// calculate a probability for each un-revealed tile on the board
public void Process()
{
this.mask = new bool[this.boxes.Count];
// create an initial solution of no mines anywhere
ProbabilityLine held = new ProbabilityLine(this.boxes.Count);
held.SetSolutionCount(1);
this.heldProbs.Add(held);
// add an empty probability line to get us started
this.workingProbs.Add(new ProbabilityLine(this.boxes.Count));
NextWitness nextWitness = FindFirstWitness();
while (nextWitness != null)
{
// mark the new boxes as processed - which they will be soon
foreach (Box box in nextWitness.GetNewBoxes())
{
this.mask[box.GetUID()] = true;
}
this.workingProbs = MergeProbabilities(nextWitness);
nextWitness = FindNextWitness(nextWitness);
}
CalculateBoxProbabilities();
}
// calculate how many ways this solution can be generated and roll them into one
private void MergeLineProbabilities(ProbabilityLine npl, ProbabilityLine pl)
{
BigInteger solutions = 1;
for (int i = 0; i < this.boxes.Count; i++)
{
solutions = solutions * (BigInteger)SMALL_COMBINATIONS[this.boxes[i].GetTiles().Count][(int)pl.GetMineBoxCount(i)];
}
npl.SetSolutionCount(npl.GetSolutionCount() + solutions);
for (int i = 0; i < this.boxes.Count; i++)
{
if (this.mask[i]) // if this box has been involved in this solution - if we don't do this the hash gets corrupted by boxes = 0 mines because they weren't part of this edge
{
npl.SetMineBoxCount(i, npl.GetMineBoxCount(i) + pl.GetMineBoxCount(i) * solutions);
}
}
}
// take a look at what edges we have and show some information - trying to get some ideas on how we can get faster good guesses
private void AnalyseAllEdges()
{
//Console.WriteLine("Number of tiles off the edge " + tilesOffEdge);
//Console.WriteLine("Number of mines to find " + minesLeft);
this.edgeMinesMin = 0;
this.edgeMinesMax = 0;
foreach (EdgeStore edge in edgeStore)
{
int edgeMinMines = edge.data[0].GetMineCount();
int edgeMaxMines = edge.data[edge.data.Count - 1].GetMineCount();
edgeMinesMin = edgeMinesMin + edgeMinMines;
edgeMinesMax = edgeMinesMax + edgeMaxMines;
}
information.Write("Min mines on all edges " + edgeMinesMin + ", max " + edgeMinesMax);
this.edgeMinesMaxLeft = this.edgeMinesMax; // these values are used in the merge logic to reduce the number of lines need to keep
this.edgeMinesMinLeft = this.edgeMinesMin;
this.mineCountLowerCutoff = this.edgeMinesMin;
this.mineCountUpperCutoff = Math.Min(this.edgeMinesMax, this.minesLeft); // can't have more mines than are left
// comment this out when doing large board analysis
return;
// the code below reduces the range of mine count values to just be the 'significant' range
List <ProbabilityLine> store = new List <ProbabilityLine>();
List <ProbabilityLine> store1 = new List <ProbabilityLine>();
ProbabilityLine init = new ProbabilityLine(0);
init.SetSolutionCount(1);
store.Add(init);
// combine all the edges to determine the relative weights of the mine count
foreach (EdgeStore edgeDetails in edgeStore)
{
foreach (ProbabilityLine pl in edgeDetails.data)
{
BigInteger plSolCount = pl.GetSolutionCount();
foreach (ProbabilityLine epl in store)
{
if (pl.GetMineCount() + epl.GetMineCount() <= this.maxTotalMines)
{
ProbabilityLine newpl = new ProbabilityLine(0);
newpl.SetMineCount(pl.GetMineCount() + epl.GetMineCount());
BigInteger eplSolCount = epl.GetSolutionCount();
newpl.SetSolutionCount(pl.GetSolutionCount() * eplSolCount);
store1.Add(newpl);
}
}
}
store.Clear();
// sort into mine order
store1.Sort();
int mc = store1[0].GetMineCount();
ProbabilityLine npl = new ProbabilityLine(0);
npl.SetMineCount(mc);
foreach (ProbabilityLine pl in store1)
{
if (pl.GetMineCount() != mc)
{
store.Add(npl);
mc = pl.GetMineCount();
npl = new ProbabilityLine(0);
npl.SetMineCount(mc);
}
npl.SetSolutionCount(npl.GetSolutionCount() + pl.GetSolutionCount());
}
store.Add(npl);
store1.Clear();
}
BigInteger total = 0;
int mineValues = 0;
foreach (ProbabilityLine pl in store)
{
if (pl.GetMineCount() >= this.minTotalMines) // if the mine count for this solution is less than the minimum it can't be valid
{
BigInteger mult = SolverMain.Calculate(this.minesLeft - pl.GetMineCount(), this.tilesOffEdge); //# of ways the rest of the board can be formed
total = total + mult * pl.GetSolutionCount();
mineValues++;
}
}
//this.mineCountLowerCutoff = this.edgeMinesMin;
//this.mineCountUpperCutoff = Math.Min(this.edgeMinesMax, this.minesLeft); // can't have more mines than are left
BigInteger soFar = 0;
foreach (ProbabilityLine pl in store)
{
if (pl.GetMineCount() >= this.minTotalMines) // if the mine count for this solution is less than the minimum it can't be valid
{
BigInteger mult = SolverMain.Calculate(this.minesLeft - pl.GetMineCount(), this.tilesOffEdge); //# of ways the rest of the board can be formed
soFar = soFar + mult * pl.GetSolutionCount();
double perc = Combination.DivideBigIntegerToDouble(soFar, total, 6) * 100;
//Console.WriteLine("Mine count " + pl.GetMineCount() + " has solution count " + pl.GetSolutionCount() + " multiplier " + mult + " running % " + perc);
//Console.WriteLine("Mine count " + pl.GetMineCount() + " has solution count " + pl.GetSolutionCount() + " has running % " + perc);
if (mineValues > 30 && perc < 2.5)
{
this.mineCountLowerCutoff = pl.GetMineCount();
}
if (mineValues > 30 && perc > 97.5)
{
this.mineCountUpperCutoff = pl.GetMineCount();
break;
}
}
}
information.Write("Significant range " + this.mineCountLowerCutoff + " - " + this.mineCountUpperCutoff);
//this.edgeMinesMaxLeft = this.edgeMinesMax;
//this.edgeMinesMinLeft = this.edgeMinesMin;
return;
// below here are experimental ideas on getting a good guess on very large boards
int midRangeAllMines = (this.mineCountLowerCutoff + this.mineCountUpperCutoff) / 2;
BigInteger[] tally = new BigInteger[boxes.Count];
double[] probability = new double[boxes.Count];
foreach (EdgeStore edgeDetails in edgeStore)
{
int sizeRangeEdgeMines = (edgeDetails.data[edgeDetails.data.Count - 1].GetMineCount() - edgeDetails.data[0].GetMineCount()) / 2;
int start = (this.mineCountLowerCutoff - edgeDetails.data[0].GetMineCount() + this.mineCountUpperCutoff - edgeDetails.data[edgeDetails.data.Count - 1].GetMineCount()) / 2;
//int start = midRangeAllMines - sizeRangeEdgeMines;
//BigInteger mult = Combination.Calculate(this.minesLeft - start, this.tilesOffEdge);
BigInteger totalTally = 0;
foreach (ProbabilityLine pl in edgeDetails.data)
{
BigInteger mult = Combination.Calculate(this.minesLeft - start - pl.GetMineCount(), this.tilesOffEdge);
totalTally += mult * pl.GetSolutionCount();
for (int i = 0; i < boxes.Count; i++)
{
if (edgeDetails.mask[i])
{
BigInteger work = pl.GetMineBoxCount(i) * mult;
tally[i] += work;
}
}
//mult = mult * (this.tilesOffEdge - start) / (start + 1);
//start++;
}
for (int i = 0; i < boxes.Count; i++)
{
if (edgeDetails.mask[i])
{
probability[i] = Combination.DivideBigIntegerToDouble(tally[i], totalTally, 6) / boxes[i].GetTiles().Count;
}
}
int minIndex = -1;
for (int i = 0; i < boxes.Count; i++)
{
if (edgeDetails.mask[i])
{
if (minIndex == -1 || probability[i] < probability[minIndex])
{
minIndex = i;
}
}
}
if (minIndex != -1)
{
information.Write("Best guess is " + boxes[minIndex].GetTiles()[0].AsText() + " with " + (1 - probability[minIndex]));
}
else
{
information.Write("No Guess found");
}
}
}
// this combines newly generated probabilities with ones we have already stored from other independent sets of witnesses
private void CombineProbabilities()
{
List <ProbabilityLine> result = new List <ProbabilityLine>();
if (this.workingProbs.Count == 0)
{
information.Write("working probabilites list is empty!!");
return;
}
// see if we can find a common divisor
BigInteger hcd = workingProbs[0].GetSolutionCount();
foreach (ProbabilityLine pl in workingProbs)
{
hcd = BigInteger.GreatestCommonDivisor(hcd, pl.GetSolutionCount());
}
foreach (ProbabilityLine pl in heldProbs)
{
hcd = BigInteger.GreatestCommonDivisor(hcd, pl.GetSolutionCount());
}
information.Write("Greatest Common Divisor is " + hcd);
solutionCountMultiplier = solutionCountMultiplier * hcd;
int mineCountMin = workingProbs[0].GetMineCount() + heldProbs[0].GetMineCount();
// shrink the window
edgeMinesMinLeft = edgeMinesMinLeft - workingProbs[0].GetMineCount();
edgeMinesMaxLeft = edgeMinesMaxLeft - workingProbs[workingProbs.Count - 1].GetMineCount();
foreach (ProbabilityLine pl in workingProbs)
{
BigInteger plSolCount = pl.GetSolutionCount() / hcd;
foreach (ProbabilityLine epl in heldProbs)
{
// if the mine count can never reach the lower cuttoff then ignore it
if (pl.GetMineCount() + epl.GetMineCount() + edgeMinesMaxLeft < this.mineCountLowerCutoff)
{
continue;
}
// if the mine count will always be pushed beyonf the upper cuttoff then ignore it
if (pl.GetMineCount() + epl.GetMineCount() + edgeMinesMinLeft > this.mineCountUpperCutoff)
{
continue;
}
ProbabilityLine newpl = new ProbabilityLine(this.boxes.Count);
newpl.SetMineCount(pl.GetMineCount() + epl.GetMineCount());
BigInteger eplSolCount = epl.GetSolutionCount() / hcd;
newpl.SetSolutionCount(pl.GetSolutionCount() * eplSolCount);
for (int k = 0; k < this.boxes.Count; k++)
{
BigInteger w1 = pl.GetMineBoxCount(k) * eplSolCount;
BigInteger w2 = epl.GetMineBoxCount(k) * plSolCount;
newpl.SetMineBoxCount(k, w1 + w2);
}
result.Add(newpl);
}
}
//Console.WriteLine("Solution multiplier is " + solutionCountMultiplier);
this.heldProbs.Clear();
// if result is empty this is an impossible position
if (result.Count == 0)
{
Console.WriteLine("Impossible position encountered");
return;
}
if (result.Count == 1)
{
heldProbs.AddRange(result);
return;
}
// sort into mine order
result.Sort();
// and combine them into a single probability line for each mine count
int mc = result[0].GetMineCount();
ProbabilityLine npl = new ProbabilityLine(this.boxes.Count);
npl.SetMineCount(mc);
int startMC = mc;
foreach (ProbabilityLine pl in result)
{
if (pl.GetMineCount() != mc)
{
this.heldProbs.Add(npl);
mc = pl.GetMineCount();
npl = new ProbabilityLine(this.boxes.Count);
npl.SetMineCount(mc);
}
npl.SetSolutionCount(npl.GetSolutionCount() + pl.GetSolutionCount());
for (int j = 0; j < this.boxes.Count; j++)
{
npl.SetMineBoxCount(j, npl.GetMineBoxCount(j) + pl.GetMineBoxCount(j));
}
}
this.heldProbs.Add(npl);
}