1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 | % % ECLiPSe Nonogram Solver % % by Joachim Schimpf, IC-Parc, Imperial College, London, January 2001 % % Problem: % % Nonograms are a popular puzzle, which goes by different names in % different countries. The player has to shade in squares in a grid so % that blocks of consecutive shaded squares satisfy constraints given % for each row and column. Constraints typically indicate the sequence % of shaded blocks (e.g. [3,1,2] means that there is a block of 3, then % a gap of unspecified size, a block of length 1, another gap, and then % a block of length 2). Data for sample problems is at the end of this file, % for more see e.g. http://www.puzzle.gr.jp/nonogram/prob/0200_e.html % % Solution: % % This code solves all the problems below, the hardest one so far % being p200 (25x25): % % ps,n2-n16 by propagation alone % p197,p199,p200 with search, takes a while % % The main idea here is to have a powerful constraint (line_lookahead/4) % which solves a single-line subproblem and exports the generalised % result (using ECLiPSe's propia library). % % No particularly clever search strategy is used, just first-fail. % :- lib(ic). :- lib(propia). go( Name , Board ) :- data( Name , M , N , RowBlocks , ColBlocks ), % get the data check_data( M , N , RowBlocks , ColBlocks ), dim( Board , [ M , N ]), ( % row constraints for ( I ,1, M ), foreach ( Blocks , RowBlocks ), foreach ( Positions , RowPositions ), param ( Board , N ) do matrix_row( Board , I , Line ), line_setup( N , Line , Blocks , Positions ), line_lookahead( N , Line , Blocks , Positions ) ), ( % column constraints for ( J ,1, N ), foreach ( Blocks , ColBlocks ), foreach ( Positions , ColPositions ), param ( Board , M ) do matrix_column( Board , J , Line ), line_setup( M , Line , Blocks , Positions ), line_lookahead( M , Line , Blocks , Positions ) ), % pretty_print(Board), flatten([ RowPositions , ColPositions ], AllPositions ), % search search( AllPositions , 0, first_fail, indomain, complete, []), pretty_print( Board ). % setup constraints on one line (row or column) % % Line is an array of boolean variables % Blocks is a list of block sizes (integers) % Positions is a list of variables representing the block positions % Gaps is a list of variables representing the gap sizes line_setup( NFields , Line , Blocks , Positions ) :- length( Blocks , NBlocks ), dim( Line , [ NFields ]), % field variables Line [1.. NFields ] :: 0..1, length( Positions , NBlocks ), % position variables Positions :: 1.. NFields , NGaps is NBlocks +1, % gap variables length( Gaps , NGaps ), Gaps = [ Gap1 | Gaps2N ], once append( InnerGaps , [ GapN ], Gaps2N ), [ Gap1 , GapN ] :: 0.. NFields , % outer gaps can be empty InnerGaps :: 1.. NFields , % inner gaps must exist sum( Line [1.. NFields ]) #= sum( Blocks ), ( foreach ( Position , Positions ), fromto ( Blocks , RightBlocks , RightBlocks1 , []), fromto ([], LeftBlocks , [ Block | LeftBlocks ], _BlocksReverse ), fromto ( Gaps2N , RightGaps , RightGaps1 , []), fromto ([ Gap1 ], LeftGaps , [ RightGap | LeftGaps ], _GapsReverse ), param ( NFields , Line ) do RightBlocks = [ Block | RightBlocks1 ], RightGaps = [ RightGap | RightGaps1 ], LeftGaps = [ LeftGap | _ ], Position #= 1 + sum( LeftBlocks ) + sum( LeftGaps ), Position #= 1 + NFields - (sum( RightBlocks ) + sum( RightGaps )), place_block( Line , Position , LeftGap , Block , RightGap ) ). % constraint to update the Line-booleans that correspond % to the block at Position and the adjacent gaps place_block( Line , Position , LeftGap , BlockSize , RightGap ) :- nonvar( Position ), get_bounds( LeftGap , MinLeftGap , _ ), ( for ( I , Position - MinLeftGap , Position -1), param ( Line ) do arg( I , Line , 0) ), ( for ( I , Position , Position + BlockSize -1), param ( Line ) do arg( I , Line , 1) ), get_bounds( RightGap , MinRightGap , _ ), ( for ( I , Position + BlockSize , Position + BlockSize + MinRightGap -1), param ( Line ) do arg( I , Line , 0) ). place_block( Line , Position , LeftGap , BlockSize , RightGap ) :- var( Position ), suspend (place_block( Line , Position , LeftGap , BlockSize , RightGap ), 2, [ Position ->inst]). % Lookahead constraint for one line: % This uses propia to compute the most general solution % for the single line subproblem line_lookahead( NFields , Line , Blocks , Positions ) :- suspend ( solve_line_problem( NFields , Line , Positions , Blocks ), 7, [ Line ->inst, Positions ->ic:min, Positions ->ic:max] ) infers most. solve_line_problem( NFields , Line , Positions , Blocks ) :- line_setup( NFields , Line , Blocks , Positions ), labeling( Positions ). %---------------------------------------------------------------------- % Auxiliaries %---------------------------------------------------------------------- matrix_row( Mat , I , Row ) :- Row is Mat [ I ]. matrix_column( Mat , J , Col ) :- dim( Mat , [ M , _N ]), ColList is Mat [1.. M , J ], Col =.. [[]| ColList ]. pretty_print( Board ) :- dim( Board , [ M , N ]), ( for ( I ,1, M ), param ( Board , N ) do ( for ( J ,1, N ), param ( Board , I ) do X is Board [ I , J ], ( X ==0 -> write( " " ) ; X ==1 -> write( " *" ) ; write( " ?" ) ) ), nl ), nl. %---------------------------------------------------------------------- % sample problems % % data(ProblemName, NRows, NColumns, RowBlocks, ColumnBlocks) %---------------------------------------------------------------------- data(ps, 9, 8, [[3],[2,1],[3,2],[2,2],[6],[1,5],[6],[1],[2]], % row blocks [[1,2],[3,1],[1,5],[7,1],[5],[3],[4],[3]] % column blocks ). % from http://www.pro.or.jp/~fuji/java/puzzle/nonogram/index-eng.html data(n2, 10, 10, [[1],[3],[1,3],[2,4],[1,2],[2,1,1],[1,1,1,1],[2,1,1],[2,2],[5]], [[4],[1,3],[2,3],[1,2],[2,2],[1,1,1],[1,1,1,1],[1,1,1],[1,2],[5]] ). data(n3, 10, 15, [[4],[1,1,6],[1,1,6],[1,1,6],[4,9],[1,1],[1,1],[2,7,2],[1,1,1,1],[2,2]], [[4],[1,2],[1,1],[5,1],[1,2],[1,1],[5,1],[1,1],[4,1],[4,1],[4,2],[4,1],[4,1],[4,2],[4]] ). data(n4, 6, 6, [[2,1],[1],[2],[2],[1],[1,2]], [[1,2],[1],[2],[2],[1],[2,1]] ). data(n5, 10, 10, [[3],[3],[1],[3],[6],[3],[3],[3,3],[2,2],[2,1]], [[1],[1,2],[1,2],[1,1],[2,5],[7],[2,5],[1],[2],[2]] ). data(n6, 15, 15, [[5],[2,2],[1,1],[1,1],[4,4],[2,2,1,2],[1,3,1],[1,1,1,1],[2,7,2],[4,1,5],[2,1,1],[1,1,2],[1,1,1],[2,5,2],[3,4]], [[4],[2,2],[1,5],[1,2,2],[5,2,1],[2,1,1,2],[1,3,1],[1,1,6],[1,3,1],[2,1,2,2],[4,2,1],[1,1,1],[1,3,2],[2,2,3],[4]] ). data(n16, 15, 15, [[4],[2,2],[2,2],[2,4,2],[2,1,1,2],[2,4,2],[1,2],[4,4,4],[1,1,1,1,1,1],[4,1,1,4],[1,1,1],[1,1,3],[10],[2,1],[4,1]], [[5,1],[2,1,1,1],[2,1,1,2],[2,3,3],[2,1],[2,3,6],[1,1,1,1,1],[1,1,1,1,1],[2,3,6],[2,1],[2,3,1],[2,1,1,1],[2,1,1,4],[7],[1,1]] ). data(n19, R , C , RB , CB ) :- data(p199, R , C , RB , CB ). data(p197, 20, 15, % difficulty 7 [[3],[1,2],[1,4],[1,1,2],[1,1,1,1],[1,3,2],[2,3,1],[1,1,1,2],[2,2,2],[1,1,2,2],[1,1,2,2],[1,1,1,1],[4,1,1],[2,2,2,1],[2,3,3],[2,2,3],[1,3,1,1],[2,1,1,1,2],[1,2,3],[1,6]], [[4,3],[6,1,2,3],[2,3],[6],[1,2,2],[1,1,2],[2,4,1,1],[1,1,2,2,2,1],[1,1,1,2,1,1],[1,3,2,3],[3,2,2],[4,3,4,2],[1,3,4,5],[2,2],[3]] ). data(p199, 20, 20, % difficulty 8 [[1,1,4],[1,6],[1,1,1,1,2,3],[1,1,2,3],[3,1,2,3],[4,5,2,2],[7,3,2],[3,5,1,2],[2,2,4,1],[2,2,3,4],[2,5,2],[2,1,5,1],[2,2,3,1],[6,2,2],[1,7],[2,2,2],[1,4],[3,1,1],[1,1],[1,1]], [[6,1],[8,3],[3,2,1],[1,1,2,2,1],[1,2,2,1,1],[1,1,1,1],[2,3],[4,1,2,2],[5,2,1],[8,1,1],[7,2],[3,5,2],[2,5],[2,1,4],[2,2,2,2],[2,2,1,1,1],[3,1,1,1,1],[5,4,2,1],[7,4,1,1],[4]] ). data(p200, 25, 25, % difficulty 9 [[1,1,2,2],[5,5,7],[5,2,2,9],[3,2,3,9],[1,1,3,2,7],[3,1,5],[7,1,1,1,3],[1,2,1,1,2,1],[4,2,4],[1,2,2,2],[4,6,2],[1,2,2,1],[3,3,2,1],[4,1,15],[1,1,1,3,1,1],[2,1,1,2,2,3],[1,4,4,1],[1,4,3,2],[1,1,2,2],[7,2,3,1,1],[2,1,1,1,5],[1,2,5],[1,1,1,3],[4,2,1],[3]], [[2,2,3],[4,1,1,1,4],[4,1,2,1,1],[4,1,1,1,1,1,1],[2,1,1,2,3,5],[1,1,1,1,2,1],[3,1,5,1,2],[3,2,2,1,2,2],[2,1,4,1,1,1,1],[2,2,1,2,1,2],[1,1,1,3,2,3],[1,1,2,7,3],[1,2,2,1,5],[3,2,2,1,2],[3,2,1,2],[5,1,2],[2,2,1,2],[4,2,1,2],[6,2,3,2],[7,4,3,2],[7,4,4],[7,1,4],[6,1,4],[4,2,2],[2,1]] ). % the example quoted in Optima#65, Mathematical Programming Society Newsletter data(optima, 20, 20, [[7,1],[1,1,2],[2,1,2],[1,2,2],[4,2,3],[3,1,4],[3,1,3],[2,1,4],[2,9],[2,1,5],[2,7],[14],[8,2],[6,2,2],[2,8,1,3],[1,5,5,2],[1,3,2,4,1],[3,1,2,4,1],[1,1,3,1,3],[2,1,1,2]], [[1,1,1,2],[3,1,2,1,1],[1,4,2,1,1],[1,3,2,4],[1,4,6,1],[1,11,1],[5,1,6,2],[14],[7,2],[7,2],[6,1,1],[9,2],[3,1,1,1],[3,1,3],[2,1,3],[2,1,5],[3,2,2],[3,3,2],[2,3,2],[2,6]] ). % simple check for typos in the data check_data( M , N , RowBlocks , ColBlocks ) :- length( RowBlocks , M ), length( ColBlocks , N ), ( foreach ( Blocks , RowBlocks ), fromto (0, S0 , S1 , RowTotal ) do S1 is S0 +sum( Blocks ) ), ( foreach ( Blocks , ColBlocks ), fromto (0, S0 , S1 , ColTotal ) do S1 is S0 +sum( Blocks ) ), RowTotal = ColTotal , !. check_data( _ , _ , _ , _ ) :- writeln( "Inconsistent input data!" ), abort. |