.MaxPot = potSize;
mind.OnlyConsiderNearlyColorableBoards = true;
mind.MissingEdgeIndex = i;
var root = @"C:\game trees\alls2\" + i;
Directory.CreateDirectory(root);
var win = mind.Analyze(template, null);
if (win)
{
int j = 0;
foreach (var board in mind.PlayableBoards)
{
var tree = mind.BuildGameTree(board);
GraphViz.DrawTree(tree, root + @"\" + i + " depth " + tree.GetDepth() + " board " + j + ".pdf");
j++;
}
}
}
void TestGraph <T>(string name, int totalPositions, bool shouldWin, bool shouldWinNearlyColorable)
where T : IMind
{
var graphFile = Path.Combine(RootPath, name);
Assert.IsTrue(File.Exists(graphFile), graphFile + " does not exist.");
var graph = GraphUtility.LoadGraph(graphFile);
var G = new Choosability.Graph(graph.GetEdgeWeights());
var potSize = graph.Vertices.Max(v => v.Label.TryParseInt().Value);
var template = new Template(G.Vertices.Select(v => potSize + G.Degree(v) - graph.Vertices[v].Label.TryParseInt().Value).ToList());
var mind = (SuperSlimMind)Activator.CreateInstance(typeof(T), G);
mind.MaxPot = potSize;
var win = mind.Analyze(template, null);
Assert.AreEqual(totalPositions, mind.TotalBoards, "total positions fail");
Assert.AreEqual(shouldWin, win, "outright win fail");
if (!win)
{
mind = (SuperSlimMind)Activator.CreateInstance(typeof(T), G);
mind.MaxPot = potSize;
mind.OnlyConsiderNearlyColorableBoards = true;
win = mind.Analyze(template, null);
Assert.AreEqual(shouldWinNearlyColorable, win, "nearly colorable fail");
}
}
static IEnumerable <Choosability.Graph> EnumerateWeightings(Choosability.Graph g)
{
var space = Not ? g.Vertices.Select(v => Enumerable.Range(0, Spread)).CartesianProduct() : g.Vertices.Select(v => Enumerable.Range(0, Spread).Reverse()).CartesianProduct();
foreach (var weighting in space)
{
var www = weighting.ToList();
if (www.Count(w => w > 0) > MaxHighs)
{
continue;
}
if (g.Vertices.Any(v => g.Degree(v) - www[v] <= 1))
{
continue;
}
if (LowMinDegree > 0)
{
var low = www.IndicesWhere(w => w == 0).ToList();
if (g.InducedSubgraph(low).MinDegree < LowMinDegree)
{
continue;
}
}
var gg = g.Clone();
gg.VertexWeight = www;
yield return(gg);
}
}
public static Supergraph CreateSatsumaGraph(this Choosability.Graph g)
{
var satsumaGraph = new CustomGraph();
var nodes = new Dictionary <int, Node>();
foreach (var v in g.Vertices)
{
var node = satsumaGraph.AddNode();
nodes[v] = node;
}
for (int i = 0; i < g.N; i++)
{
for (int j = i + 1; j < g.N; j++)
{
if (g.Directed[i, j])
{
satsumaGraph.AddArc(nodes[i], nodes[j], Directedness.Directed);
}
else if (g.Directed[j, i])
{
satsumaGraph.AddArc(nodes[j], nodes[i], Directedness.Directed);
}
else if (g.Adjacent[i, j])
{
satsumaGraph.AddArc(nodes[i], nodes[j], Directedness.Undirected);
}
}
}
return(satsumaGraph);
}
static bool Filter(Choosability.Graph g)
{
if (TwoConnectedOnly)
{
return(g.Vertices.All(v => g.FindComponents(g.Vertices.Except(new[] { v }).ToList()).GetEquivalenceClasses().Count() <= 1));
}
return(true);
}
public static Graphs.Graph GraphFromGraph6(string graph6)
{
var w = GetEdgeWeights(graph6);
var h = new Choosability.Graph(w);
var g = new Graphs.Graph(h, h.GetSpringsLayout(12), false);
g.Name = graph6;
return(g);
}
public static string ToWeightString(this Choosability.Graph g)
{
var edgeWeights = string.Join(" ", g.GetEdgeWeights().Select(x => x.ToString()));
var vertexWeights = "";
if (g.VertexWeight != null)
{
vertexWeights = " [" + string.Join(",", g.VertexWeight) + "]";
}
return(edgeWeights + vertexWeights);
}
public static List <Graphs.Vector> GetLaplacianLayout(this Choosability.Graph g, List <Graphs.Vector> layout = null, object data = null)
{
var D = Matrix.Build.Diagonal(g.N, g.N, v => g.Degree(v));
var A = Matrix.Build.Dense(g.N, g.N, (v, w) => g[v, w] ? 1 : 0);
var L = D - A;
var evd = L.Evd(MathNet.Numerics.LinearAlgebra.Symmetricity.Symmetric);
var x = evd.EigenVectors.Column(1);
var y = evd.EigenVectors.Column(2);
return(GetEigenVectorLayout(x, y));
}
static IEnumerable <Choosability.Graph> EnumerateWeightings(Choosability.Graph g)
{
if (g.MaxDegree > 4)
{
yield break;
}
foreach (var weighting in g.Vertices.Select(v => Enumerable.Range(g.Degree(v), 2)).CartesianProduct())
{
var www = weighting.ToList();
var gg = g.Clone();
gg.VertexWeight = www;
yield return(gg);
}
}
public static void DoUiGraph()
{
var output = "generated.txt";
File.Delete(output);
Graphs.Graph uiG;
using (var sr = new StreamReader("uigraph.txt"))
uiG = GraphsCore.CompactSerializer.Deserialize(sr.ReadToEnd());
var excluded = "excluded.txt".EnumerateWeightedGraphs().ToList();
var g = new Choosability.Graph(uiG.GetEdgeWeights(), uiG.Vertices.Select(v =>
{
int d;
if (!int.TryParse(v.Label, out d))
{
return(0);
}
return(d - 5);
}).ToList());
var all = new List <Graph>();
var zi = g.VertexWeight.IndicesWhere(w => w == 0).ToList();
foreach (var a in zi.Select(i => new[] { 1, 2 }).CartesianProduct())
{
var aa = a.ToList();
for (int j = 0; j < aa.Count; j++)
{
g.VertexWeight[zi[j]] = aa[j];
}
all.Add(g.Clone());
}
foreach (var gg in all.RemoveIsomorphs(excluded))
{
gg.AppendWeightStringToFile(output);
}
}
public static Graphs.Graph GraphFromEdgeWeightString(string s)
{
var isDirected = s.Contains("-1");
var parts = s.Split(' ');
var edgeWeights = parts.Where(p => !p.StartsWith("[")).Select(x => int.Parse(x)).ToList();
List <int> vertexWeights = null;
var vwp = parts.FirstOrDefault(p => p.StartsWith("["));
if (vwp != null)
{
vertexWeights = vwp.Trim('[').Trim(']').Split(',').Select(x => int.Parse(x)).ToList();
}
var h = new Choosability.Graph(edgeWeights, vertexWeights);
return(new Graphs.Graph(h, h.GetSpringsLayout(12), isDirected));
}
public static void BuildTreePictures()
{
var root = @"C:\game trees\smalltree\fixable";
Directory.CreateDirectory(root);
// var uiG = GraphsCore.CompactSerializer.Deserialize("webgraph:7p5lm!.4bH!!#8TV?g9C\\-lgI!AXXW)k[^-#;Z?F*sJ5a,6aYM-O65sh^B_'h`q79;LfjChZj,^!!*)@!!!'$'Z^@ja9NC\"!sTF[\">gYm\"T\\VE!!!");
// var uiG = GraphsCore.CompactSerializer.Deserialize("webgraph:7s+e3!3?/#!!#:+U^KF0PS%F+!AXX?+05o;#;\\Xf`!Jd9-mM7W`P)m27JKt(6hiE-#!f!b-mM`?paS`-&1>N4<IG2S!<<-#a8c2A!>NTW'Z^Ila9)SZa98IB!.Zm;#6Y^]#ZM?A<\"KBC!<C1@!!");
var uiG = GraphsCore.CompactSerializer.Deserialize("webgraph:7qM`$!.4bH!!!R&a9[/.`!KrS!Aa_K%n$+I!*C1-pbPd:TFX<n1&s-S7JJ\\_\"eHt>8?!.J7JQ4#6hiD:#64`)!<=YO!!!'6/-5ne/-I40\"U#Ji#\"0\"-!!!\"L\"p\"]T!<<");
var potSize = uiG.Vertices.Max(v => int.Parse(v.Label));
var g = new Choosability.Graph(uiG.GetEdgeWeights());
var template = new Template(g.Vertices.Select(v => potSize + g.Degree(v) - uiG.Vertices[v].Label.TryParseInt().Value).ToList());
GraphViz.DrawGraph(g, root + @"\G.pdf", true);
var mind = new Choosability.FixerBreaker.KnowledgeEngine.Slim.Super.SuperSlimMind(g, proofFindingMode: true);
mind.MaxPot = potSize;
// mind.OnlyConsiderNearlyColorableBoards = true;
// mind.MissingEdgeIndex = 0;
int j = 0;
var win = mind.Analyze(template);
if (win)
{
foreach (var board in mind.PlayableBoards)
{
var tree = mind.BuildGameTree(board, win);
GraphViz.DrawTree(tree, root + @"\" + " depth " + tree.GetDepth() + " board " + j + ".png");
j++;
}
}
else
{
foreach (var board in mind.BreakerWonBoards)
{
var tree = mind.BuildGameTree(board, win);
GraphViz.DrawTree(tree, root + @"\" + " depth " + tree.GetDepth() + " board " + j + ".png");
j++;
}
}
}
public static List <Graphs.Vector> GetWalkMatrixLayout(this Choosability.Graph g, List <Graphs.Vector> layout = null, object data = null)
{
var D = Matrix.Build.Diagonal(g.N, g.N, v => g.Degree(v));
var A = Matrix.Build.Dense(g.N, g.N, (v, w) => g[v, w] ? 1 : 0);
var L = D.Inverse() * A;
var evd = L.Evd(MathNet.Numerics.LinearAlgebra.Symmetricity.Symmetric);
int xi = 1;
int yi = 2;
for (int i = 0; i < evd.EigenValues.Count - 1; i++)
{
if (evd.EigenValues[i].Real <= 1 && evd.EigenValues[i + 1].Real >= 1)
{
xi = i;
yi = i + 1;
break;
}
}
var x = evd.EigenVectors.Column(xi);
var y = evd.EigenVectors.Column(yi);
return(GetEigenVectorLayout(x, y));
}
static void Main(string[] args)
{
var vertices = Enumerable.Range(1, N).Select(i => new Fraction()
{
Top = (int)f((uint)i), Bottom = (int)f((uint)i + 1)
}).ToList();
// var vertices = new FareySequence(N).ToList();
var adjacent = new bool[vertices.Count, vertices.Count];
for (int i = 0; i < vertices.Count; i++)
{
for (int j = 0; j < vertices.Count; j++)
{
adjacent[i, j] = adjacent[j, i] = Math.Abs(vertices[i].Top * vertices[j].Bottom - vertices[i].Bottom * vertices[j].Top) == 1.0;
}
}
//var g = new Choosability.Graph(adjacent);
//var R = g.Vertices;
//var G = g.Vertices.Except(g.Vertices).ToList();
List <int> R = null;
List <int> G = null;
var g = new Choosability.Graph(adjacent);
foreach (var red in g.EnumerateMaximalIndependentSets())
{
var bluegreen = g.Vertices.Except(red).ToList();
var h = g.InducedSubgraph(bluegreen);
if (!h.IsTwoColorableSlow())
{
continue;
}
R = red;
foreach (var green in g.EnumerateMaximalIndependentSets(bluegreen))
{
if (g.EdgesOn(bluegreen.Except(green).ToList()) <= 0)
{
G = green;
break;
}
}
if (G != null)
{
break;
}
}
var B = g.Vertices.Except(R).Except(G).ToList();
using (var sw = new StreamWriter("Ford" + N + ".tex"))
{
sw.WriteLine(@"\documentclass{standalone}");
sw.WriteLine(@"\usepackage{tikz}");
sw.WriteLine(@"\begin{document}");
sw.WriteLine(@"\begin{tikzpicture}");
var circles = string.Join(Environment.NewLine, Enumerable.Range(1, N).Select(i => new Fraction()
{
Top = (int)f((uint)i), Bottom = (int)f((uint)i + 1)
}).Select(f => new FordCircle(f)).Select((f, i) => string.Format(@"\fill[{3}] ({0},{1}) circle [radius={2}];", f.X, f.Y, f.R, Fill(f.F, i, R, G))));
sw.WriteLine(circles);
sw.WriteLine(@"\end{tikzpicture}");
sw.WriteLine(@"\end{document}");
//var k = g.CliqueNumberBronKerbosch();
//var gg = GraphIO.GraphFromEdgeWeightString(string.Join(" ", g.GetEdgeWeights()));
//var s = CompactSerializer.Serialize(gg);
}
}
public static List <Vector> RotateDiamondsLayout(Choosability.Graph g, List <Vector> layout = null, object data = null)
{
var dd = data as Tuple <List <Vector>, List <SpindleAnalyzer.DiamondType> >;
return(layout.Select((v, i) => Rotate(dd.Item1[i], v, !(dd.Item2[i] == DiamondType.U || dd.Item2[i] == DiamondType.DR || dd.Item2[i] == DiamondType.DL))).ToList());
}
public static List <Graphs.Vector> GetSpringsLayout(this Choosability.Graph g, List <Graphs.Vector> layout = null, object data = null)
{
return(GetSpringsLayout(g, 0));
}
public static void AppendGraph6ToFile(this Choosability.Graph g, string path)
{
using (var sw = new StreamWriter(path, append: true))
sw.WriteLine(g.ToGraph6());
}
public static List <Graphs.Vector> GetUnitDistanceLayout(this Choosability.Graph g, List <Graphs.Vector> layout = null, object data = null)
{
var modifiedLayout = layout.ToList();
var maxDegree = g.MaxDegree;
for (int qqq = 0; qqq < 10; qqq++)
{
var maxes = g.Vertices.ToList();
maxes.Shuffle();
foreach (var first in maxes)
{
var nonzeroCount = 0;
var total = 0.0;
for (int i = 0; i < g.N; i++)
{
for (int j = i + 1; j < g.N; j++)
{
if (g[i, j])
{
var d = modifiedLayout[i].Distance(modifiedLayout[j]);
if (d > 0)
{
nonzeroCount++;
total += d;
}
}
}
}
var length = total / Math.Max(1, nonzeroCount);
for (int qq = 0; qq < 10; qq++)
{
modifiedLayout = modifiedLayout.ToList();
var remaining = g.Vertices.Where(v => v != first).ToList();
remaining.Shuffle();
var anchor = new List <Tuple <int, Graphs.Vector> >()
{
new Tuple <int, Graphs.Vector>(first, modifiedLayout[first])
};
while (remaining.Count > 0)
{
var count = remaining.Count;
var removed = new List <int>();
foreach (var v in remaining)
{
var neighbors = anchor.Where(a => g[a.Item1, v]).ToList();
if (neighbors.Count <= 0)
{
continue;
}
if (neighbors.Count >= 2)
{
var a = neighbors.First().Item2;
var b = neighbors.Skip(1).First().Item2;
double x1, y1, x2, y2;
if (IntersectionOfTwoCircles(a.X, a.Y, length, b.X, b.Y, length, out x1, out y1, out x2, out y2))
{
var d1 = new Graphs.Vector(x1, y1).Distance(modifiedLayout[v]);
var d2 = new Graphs.Vector(x2, y2).Distance(modifiedLayout[v]);
if (d1 < d2 && d1 > 0.001)
{
modifiedLayout[v] = new Graphs.Vector(x1, y1);
}
else if (d2 < d1 && d2 > 0.001)
{
modifiedLayout[v] = new Graphs.Vector(x2, y2);
}
removed.Add(v);
anchor.Add(new Tuple <int, Graphs.Vector>(v, modifiedLayout[v]));
}
}
}
var tt = remaining.RemoveAll(v => removed.Contains(v));
removed.Clear();
if (tt == 0)
{
foreach (var v in remaining)
{
var neighbors = anchor.Where(a => g[a.Item1, v]).ToList();
if (neighbors.Count <= 0)
{
continue;
}
var p = neighbors.First().Item2;
var q = modifiedLayout[v];
var offset = q - p;
var ok = offset.Normalize();
if (ok)
{
offset *= length;
modifiedLayout[v] = p + offset;
removed.Add(v);
anchor.Add(new Tuple <int, Graphs.Vector>(v, modifiedLayout[v]));
goto skipper;
}
}
skipper:
remaining.RemoveAll(v => removed.Contains(v));
if (remaining.Count == count)
{
var x = remaining[0];
remaining.RemoveAt(0);
anchor.Add(new Tuple <int, Graphs.Vector>(x, modifiedLayout[x]));
}
}
}
}
}
}
return(modifiedLayout);
}