public GameTree BuildGameTree(SuperSlimBoard board, bool win = true)
{
var seenBoards = new Dictionary <SuperSlimBoard, int>();
_gameTreeIndex = 1;
return(BuildGameTree(board, seenBoards, win));
}
public static bool IsSuperabundantForGraph(SuperSlimBoard b, Graph g, int extraPsi = 0)
{
ulong subset = 0;
int total = 0;
while (subset < (1UL << b._stackCount))
{
total = 0;
for (int i = 0; i < b._length; i++)
{
total += (subset & b._trace[i]).PopulationCount() / 2;
}
var e = g.EdgesOn(subset.ToSet());
if (total < e)
{
return(false);
}
subset++;
}
if (extraPsi > 0)
{
return(total >= g.E + extraPsi);
}
return(true);
}
static int InternalIntersectionInCommonCount(Graph g, SuperSlimBoard board)
{
long and = -1L;
foreach (var v in g.Vertices)
{
if (g.Degree(v) <= 1)
{
continue;
}
var neighborStack = 0L;
foreach (var w in g.Neighbors[v])
{
if (g.Degree(w) > 1)
{
continue;
}
neighborStack |= board.Stacks.Value[w];
}
and &= board.Stacks.Value[v] & neighborStack;
}
return(and.PopulationCount());
}
long GetEdgeColorList(SuperSlimBoard b, int e)
{
var v1 = _edges[e].Item1;
var v2 = _edges[e].Item2;
var stacks = b.Stacks.Value;
return(stacks[v1] & stacks[v2]);
}
GameTree BuildGameTree(SuperSlimBoard board, Dictionary <SuperSlimBoard, int> seenBoards, bool win = true)
{
seenBoards[board] = _gameTreeIndex;
var tree = new GameTree()
{
Board = board
};
tree.IsColorable = _coloringAnalyzer.Analyze(board);
tree.IsSuperabundant = win || IsSuperabundant(board);
tree.GameTreeIndex = _gameTreeIndex;
tree.Reduction = CheckReducibility(board);
_gameTreeIndex++;
if (tree.IsColorable)
{
return(tree);
}
if (!tree.IsSuperabundant)
{
return(tree);
}
if (tree.Reduction != null)
{
return(tree);
}
var treeInfo = win ? _swapAnalyzer.WinTreeInfo[board] : _swapAnalyzer.LossTreeInfo[board];
foreach (var bc in treeInfo)
{
var childBoard = new SuperSlimBoard(board._trace, bc.Alpha, bc.Beta, bc.Response, board._stackCount);
int index;
if (seenBoards.TryGetValue(childBoard, out index))
{
var ct = new GameTree()
{
Board = childBoard
};
ct.IsColorable = _coloringAnalyzer.Analyze(childBoard);
ct.IsSuperabundant = win || IsSuperabundant(board);
ct.GameTreeIndex = _gameTreeIndex++;
ct.SameAsIndex = index;
tree.AddChild(ct, bc);
continue;
}
var childTree = BuildGameTree(childBoard, seenBoards, win);
tree.AddChild(childTree, bc);
}
return(tree);
}
bool CheckOrdering(SuperSlimBoard a, SuperSlimBoard b)
{
var order = PartialOrderOnBoards;
if (order == null)
{
return(false);
}
return(order(this, a, b) > 0);
}
public int ComputeAbundanceSurplus(SuperSlimBoard b)
{
int total = 0;
for (int i = 0; i < b._length; i++)
{
total += b._trace[i].PopulationCount() / 2;
}
return(total - G.E);
}
public bool ColorableWithoutEdge(SuperSlimBoard b, int edgeIndex)
{
return(_lineGraph.IsChoosable(Enumerable.Range(0, _lineGraph.N).Select(e =>
{
if (e == edgeIndex)
{
return -1;
}
return _getEdgeColorList(b, e);
}).ToList()));
}
Reduction CanReduce(Graph g, SuperSlimBoard board, Func <Graph, List <Reduction>, Reduction> reducibilityChecker)
{
var edges = g.Edges.Value;
var pendantEdges = g.PendantEdges.Value;
foreach (var tup in pendantEdges)
{
var v = tup.Item1;
var w = tup.Item2;
if (g.Degree(w) > 1)
{
v = tup.Item2;
w = tup.Item1;
}
var dv = g.Degree(v);
var dw = g.Degree(w);
if (ForbiddenEdge != null && (w == ForbiddenEdge.Item1 || w == ForbiddenEdge.Item2))
{
continue;
}
var h = g.RemoveEdge(tup);
var list = board.Stacks.Value[v] & board.Stacks.Value[w];
var reductions = new List <Reduction>();
foreach (var c in list.GetBits())
{
var reducedStacks = board.Stacks.Value.ToList();
reducedStacks[w] = 0;
reducedStacks[v] ^= c;
var reducedBoard = new SuperSlimBoard(reducedStacks);
reductions.Add(new Reduction()
{
Color = c,
Board = reducedBoard,
Stem = v,
Leaf = w
});
}
var r = reducibilityChecker(h, reductions);
if (r != null)
{
return(r);
}
}
return(null);
}
public Reduction CheckReducibility(SuperSlimBoard board, Action <Tuple <string, int> > progress = null)
{
if (ReductionMode == FixerBreakeReductionMode.None)
{
return(null);
}
SubFixableMind.Value.Progress = progress;
if (ReductionMode == FixerBreakeReductionMode.Superabundant)
{
return(SubFixableMind.Value.CanReduceToSuperabundant(G, board, ExtraPsi));
}
return(SubFixableMind.Value.CanReduceToWin(G, board));
}
public static int InternalIntersectionOrder(SuperSlimMind mind, SuperSlimBoard a, SuperSlimBoard b)
{
var asum = -InternalIntersectionCount(mind.G, a);
var bsum = -InternalIntersectionCount(mind.G, b);
if (asum < bsum)
{
return(-1);
}
if (asum > bsum)
{
return(1);
}
return(0);
}
static int InternalIntersectionCount(Graph g, SuperSlimBoard board)
{
long and = -1L;
foreach (var v in g.Vertices)
{
if (g.Degree(v) <= 1)
{
continue;
}
and &= board.Stacks.Value[v];
}
return(and.PopulationCount());
}
bool AnalyzeInternal(SuperSlimBoard board, HashSet <SuperSlimBoard> wonBoards)
{
for (int i = 0; i < board._length; i++)
{
for (int j = i + 1; j < board._length; j++)
{
var x = board._trace[i];
var y = board._trace[j];
var swappable = x ^ y;
var winningSwapAlwaysExists = true;
foreach (var breakerChoice in GetBreakerChoices(swappable))
{
var winningSwapExists = false;
GetFixerResponses(breakerChoice);
for (int k = 1; k < _fixerResponseCount; k++)
{
if (_swapMode == FixerBreakerSwapMode.SingleSwap && _fixerResponses[k].PopulationCount() > 2)
{
continue;
}
var childBoard = new SuperSlimBoard(board._trace, i, j, _fixerResponses[k], board._stackCount);
if (wonBoards.Contains(childBoard))
{
winningSwapExists = true;
break;
}
}
if (!winningSwapExists)
{
winningSwapAlwaysExists = false;
break;
}
}
if (winningSwapAlwaysExists)
{
return(true);
}
}
}
return(false);
}
public bool Equals(SuperSlimBoard other)
{
if (other == null || _length != other._length)
{
return(false);
}
for (int i = 0; i < _length; i++)
{
if (_trace[i] != other._trace[i])
{
return(false);
}
}
return(true);
}
bool AnalyzeOriginalFixerBreaker(SuperSlimBoard board, HashSet <SuperSlimBoard> wonBoards)
{
var colorPairs = new List <Tuple <int, int> >();
for (int i = 0; i < board._length; i++)
{
for (int j = i + 1; j < board._length; j++)
{
colorPairs.Add(new Tuple <int, int>(i, j));
}
}
foreach (var cp in colorPairs.OrderBy(cp => (board._trace[cp.Item1] ^ board._trace[cp.Item2]).PopulationCount()))
{
var i = cp.Item1;
var j = cp.Item2;
var x = board._trace[i];
var y = board._trace[j];
var swappable = x ^ y;
foreach (var v in swappable.GetBits())
{
var good = true;
var responses = new [] { v }.Concat((swappable ^ v).GetBits().Select(w => w | v));
foreach (var response in responses)
{
var childBoard = new SuperSlimBoard(board._trace, i, j, response, board._stackCount);
if (!wonBoards.Contains(childBoard))
{
good = false;
break;
}
}
if (good)
{
return(true);
}
}
}
return(false);
}
public static int BestKnownOrder(SuperSlimMind mind, SuperSlimBoard a, SuperSlimBoard b)
{
var ep = GlobalExtraPsiOrder(mind, a, b);
if (ep != 0)
{
return(ep);
}
var ii = InternalIntersectionOrder(mind, a, b);
if (ii != 0)
{
return(ii);
}
return(0);
}
public bool Analyze(SuperSlimBoard board, HashSet <SuperSlimBoard> wonBoards)
{
if (ProofFindingMode)
{
if (_swapMode == FixerBreakerSwapMode.Original)
{
return(AnalyzeForProofInternalOriginalFixerBreaker(board, wonBoards));
}
return(AnalyzeForProofInternal(board, wonBoards));
}
if (_swapMode == FixerBreakerSwapMode.Original)
{
return(AnalyzeOriginalFixerBreaker(board, wonBoards));
}
return(AnalyzeInternal(board, wonBoards));
}
bool AnalyzeForProofInternal(SuperSlimBoard board, HashSet <SuperSlimBoard> wonBoards)
{
var winInfo = new GameTreeInfo();
WinTreeInfo[board] = winInfo;
var lossInfo = new GameTreeInfo();
LossTreeInfo[board] = lossInfo;
var colorPairs = new List <Tuple <int, int> >();
for (int i = 0; i < board._length; i++)
{
for (int j = i + 1; j < board._length; j++)
{
colorPairs.Add(new Tuple <int, int>(i, j));
}
}
foreach (var cp in colorPairs.OrderBy(cp => (board._trace[cp.Item1] ^ board._trace[cp.Item2]).PopulationCount()))
{
var i = cp.Item1;
var j = cp.Item2;
var x = board._trace[i];
var y = board._trace[j];
var swappable = x ^ y;
var winningSwapAlwaysExists = true;
foreach (var breakerChoice in GetBreakerChoices(swappable))
{
var winningSwapExists = false;
GetFixerResponses(breakerChoice);
var responses = Enumerable.Range(1, _fixerResponseCount - 1).Select(k => _fixerResponses[k]).OrderBy(fr => fr.PopulationCount());
foreach (var response in responses)
{
if (_swapMode == FixerBreakerSwapMode.SingleSwap && response.PopulationCount() > 2)
{
break;
}
var childBoard = new SuperSlimBoard(board._trace, i, j, response, board._stackCount);
if (wonBoards.Contains(childBoard))
{
winningSwapExists = true;
winInfo.Add(breakerChoice, i, j, response);
break;
}
else
{
lossInfo.Add(breakerChoice, i, j, response);
}
}
if (!winningSwapExists)
{
winInfo.Clear();
winningSwapAlwaysExists = false;
break;
}
}
if (winningSwapAlwaysExists)
{
return(true);
}
}
return(false);
}
public Reduction CanReduceToSuperabundant(Graph g, SuperSlimBoard board, int extraPsi)
{
return(CanReduce(g, board, (h, l) => l.FirstOrDefault(r => SuperSlimMind.IsSuperabundantForGraph(r.Board, h, extraPsi))));
}
public static int GlobalExtraPsiOrder(SuperSlimMind mind, SuperSlimBoard a, SuperSlimBoard b)
{
return(mind.ComputeAbundanceSurplus(a).CompareTo(mind.ComputeAbundanceSurplus(b)));
}
public Reduction CanReduceToWin(Graph g, SuperSlimBoard board)
{
return(CanReduce(g, board, CheckReductionForWin));
}
public static int CurrentOrder(SuperSlimMind mind, SuperSlimBoard a, SuperSlimBoard b)
{
return(BestKnownOrder(mind, a, b));
}
public bool Analyze(SuperSlimBoard b, out Dictionary <int, long> coloring)
{
return(IsChoosable(Enumerable.Range(0, _lineGraph.N).Select(e => _getEdgeColorList(b, e)).ToList(), out coloring));
}
bool NearlyColorableForEdge(SuperSlimBoard board, int edgeIndex)
{
return(_coloringAnalyzer.ColorableWithoutEdge(board, edgeIndex));
}
public bool Analyze(SuperSlimBoard b)
{
return(_lineGraph.IsChoosable(Enumerable.Range(0, _lineGraph.N).Select(e => _getEdgeColorList(b, e)).ToList()));
}
public bool NearlyColorableForSomeEdge(SuperSlimBoard board)
{
return(Enumerable.Range(0, _lineG.N).Any(e => NearlyColorableForEdge(board, e)));
}
public bool IsSuperabundant(SuperSlimBoard b)
{
return(IsSuperabundantForGraph(b, G));
}
public GameTreeInfo GetWinTreeInfo(SuperSlimBoard board)
{
return(_swapAnalyzer.WinTreeInfo[board]);
}