public GameTree BuildGameTree(SuperSlimBoard board, bool win = true)
{
var seenBoards = new Dictionary <SuperSlimBoard, int>();
_gameTreeIndex = 1;
return(BuildGameTree(board, seenBoards, win));
}
public bool IsSuperabundant(SuperSlimBoard b)
{
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 = _graph.EdgesOn(subset.ToSet());
if (total < e)
{
return(false);
}
subset++;
}
if (ExtraPsi > 0)
{
return(total >= _graph.E + ExtraPsi);
}
return(true);
}
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, int depth = 0)
{
seenBoards[board] = _gameTreeIndex;
var tree = new GameTree()
{
Board = board, IsFixerWin = win
};
tree.IsColorable = _coloringAnalyzer.Analyze(board);
tree.IsSuperabundant = win || IsSuperabundant(board);
tree.GameTreeIndex = _gameTreeIndex;
_gameTreeIndex++;
if (tree.IsColorable)
{
return(tree);
}
if (!tree.IsSuperabundant)
{
return(tree);
}
GameTreeInfo treeInfo;
if (win)
{
_swapAnalyzer.WinTreeInfo.TryGetValue(board, out treeInfo);
}
else
{
_swapAnalyzer.LossTreeInfo.TryGetValue(board, out treeInfo);
}
if (treeInfo != null)
{
var localSeenBoards = new HashSet <SuperSlimBoard>();
foreach (var bc in treeInfo)
{
var childBoard = new SuperSlimBoard(board._trace, bc.Alpha, bc.Beta, bc.Response, board._stackCount);
if (localSeenBoards.Contains(childBoard))
{
continue;
}
localSeenBoards.Add(childBoard);
if (!win && seenBoards.ContainsKey(childBoard))
{
continue;
}
var childTree = BuildGameTree(childBoard, seenBoards, win, depth + 1);
tree.AddChild(childTree, bc);
}
}
return(tree);
}
public bool Analyze(SuperSlimBoard board, HashSet <SuperSlimBoard> wonBoards)
{
if (ProofFindingMode)
{
return(AnalyzeForProofInternal(board, wonBoards));
}
return(AnalyzeInternal(board, wonBoards));
}
public int ComputeAbundanceSurplus(SuperSlimBoard b)
{
int total = 0;
for (int i = 0; i < b._length; i++)
{
total += b._trace[i].PopulationCount() / 2;
}
return(total - _graph.E);
}
public bool AnalyzeWithoutEdge(SuperSlimBoard b, out Dictionary <int, long> coloring, int edgeIndex)
{
return(IsChoosable(Enumerable.Range(0, _lineGraph.N).Select(e =>
{
if (e == edgeIndex)
{
return -1;
}
return _getEdgeColorList(b, e);
}).ToList(), out coloring));
}
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()));
}
void GenerateAllBoards(Template template, int colorCount, Action <Tuple <string, int> > progress = null)
{
if (progress != null)
{
progress(new Tuple <string, int>("Finding all positions...", 0));
}
foreach (var t in BitLevelGeneration.Assignments_ulong.Generate(template.Sizes, colorCount))
{
var b = new SuperSlimBoard(t, template.Sizes.Count);
_remainingBoards.Add(b);
}
}
bool IsMatchingAbundant(SuperSlimBoard b, ulong subset, out int e)
{
e = _graph.EdgesOn(subset.ToSet());
int total = 0;
for (int i = 0; i < b._length; i++)
{
var vc = (subset & b._trace[i]).ToSet();
total += _lineGraph.IndependenceNumber(_graph.EdgeIndicesOn(vc));
}
return(total >= e);
}
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 (WeaklyFixable && _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);
}
IEnumerable <ColorPairOutcome> Analyze(SuperSlimBoard board)
{
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));
}
}
return(colorPairs.OrderBy(cp => (board._trace[cp.Item1] ^ board._trace[cp.Item2]).PopulationCount())
.Select(cp => new ColorPairOutcome()
{
Colors = cp, FixerOutcomes = AnalyzeColorPair(cp, board)
}));
}
IEnumerable <FixerOutcome> AnalyzeColorPair(Tuple <int, int> colors, SuperSlimBoard board)
{
var i = colors.Item1;
var j = colors.Item2;
var x = board._trace[i];
var y = board._trace[j];
var swappable = x ^ y;
foreach (var breakerChoice in GetBreakerChoices(swappable))
{
GetFixerResponses(breakerChoice);
var responses = Enumerable.Range(1, _fixerResponseCount - 1).Select(k => _fixerResponses[k]).Where(fr => fr.PopulationCount() <= 1);
yield return(new FixerOutcome()
{
BreakerChoice = breakerChoice, Exits = responses.Select(response => new SuperSlimBoard(board._trace, i, j, response, board._stackCount)).ToList()
});
}
}
List <int> ComputeMatchingAbundanceShadow(SuperSlimBoard b)
{
var shadow = new List <int>();
ulong subset = 0;
while (subset < (1UL << b._stackCount))
{
int e;
if (!IsMatchingAbundant(b, subset, out e))
{
shadow.Add(e);
}
subset++;
}
shadow.Sort();
return(shadow);
}
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 (WeaklyFixable && 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)
{
LastWinChildCount = swappable.PopulationCount();
return(true);
}
}
return(false);
}
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 NearlyColorableForSomeEdge(SuperSlimBoard board)
{
return(Enumerable.Range(0, _lineGraph.N).Any(e => NearlyColorableForEdge(board, e)));
}
public GameTreeInfo GetWinTreeInfo(SuperSlimBoard board)
{
return(_swapAnalyzer.WinTreeInfo[board]);
}
public bool Analyze(SuperSlimBoard b)
{
return(_lineGraph.IsChoosable(Enumerable.Range(0, _lineGraph.N).Select(e => _getEdgeColorList(b, e)).ToList()));
}