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November 26, 2017 21:24
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Impuzzable in Picat
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% Impuzzable | |
% https://nrich.maths.org/1388 | |
import cp. | |
import util. | |
main => | |
puzzle(Pieces), | |
time2(Arrangements = find_all_arrangements(Pieces)), | |
foreach(Solution in Arrangements) | |
[Rows, Rotations] = Solution, | |
foreach(Row in Rows) | |
Pieces2 = [P2 : P in Row, P2 = (P - 1) // 4 + 1], | |
writeln(Pieces2) | |
end, | |
foreach(RotRow in Rotations) | |
writeln(RotRow) | |
end, | |
println('') | |
end, | |
printf("%w solutions\n", Arrangements.length) | |
. | |
find_all_arrangements(Pieces) = Solutions => | |
Solutions = findall([Positions, Rotations], arrange(Pieces, Positions, Rotations)). | |
arrange(Pieces, Positions, Rotations) => | |
FlatPieces = flatten(Pieces), | |
Size = ceiling(sqrt(Pieces.length)), | |
Positions = new_array(Size, Size), | |
Indexes = [J : I in 0 .. (Size*Size-1), J = I * 4 + 1], | |
Positions :: Indexes, | |
all_different(array_matrix_to_list(Positions)), | |
Rotations = new_array(Size, Size), | |
Rotations :: 0 .. 3, | |
Center = Size // 2 + 1, | |
Rotations[Center, Center] = 0, % Symmetry breaking | |
Top = 0, Right = 1, Bottom = 2, Left = 3, | |
% Right | |
foreach(Row in 1..Size) | |
foreach(Col in 1..(Size - 1)) | |
PieceIndex = Positions[Row, Col], | |
PieceIndex2 = Positions[Row, Col + 1], | |
Rotation1 = Rotations[Row, Col], | |
RR #= Right + Rotation1, | |
RightIndex #= cond(RR #>= 4, RR - 4, RR), | |
Rotation2 = Rotations[Row, Col + 1], | |
RR2 #= Left + Rotation2, | |
LeftIndex #= cond(RR2 #>= 4, RR2 - 4, RR2), | |
ThisRight #= RightIndex + PieceIndex, | |
OtherLeft #= LeftIndex + PieceIndex2, | |
constrain(ThisRight, OtherLeft, FlatPieces), | |
end, | |
end, | |
% Down | |
foreach(Row in 1..(Size - 1)) | |
foreach(Col in 1..Size) | |
PieceIndex = Positions[Row, Col], | |
PieceIndex2 = Positions[Row + 1, Col], | |
Rotation1 = Rotations[Row, Col], | |
RR #= Bottom + Rotation1, | |
BottomIndex #= cond(RR #>= 4, RR - 4, RR), | |
Rotation2 = Rotations[Row + 1, Col], | |
RR2 #= Top + Rotation2, | |
TopIndex #= cond(RR2 #>= 4, RR2 - 4, RR2), | |
ThisBottom #= BottomIndex + PieceIndex, | |
OtherTop #= TopIndex + PieceIndex2, | |
constrain(ThisBottom, OtherTop, FlatPieces), | |
end, | |
end, | |
solve(Positions ++ Rotations) | |
. | |
constrain(I1, I2, L) => | |
element(I1, L, Side1), | |
element(I2, L, Side2), | |
Side1 + Side2 #= 0 | |
. | |
puzzle(Pieces) => | |
HeP = 1, HeN = -1, | |
DiP = 2, DiN = -2, | |
ClP = 3, ClN = -3, | |
SpP = 4, SpN = -4, | |
Pieces = [ | |
[HeN, DiN, HeP, ClP], | |
[DiP, ClP, SpN, DiN], | |
[SpP, DiP, HeN, DiN], | |
[ClN, ClN, SpP, SpN], | |
[SpN, SpP, DiP, ClN], | |
[ClP, ClN, DiN, DiP], | |
[HeP, ClP, DiN, ClN], | |
[HeN, SpN, DiP, HeP], | |
[SpN, HeP, HeP, DiN] | |
]. |
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