/**
* 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 = Functions.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)
{
Assert(false, e.Message, e);
return(null);
}
}
return(ab.GetStateAndGenerator());
}
public static PuzzleStateAndGenerator ApplyOrientation(CubePuzzle puzzle, CubeMove[] randomOrientation,
PuzzleStateAndGenerator psag, bool discardRedundantMoves)
{
if (randomOrientation.Length == 0)
{
return(psag);
}
// Append reorientation to scramble.
try
{
var ab = new AlgorithmBuilder(MergingMode.NoMerging, puzzle.GetSolvedState());
ab.AppendAlgorithm(psag.Generator);
foreach (var cm in randomOrientation)
{
ab.AppendMove(cm.ToString());
}
psag = ab.GetStateAndGenerator();
return(psag);
}
catch (InvalidMoveException e)
{
Assert(false, e.Message, e);
return(null);
}
}
public override PuzzleStateAndGenerator GenerateRandomMoves(Random r)
{
var scramble = _threePhaseSearcher.RandomState(r);
var ab = new AlgorithmBuilder(MergingMode.CanonicalizeMoves, GetSolvedState());
try
{
ab.AppendAlgorithm(scramble);
}
catch (InvalidMoveException e)
{
Assert(false, e.Message, new InvalidScrambleException(scramble, e));
}
return(ab.GetStateAndGenerator());
}
public PuzzleStateAndGenerator GenerateRandomMoves(Random r, string firstAxisRestriction,
string lastAxisRestriction)
{
var randomState = Tools.RandomCube(r);
var scramble =
_twoPhaseSearcher.Solution(randomState, ThreeByThreeMaxScrambleLength, ThreeByThreeTimeout,
ThreeByThreeTimemin, Search.INVERSE_SOLUTION, firstAxisRestriction, lastAxisRestriction).Trim();
var ab = new AlgorithmBuilder(MergingMode.CanonicalizeMoves, GetSolvedState());
try
{
ab.AppendAlgorithm(scramble);
}
catch (InvalidMoveException e)
{
Assert(false, e.Message, new InvalidScrambleException(scramble, e));
}
return(ab.GetStateAndGenerator());
}
public static PuzzleStateAndGenerator ApplyOrientation(CubePuzzle puzzle, CubeMove[] randomOrientation,
PuzzleStateAndGenerator psag, bool discardRedundantMoves)
{
if (randomOrientation.Length == 0)
{
return(psag);
}
// Append reorientation to scramble.
try
{
var ab = new AlgorithmBuilder(MergingMode.NoMerging, puzzle.GetSolvedState());
ab.AppendAlgorithm(psag.Generator);
// Check if our reorientation is going to cancel with the last
// turn of our scramble. If it does, then we just discard
// that last turn of our scramble. This ensures we have a scramble
// with no redundant turns, and I can't see how it could hurt the
// quality of our scrambles to do this.
var firstReorientMove = randomOrientation[0].ToString();
while (ab.IsRedundant(firstReorientMove))
{
//azzert(discardRedundantMoves);
var im = ab.FindBestIndexForMove(firstReorientMove, MergingMode.CanonicalizeMoves);
ab.PopMove(im.Index);
}
foreach (var cm in randomOrientation)
{
ab.AppendMove(cm.ToString());
}
psag = ab.GetStateAndGenerator();
return(psag);
}
catch (InvalidMoveException e)
{
Assert(false, e.Message, e);
return(null);
}
}
public override PuzzleStateAndGenerator GenerateRandomMoves(Random r)
{
// For fewest moves, we want to minimize the probability that the
// scramble has useful "stuff" in it. The problem with conventional
// Kociemba 2 phase solutions is that there's a pretty obvious
// orientation step, which competitors might intentionally (or even
// accidentally!) use in their solution. To lower the probability of this happening,
// we intentionally generate dumbed down solutions.
// We eventually decided to go with "Tom2", which is described by Tom
// Rokicki (https://groups.google.com/d/msg/wca-admin/vVnuhk92hqg/P5oaJJQjDQAJ):
// START TOM MESSAGE
// If we're going this direction, and the exact length isn't critical, why not combine a bunch of the
// ideas we've seen so far into something this simple:
//
// 1. Fix a set of prefix/suffix moves, say, U F R / U F R.
// 2. For a given position p, find *any* solution where that solution prefixed and suffixed with
// the appropriate moves is canonical.
//
// That's it. So we generate a random position, then find any two-phase solution g such
// that U F R g U F R is a canonical sequence, and that's our FMC scramble.
//
// The prefix/suffix will be easily recognizable and memorable and ideally finger-trick
// friendly (if it matters).
//
// Someone wanting to practice speed FMC (hehe) can make up their own scrambles just
// by manually doing the prefix/suffix thing on any existing scrambler.
//
// It does not perturb the uniformity of the random position selection.
//
// It's simple enough that it is less likely to suffer from subtle defects due to the
// perturbation of the two-phase search (unlikely those these may be).
//
// And even if the two-phase solution is short, adding U F R to the front and back makes it
// no longer be unusually short (with high probability).
// END TOM MESSAGE
// Michael Young suggested using R' U' F as our padding (https://groups.google.com/d/msg/wca-admin/vVnuhk92hqg/EzQfG_vPBgAJ):
// START MICHAEL MESSSAGE
// I think that something more like R' U' F (some sequence that
// involves a quarter-turn on all three "axes") is better because it
// guarantees at least one bad edge in every orientation; with EO-first
// options becoming more popular, "guaranteeing" that solving EO
// optimally can't be derived from the scramble is a nice thing to
// have, I think. (Someone who was both unscrupulous and lucky could
// see that R' F R doesn't affect U2/D2 EO, and therefore find out how
// to solve EO by looking at the solution ignoring the R' F R. That
// being said, it still does change things, and I like how
// finger-tricky/reversible the current prefix is.) Just my two cents,
// 'tho.
// END MICHAEL MESSSAGE
var scramblePrefix = SplitAlgorithm("R' U' F");
var scrambleSuffix = SplitAlgorithm("R' U' F");
// super.generateRandomMoves(...) will pick a random state S and find a solution:
// solution = sol_0, sol_1, ..., sol_n-1, sol_n
// We then invert that solution to create a scramble:
// scramble = sol_n' + sol_(n-1)' + ... + sol_1' + sol_0'
// We then prefix the scramble with scramblePrefix and suffix it with
// scrambleSuffix to create paddedScramble:
// paddedScramble = scramblePrefix + scramble + scrambleSuffix
// paddedScramble = scramblePrefix + (sol_n' + sol_(n-1)' + ... + sol_1' + sol_0') + scrambleSuffix
//
// We don't want any moves to cancel here, so we need to make sure that
// sol_n' doesn't cancel with the first move of scramblePrefix:
var solutionLastAxisRestriction = scramblePrefix[scramblePrefix.Length - 1].Substring(0, 1);
// and we need to make sure that sol_0' doesn't cancel with the first move of
// scrambleSuffix:
var solutionFirstAxisRestriction = scrambleSuffix[0].Substring(0, 1);
var psag = GenerateRandomMoves(r, solutionFirstAxisRestriction, solutionLastAxisRestriction);
var ab = new AlgorithmBuilder(MergingMode.NoMerging, GetSolvedState());
try
{
ab.AppendAlgorithms(scramblePrefix);
ab.AppendAlgorithm(psag.Generator);
ab.AppendAlgorithms(scrambleSuffix);
}
catch (InvalidMoveException e)
{
Assert(false, e.Message, e);
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;
int i = 0;
int j = 0;
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)
{
i++;
seenExtending = seenSolved;
fringeExtending = fringeSolved;
seenComparing = seenScrambled;
minComparingFringe = minFringeScrambled;
}
else
{
j++;
seenExtending = seenScrambled;
fringeExtending = fringeScrambled;
seenComparing = seenSolved;
minComparingFringe = minFringeSolved;
}
PuzzleState node = fringeExtending.Pop();
int distance = seenExtending[node];
if (seenComparing.ContainsKey(node))
{
// We found an intersection! Compute the total cost of the
// path going through this node.
int 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.
int bestPossibleSolution = distance + minComparingFringe;
if (bestPossibleSolution >= bestIntersectionCost)
{
continue;
}
if (distance >= (n + 1) / 2)
{
continue;
}
var movesByState = node.GetCanonicalMovesByState();
foreach (PuzzleState next in movesByState.Keys)
{
int moveCost = node.GetMoveCost(movesByState[next]);
int nextDistance = distance + moveCost;
//next = next.getNormalized();
PuzzleState 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
Assert(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;
}
Assert(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)
{
Assert(false, e.Message, e);
}
distanceFromScrambled = seenScrambled[state.GetNormalized()];
goto outer2;
}
Assert(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)
{
Assert(false, e.Message, e);
}
goto outer3;
}
Assert(false);
outer3:
;
}
return(solution.ToString());
}
