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();
}
}
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 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 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));
}
