// 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");
}
}
}
// here we expand the localised solution to one across the whole board and
// sum them together to create a definitive probability for each box
private void CalculateBoxProbabilities()
{
//long start = DateTime.Now.Ticks;
if (truncatedProbs)
{
Console.WriteLine("probability line combining was truncated");
}
information.Write("Solution count multiplier is " + this.solutionCountMultiplier);
BigInteger[] tally = new BigInteger[this.boxes.Count];
// total game tally
BigInteger totalTally = 0;
// outside a box tally
BigInteger outsideTally = 0;
//console.log("There are " + this.heldProbs.length + " different mine counts on the edge");
bool[] emptyBox = new bool[boxes.Count];
for (int i = 0; i < emptyBox.Length; i++)
{
emptyBox[i] = true;
}
int linesProcessed = 0;
// calculate how many mines
foreach (ProbabilityLine pl in this.heldProbs)
{
//console.log("Mine count is " + pl.mineCount + " with solution count " + pl.solutionCount + " mineBoxCount = " + pl.mineBoxCount);
if (pl.GetMineCount() >= this.minTotalMines) // if the mine count for this solution is less than the minimum it can't be valid
{
linesProcessed++;
//console.log("Mines left " + this.minesLeft + " mines on PL " + pl.mineCount + " squares left = " + this.squaresLeft);
BigInteger mult = SolverMain.Calculate(this.minesLeft - pl.GetMineCount(), this.tilesOffEdge); //# of ways the rest of the board can be formed
information.Write("Mines in solution " + pl.GetMineCount() + " solution count " + pl.GetSolutionCount() + " multiplier " + mult);
outsideTally = outsideTally + mult * new BigInteger(this.minesLeft - pl.GetMineCount()) * (pl.GetSolutionCount());
// this is all the possible ways the mines can be placed across the whole game
totalTally = totalTally + mult * (pl.GetSolutionCount());
for (int i = 0; i < emptyBox.Length; i++)
{
if (pl.GetMineBoxCount(i) != 0)
{
emptyBox[i] = false;
}
}
}
}
// determine how many clear squares there are
if (totalTally > 0)
{
for (int i = 0; i < emptyBox.Length; i++)
{
if (emptyBox[i])
{
clearCount = clearCount + boxes[i].GetTiles().Count;
}
}
}
this.finalSolutionCount = totalTally * solutionCountMultiplier;
information.Write("Game has " + this.finalSolutionCount + " candidate solutions");
}
public static SolverActionHeader FindActions(SolverInfo information)
{
long time1 = DateTime.Now.Ticks;
List <SolverAction> actions;
if (information.GetGameStatus() == GameStatus.Lost)
{
information.Write("Game has been lost already - no valid moves");
return(new SolverActionHeader());
}
else if (information.GetGameStatus() == GameStatus.Won)
{
information.Write("Game has been won already - no valid moves");
return(new SolverActionHeader());
}
else if (information.GetGameStatus() == GameStatus.NotStarted)
{
information.Write("Game has not yet started - currently unable to provide help");
return(new SolverActionHeader());
}
// are we walking down a brute force deep analysis tree?
BruteForceAnalysis lastBfa = information.GetBruteForceAnalysis();
if (lastBfa != null) // yes
{
SolverTile expectedMove = lastBfa.GetExpectedMove();
if (expectedMove != null && expectedMove.IsHidden()) // the expected move wasn't played !
{
information.Write("The expected Brute Force Analysis move " + expectedMove.AsText() + " wasn't played");
information.SetBruteForceAnalysis(null);
}
else
{
SolverAction move = lastBfa.GetNextMove();
if (move != null)
{
information.Write("Next Brute Force Deep Analysis move is " + move.AsText());
actions = new List <SolverAction>(1);
actions.Add(move);
return(BuildActionHeader(information, actions));
}
}
}
actions = FindTrivialActions(information);
long time2 = DateTime.Now.Ticks;
information.Write("Finding Trivial Actions took " + (time2 - time1) + " ticks");
// if we have some actions from the trivial search use them
if (actions.Count > 0)
{
return(BuildActionHeader(information, actions));
}
if (information.GetTilesLeft() == information.GetDeadTiles().Count)
{
information.Write("All tiles remaining are dead");
// when all the tiles are dead return the first one (they are all equally good or bad)
foreach (SolverTile guess in information.GetDeadTiles())
{
actions.Add(new SolverAction(guess, ActionType.Clear, 0.5)); // not all 0.5 safe though !!
return(BuildActionHeader(information, actions));
}
}
// get all the witnessed tiles
List <SolverTile> witnesses = new List <SolverTile>(information.GetWitnesses());
HashSet <SolverTile> witnessedSet = new HashSet <SolverTile>();
foreach (SolverTile witness in witnesses)
{
foreach (SolverTile adjTile in information.GetAdjacentTiles(witness))
{
if (adjTile.IsHidden())
{
witnessedSet.Add(adjTile);
}
}
}
List <SolverTile> witnessed = new List <SolverTile>(witnessedSet);
int livingTilesLeft = information.GetTilesLeft();
int livingMinesLeft = information.GetMinesLeft();
int offEdgeTilesLeft = information.GetTilesLeft() - witnessed.Count;
//information.Write("Excluded tiles " + information.GetExcludedTiles().Count + " out of " + information.GetTilesLeft());
//information.Write("Excluded witnesses " + information.GetExcludedWitnesses().Count);
//information.Write("Excluded mines " + information.GetExcludedMineCount() + " out of " + information.GetMinesLeft());
// if there are no living mines but some living tiles then the living tiles can be cleared
if (livingMinesLeft == 0 && livingTilesLeft > 0)
{
information.Write("There are no living mines left - all living tiles must be clearable");
for (int x = 0; x < information.description.width; x++)
{
for (int y = 0; y < information.description.height; y++)
{
SolverTile tile = information.GetTile(x, y);
if (tile.IsHidden() && !tile.IsMine())
{
actions.Add(new SolverAction(tile, ActionType.Clear, 1));
}
}
}
return(BuildActionHeader(information, actions));
}
SolutionCounter solutionCounter = new SolutionCounter(information, witnesses, witnessed, livingTilesLeft, livingMinesLeft);
solutionCounter.Process();
information.Write("Solution counter says " + solutionCounter.GetSolutionCount() + " solutions and " + solutionCounter.getClearCount() + " clears");
//ProbabilityEngine pe = new ProbabilityEngine(information, witnesses, witnessed, information.GetTilesLeft(), information.GetMinesLeft());
ProbabilityEngine pe = new ProbabilityEngine(information, witnesses, witnessed, livingTilesLeft, livingMinesLeft);
pe.Process();
long time3 = DateTime.Now.Ticks;
information.Write("Probability Engine took " + (time3 - time2) + " ticks");
// have we found any local clears which we can use
List <SolverTile> localClears = pe.GetLocalClears();
if (localClears.Count > 0)
{
foreach (SolverTile tile in localClears) // place each local clear into an action
{
actions.Add(new SolverAction(tile, ActionType.Clear, 1));
}
information.Write("The probability engine has found " + localClears.Count + " safe Local Clears");
// add any mines to it
List <SolverTile> minesFound = pe.GetMinesFound();
foreach (SolverTile tile in minesFound) // place each mine found into an action
{
information.MineFound(tile);
actions.Add(new SolverAction(tile, ActionType.Flag, 0));
}
information.Write("The probability engine has found " + minesFound.Count + " mines");
return(BuildActionHeader(information, actions));
}
if (pe.GetBestEdgeProbability() == 1)
{
actions = pe.GetBestCandidates(1);
information.Write("The probability engine has found " + actions.Count + " safe Clears");
// add any mines to it
List <SolverTile> minesFound = pe.GetMinesFound();
foreach (SolverTile tile in minesFound) // place each mine found into an action
{
information.MineFound(tile);
actions.Add(new SolverAction(tile, ActionType.Flag, 0));
}
information.Write("The probability engine has found " + minesFound.Count + " mines");
return(BuildActionHeader(information, actions));
}
// dead edge (all tiles on the edge are dead and there is only one mine count value)
if (pe.GetDeadEdge().Count != 0)
{
SolverTile tile = pe.GetDeadEdge()[0];
information.Write("Probability engine has found a dead area, guessing at " + tile.AsText());
double probability = Combination.DivideBigIntegerToDouble(BigInteger.One, pe.GetDeadEdgeSolutionCount(), 6);
actions.Add(new SolverAction(tile, ActionType.Clear, probability));
return(BuildActionHeader(information, actions));
}
// Isolated edges found (all adjacent tiles are also on the edge and there is only one mine count value)
if (pe.GetOutcome() == ProbabilityEngine.Outcome.ISOLATED_EDGE)
{
information.Write("Probability engine has found an isolated area");
Cruncher cruncher = pe.getIsolatedEdgeCruncher();
// determine all possible solutions
cruncher.Crunch();
// determine best way to solver them
BruteForceAnalysis bfa = cruncher.GetBruteForceAnalysis();
bfa.process();
// if after trying to process the data we can't complete then abandon it
if (!bfa.IsComplete())
{
information.Write("Abandoned the Brute Force Analysis after " + bfa.GetNodeCount() + " steps");
bfa = null;
}
else // otherwise try and get the best long term move
{
information.Write("Built probability tree from " + bfa.GetSolutionCount() + " solutions in " + bfa.GetNodeCount() + " steps");
SolverAction move = bfa.GetNextMove();
if (move != null)
{
information.SetBruteForceAnalysis(bfa); // save the details so we can walk the tree
information.Write("Brute Force Analysis: " + move.AsText());
actions.Add(move);
return(BuildActionHeader(information, actions));
}
else if (bfa.GetAllDead())
{
SolverTile tile = cruncher.getTiles()[0];
information.Write("Brute Force Analysis has decided all tiles are dead on the Isolated Edge, guessing at " + tile.AsText());
double probability = Combination.DivideBigIntegerToDouble(BigInteger.One, bfa.GetSolutionCount(), 6);
actions.Add(new SolverAction(tile, ActionType.Clear, probability));
return(BuildActionHeader(information, actions));
}
else
{
information.Write("Brute Force Analysis: no move found!");
}
}
}
// after this point we know the probability engine didn't return any certain clears. But there are still some special cases when everything off edge is either clear or a mine
// If there are tiles off the edge and they are definitely safe then clear them all, or mines then flag them
if (offEdgeTilesLeft > 0 && (pe.GetOffEdgeProbability() == 1 || pe.GetOffEdgeProbability() == 0))
{
information.Write("Looking for the certain moves off the edge found by the probability engine");
bool clear;
if (pe.GetOffEdgeProbability() == 1)
{
information.Write("All off edge tiles are clear");
clear = true;
}
else
{
information.Write("All off edge tiles are mines");
clear = false;
}
for (int x = 0; x < information.description.width; x++)
{
for (int y = 0; y < information.description.height; y++)
{
SolverTile tile = information.GetTile(x, y);
if (tile.IsHidden() && !witnessedSet.Contains(tile))
{
if (clear)
{
information.Write(tile.AsText() + " is clear");
actions.Add(new SolverAction(tile, ActionType.Clear, 1));
}
else
{
information.Write(tile.AsText() + " is mine");
information.MineFound(tile);
actions.Add(new SolverAction(tile, ActionType.Flag, 0));
}
}
}
}
if (actions.Count > 0)
{
// add any mines to it
List <SolverTile> minesFound = pe.GetMinesFound();
foreach (SolverTile tile in minesFound) // place each mine found into an action
{
information.MineFound(tile);
actions.Add(new SolverAction(tile, ActionType.Flag, 0));
}
information.Write("The probability engine has found " + minesFound.Count + " mines");
return(BuildActionHeader(information, actions));
}
else
{
Console.WriteLine("No Actions found!");
}
}
// these are guesses
List <SolverAction> guesses = pe.GetBestCandidates(1);
// we know the Probability Engine completed so hold onto the information for the gui
information.SetProbabilityEngine(pe);
// if there aren't many possible solutions then do a brute force search
if (pe.GetSolutionCount() <= MAX_BFDA_SOLUTIONS)
{
//if (minesFound.Count > 0) {
// information.Write("Not doing a brute force analysis because we found some mines using the probability engine");
// return BuildActionHeader(information, actions);
//}
// find a set of independent witnesses we can use as the base of the iteration
pe.GenerateIndependentWitnesses();
BigInteger expectedIterations = pe.GetIndependentIterations() * SolverMain.Calculate(livingMinesLeft - pe.GetIndependentMines(), livingTilesLeft - pe.GetIndependentTiles());
information.Write("Expected Brute Force iterations " + expectedIterations);
// do the brute force if there are not too many iterations
if (expectedIterations < MAX_BRUTE_FORCE_ITERATIONS)
{
List <SolverTile> allCoveredTiles = new List <SolverTile>();
for (int x = 0; x < information.description.width; x++)
{
for (int y = 0; y < information.description.height; y++)
{
SolverTile tile = information.GetTile(x, y);
if (tile.IsHidden() && !tile.IsMine())
{
allCoveredTiles.Add(tile);
}
}
}
WitnessWebIterator[] iterators = BuildParallelIterators(information, pe, allCoveredTiles, expectedIterations);
BruteForceAnalysis bfa = Cruncher.PerformBruteForce(information, iterators, pe.GetDependentWitnesses());
bfa.process();
// if after trying to process the data we can't complete then abandon it
if (!bfa.IsComplete())
{
information.Write("Abandoned the Brute Force Analysis after " + bfa.GetNodeCount() + " steps");
bfa = null;
}
else // otherwise try and get the best long term move
{
information.Write("Built probability tree from " + bfa.GetSolutionCount() + " solutions in " + bfa.GetNodeCount() + " steps");
SolverAction move = bfa.GetNextMove();
if (move != null)
{
information.SetBruteForceAnalysis(bfa); // save the details so we can walk the tree
information.Write("Brute Force Analysis: " + move.AsText());
actions.Add(move);
return(BuildActionHeader(information, actions));
}
else
{
information.Write("Brute Force Analysis: no move found!");
}
}
}
else
{
information.Write("Too many iterations, Brute Force not atempted");
}
}
if (guesses.Count == 0) // find an off edge guess
{
if (offEdgeTilesLeft > 0)
{
information.Write("getting an off edge guess");
SolverTile tile = OffEdgeGuess(information, witnessedSet);
SolverAction action = new SolverAction(tile, ActionType.Clear, pe.GetOffEdgeProbability());
information.Write(action.AsText());
actions.Add(action);
}
else
{
if (information.GetDeadTiles().Count > 0)
{
information.Write("Finding a dead tile to guess");
SolverTile tile = null;
foreach (SolverTile deadTile in information.GetDeadTiles()) // get the first dead tile
{
tile = deadTile;
break;
}
SolverAction action = new SolverAction(tile, ActionType.Clear, 0.5); // probability may not be 0.5
actions.Add(action);
}
}
}
else if (guesses.Count > 1) // if we have more than 1 guess then do some tie break logic
{
information.Write("Doing a tie break for " + guesses.Count + " actions");
actions = DoTieBreak(guesses);
}
else
{
actions = guesses;
}
return(BuildActionHeader(information, actions));
}