public override string WriteProof()
{
var sb = new StringBuilder();
_isWin = Cases.All(c => !c.BreakerWin);
AddFigure(sb);
BeginProof(sb);
GeneratePossibleLists();
GeneralizeAllBoards(sb);
var wonBoards = new List <SuperSlimBoard>();
for (int caseNumber = 1; caseNumber <= Cases.Count; caseNumber++)
{
var c = Cases[caseNumber - 1];
var boards = c.Boards.OrderBy(b => ToListString(b)).ToList();
List <SuperSlimBoard> thisClaimBoards;
if (caseNumber > 1 && !c.BreakerWin)
{
thisClaimBoards = boards.SelectMany(b => new[] { b }.Union(_permutationLinked[b].Select(tup => tup.Item2))).ToList();
}
else
{
thisClaimBoards = boards;
}
if (!c.BreakerWin)
{
wonBoards.AddRange(thisClaimBoards);
}
var thisClaimBoardsTex = GeneralizeBoards(thisClaimBoards);
sb.AppendLine();
sb.AppendLine("\\bigskip");
sb.AppendLine(string.Format("\\case{{{0}}}{{$B$ is one of " + thisClaimBoardsTex + ".}}", caseNumber));
sb.AppendLine();
sb.AppendLine("\\bigskip");
if (c.BreakerWin)
{
sb.AppendLine();
if (c.Superabundant)
{
sb.AppendLine("No single Kempe exchange gets from these boards to a previous case.");
}
else
{
sb.AppendLine("These boards are not superabundant.");
}
}
else if (caseNumber == 1)
{
sb.AppendLine();
sb.AppendLine("In all these cases, $H$ is immediately colorable from the lists.");
}
else
{
sb.AppendLine();
var swapCountGroups = boards.GroupBy(b => Mind.GetWinTreeInfo(b).Max(ti => ti.SwapVertices.Count)).ToList();
foreach (var swapCountGroup in swapCountGroups)
{
if (swapCountGroup.Key == 1)
{
sb.AppendLine("Each of the following boards can be handled by a single Kempe change that has an endpoint at infinity.");
foreach (var b in swapCountGroup)
{
Permutation pp;
var listString = ToListString(b, out pp);
var treeInfo = Mind.GetWinTreeInfo(b);
var alpha = Math.Min(pp[treeInfo.First().Alpha], pp[treeInfo.First().Beta]);
var beta = Math.Max(pp[treeInfo.First().Alpha], pp[treeInfo.First().Beta]);
var groups = treeInfo.GroupBy(ss => ss.SwapVertices[0]);
if (!CheckPermutationGoodNess(alpha, beta, listString, treeInfo.Select(ss => ss.SwapVertices[0]).Distinct().ToList()))
{
sb.AppendLine();
sb.AppendLine("there is badness here");
sb.AppendLine();
}
sb.Append("$\\K_{" + alpha + "" + beta + ",\\infty}(" + listString + "," + groups.OrderBy(gg => gg.Key).Select(gg => gg.Key.GetActiveListIndex(b, _maxPot) + 1).Listify(null) + ")");
sb.AppendLine("\\Rightarrow $ " + groups.OrderBy(gg => gg.Key).Select(gg => "$" + GetChildBoardName(b, gg.First()) + "$").Listify(null) + " (Case " + treeInfo.Select(bc => GetHandledCaseNumber(b, bc)).Distinct().OrderBy(xx => xx).Listify() + ").");
sb.AppendLine();
if (_permutationLinked[b].Count > 0)
{
sb.AppendLine();
sb.AppendLine();
sb.AppendLine("Free by vertex permutation: " + _permutationLinked[b].Select(ppp => "$" + ppp.Item1 + "\\Rightarrow " + ToListString(ppp.Item2) + "$").Listify());
sb.AppendLine();
sb.AppendLine();
}
sb.AppendLine("\\bigskip");
sb.AppendLine();
}
}
else if (swapCountGroup.Key == 2)
{
sb.AppendLine("\\bigskip");
sb.AppendLine();
sb.AppendLine("Each of the following boards can be handled by a single Kempe change.");
foreach (var b in swapCountGroup)
{
Permutation pp;
var listString = ToListString(b, out pp);
var treeInfo = Mind.GetWinTreeInfo(b);
var alpha = Math.Min(pp[treeInfo.First().Alpha], pp[treeInfo.First().Beta]);
var beta = Math.Max(pp[treeInfo.First().Alpha], pp[treeInfo.First().Beta]);
var leftover = treeInfo.ToList();
if (!CheckPermutationGoodNess(alpha, beta, listString, treeInfo.SelectMany(ss => ss.SwapVertices).Distinct().ToList()))
{
sb.AppendLine();
sb.AppendLine("there is badness here");
sb.AppendLine();
}
while (leftover.Count > 0)
{
var commonestSwapper = Enumerable.Range(0, b._stackCount).MaxIndex(v => leftover.Count(bc => bc.SwapVertices.Contains(v)));
var handledAll = leftover.Where(bc => bc.SwapVertices.Contains(commonestSwapper)).ToList();
var handled = handledAll.Distinct(bc => bc.SwapVertices.Count == 1 ? -1 : bc.SwapVertices.Except(commonestSwapper).First()).ToList();
sb.Append("$\\K_{" + alpha + "" + beta + "," + (commonestSwapper.GetActiveListIndex(b, _maxPot) + 1) + "}(" + listString);
var single = handled.FirstOrDefault(bc => bc.SwapVertices.Count == 1);
if (single != null)
{
sb.Append(",\\infty");
}
if (handled.Where(bc => bc.SwapVertices.Count > 1).Count() > 0)
{
sb.Append("," + handled.Where(bc => bc.SwapVertices.Count > 1).OrderBy(bc => bc.SwapVertices.Except(commonestSwapper).First()).Select(bc => bc.SwapVertices.Except(commonestSwapper).First().GetActiveListIndex(b, _maxPot) + 1).Listify(null));
}
sb.Append(")");
sb.AppendLine("\\Rightarrow $ " + handled.OrderBy(bc => bc.SwapVertices.Count == 1 ? -1 : bc.SwapVertices.Except(commonestSwapper).First()).Select(bc => "$" + GetChildBoardName(b, bc) + "$").Listify(null) + " (Case " + handled.Select(bc => GetHandledCaseNumber(b, bc)).Distinct().OrderBy(xx => xx).Listify() + ").");
sb.AppendLine();
foreach (var bc in handledAll)
{
leftover.Remove(bc);
}
}
if (_permutationLinked[b].Count > 0)
{
sb.AppendLine();
sb.AppendLine();
sb.AppendLine("Free by vertex permutation: " + _permutationLinked[b].Select(ppp => "$" + ppp.Item1 + "\\Rightarrow " + ToListString(ppp.Item2) + "$").Listify());
sb.AppendLine();
sb.AppendLine();
}
sb.AppendLine();
sb.AppendLine("\\bigskip");
sb.AppendLine();
}
}
}
}
}
EndProof(sb);
return(sb.ToString());
}
private bool AllCasesClosed()
{
return(Cases.All(x => x.Type.StatusStrategy.IsStatusClosed(x)));
}