/**
* This function will generate getRandomTurnCount() number of non cancelling,
* random turns. If a puzzle wants to provide custom scrambles
* (for example: Pochmann style megaminx or MRSS), it should override this method.
*
* NOTE: It is assumed that this method is thread safe! That means that if you're
* overriding this method and you don't know what you're doing,
* use the synchronized keyword when implementing this method:<br>
* <code>protected synchronized String generateScramble(Random r);</code>
* @param r An instance of Random
* @return A PuzzleStateAndGenerator that contains a scramble string, and the
* state achieved by applying that scramble.
*/
public virtual PuzzleStateAndGenerator GenerateRandomMoves(Random r)
{
var ab = new AlgorithmBuilder(MergingMode.NoMerging, GetSolvedState());
while (ab.GetTotalCost() < GetRandomMoveCount())
{
var successors = ab.GetState().GetScrambleSuccessors();
try
{
string move;
do
{
move = choose(r, successors.Keys);
// If this move happens to be redundant, there is no
// reason to select this move again in vain.
successors.Remove(move);
} while (ab.IsRedundant(move));
ab.AppendMove(move);
}
catch (InvalidMoveException e)
{
azzert(false, e.Message);
return(null);
}
}
return(ab.GetStateAndGenerator());
}
protected virtual string SolveIn(PuzzleState ps, int n)
{
if (ps.IsSolved())
{
return("");
}
var seenSolved = new Dictionary <PuzzleState, int>();
var fringeSolved = new SortedBuckets <PuzzleState>();
var seenScrambled = new Dictionary <PuzzleState, int>();
var fringeScrambled = new SortedBuckets <PuzzleState>();
// We're only interested in solutions of cost <= n
var bestIntersectionCost = n + 1;
PuzzleState bestIntersection = null;
var solvedNormalized = GetSolvedState().GetNormalized();
fringeSolved.Add(solvedNormalized, 0);
seenSolved[solvedNormalized] = 0;
fringeScrambled.Add(ps.GetNormalized(), 0);
seenScrambled[ps.GetNormalized()] = 0;
//TimedLogRecordStart start = new TimedLogRecordStart(Level.FINER, "Searching for solution in " + n + " moves.");
//l.log(start);
var fringeTies = 0;
// The task here is to do a breadth-first search starting from both the solved state and the scrambled state.
// When we got an intersection from the two hash maps, we are done!
int minFringeScrambled = -1, minFringeSolved = -1;
while (!fringeSolved.IsEmpty() || !fringeScrambled.IsEmpty())
{
// We have to choose on which side we are extending our search.
// I'm choosing the non empty fringe with the node nearest
// its origin. In the event of a tie, we make sure to alternate.
if (!fringeScrambled.IsEmpty())
{
minFringeScrambled = fringeScrambled.SmallestValue();
}
if (!fringeSolved.IsEmpty())
{
minFringeSolved = fringeSolved.SmallestValue();
}
bool extendSolved;
if (fringeSolved.IsEmpty() || fringeScrambled.IsEmpty())
{
// If the solved fringe is not empty, we'll expand it.
// Otherwise, we're expanding the scrambled fringe.
extendSolved = !fringeSolved.IsEmpty();
}
else
{
if (minFringeSolved < minFringeScrambled)
{
extendSolved = true;
}
else if (minFringeSolved > minFringeScrambled)
{
extendSolved = false;
}
else
{
extendSolved = fringeTies++ % 2 == 0;
}
}
// We are using references for a more concise code.
Dictionary <PuzzleState, int> seenExtending;
SortedBuckets <PuzzleState> fringeExtending;
Dictionary <PuzzleState, int> seenComparing;
int minComparingFringe;
if (extendSolved)
{
seenExtending = seenSolved;
fringeExtending = fringeSolved;
seenComparing = seenScrambled;
minComparingFringe = minFringeScrambled;
}
else
{
seenExtending = seenScrambled;
fringeExtending = fringeScrambled;
seenComparing = seenSolved;
minComparingFringe = minFringeSolved;
}
var node = fringeExtending.Pop();
var distance = seenExtending[node];
if (seenComparing.ContainsKey(node))
{
// We found an intersection! Compute the total cost of the
// path going through this node.
var cost = seenComparing[node] + distance;
if (cost < bestIntersectionCost)
{
bestIntersection = node;
bestIntersectionCost = cost;
}
continue;
}
// The best possible solution involving this node would
// be through a child of this node that gets us across to
// the other fringe's smallest distance node.
var bestPossibleSolution = distance + minComparingFringe;
if (bestPossibleSolution >= bestIntersectionCost)
{
continue;
}
if (distance >= (n + 1) / 2)
{
continue;
}
var movesByState = node.GetCanonicalMovesByState();
foreach (var next in movesByState.Keys)
{
var moveCost = node.GetMoveCost(movesByState[next]);
var nextDistance = distance + moveCost;
//next = next.getNormalized();
var nNext = next.GetNormalized();
if (seenExtending.ContainsKey(nNext))
{
if (nextDistance >= seenExtending[nNext])
{
continue;
}
}
fringeExtending.Add(nNext, nextDistance);
seenExtending[nNext] = nextDistance;
}
}
//l.log(start.finishedNow("expanded " + (seenSolved.size() + seenScrambled.size()) + " nodes"));
if (bestIntersection == null)
{
return(null);
}
// We have found a solution, but we still have to recover the move sequence.
// the `bestIntersection` is the bound between the solved and the scrambled states.
// We can travel from `bestIntersection` to either states, like that:
// solved <----- bestIntersection -----> scrambled
// However, to build a solution, we need to travel like that:
// solved <----- bestIntersection <----- scrambled
// So we have to travel backward for the scrambled side.
// Step 1: bestIntersection -----> scrambled
azzert(bestIntersection.IsNormalized());
var state = bestIntersection;
var distanceFromScrambled = seenScrambled[state];
// We have to keep track of all states we have visited
var linkedStates = new PuzzleState[distanceFromScrambled + 1];
linkedStates[distanceFromScrambled] = state;
while (distanceFromScrambled > 0)
{
foreach (var next in state.GetCanonicalMovesByState().Keys)
{
var nNext = next.GetNormalized();
if (!seenScrambled.ContainsKey(nNext))
{
continue;
}
var newDistanceFromScrambled = seenScrambled[nNext];
if (newDistanceFromScrambled >= distanceFromScrambled)
{
continue;
}
state = nNext;
distanceFromScrambled = newDistanceFromScrambled;
linkedStates[distanceFromScrambled] = state;
goto outer1;
}
azzert(false);
outer1:
;
}
// Step 2: bestIntersection <----- scrambled
var solution = new AlgorithmBuilder(MergingMode.CanonicalizeMoves, ps);
state = ps;
distanceFromScrambled = 0;
while (!state.EqualsNormalized(bestIntersection))
{
foreach (var next in state.GetCanonicalMovesByState())
{
var nextState = next.Key;
var moveName = next.Value;
if (!nextState.EqualsNormalized(linkedStates[distanceFromScrambled + 1]))
{
continue;
}
state = nextState;
try
{
solution.AppendMove(moveName);
}
catch (InvalidMoveException e)
{
azzert(false, e.Message);
}
distanceFromScrambled = seenScrambled[state.GetNormalized()];
goto outer2;
}
azzert(false);
outer2:
;
}
// Step 3: solved <----- bestIntersection
var distanceFromSolved = seenSolved[state.GetNormalized()];
while (distanceFromSolved > 0)
{
foreach (var next in state.GetCanonicalMovesByState())
{
var nextState = next.Key;
var nextStateNormalized = nextState.GetNormalized();
var moveName = next.Value;
if (!seenSolved.ContainsKey(nextStateNormalized))
{
continue;
}
var newDistanceFromSolved = seenSolved[nextStateNormalized];
if (newDistanceFromSolved >= distanceFromSolved)
{
continue;
}
state = nextState;
distanceFromSolved = newDistanceFromSolved;
try
{
solution.AppendMove(moveName);
}
catch (InvalidMoveException e)
{
azzert(false, e.Message);
}
goto outer3;
}
azzert(false);
outer3:
;
}
return(solution.ToString());
}
