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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 | /* Crossfigure problem (CSPLib #21) in B-Prolog. CSPLib problem 21 """ Crossfigures are the numerical equivalent of crosswords. You have a grid and some clues with numerical answers to place on this grid. Clues come in several different forms (for example: Across 1. 25 across times two, 2. five dozen, 5. a square number, 10. prime, 14. 29 across times 21 down ...). """ Also, see William Y. Sit: "On Crossnumber Puzzles and The Lucas-Bonaccio Farm 1998 http://scisun.sci.ccny.cuny.edu/~wyscc/CrossNumber.pdf Bill Williams: Crossnumber Puzzle, The Little Pigley Farm Model created by Hakan Kjellerstrand, hakank@gmail.com*/% Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0//* This model was inspired by the ECLiPSe model written by Warwick Harvey: http://www.cs.st-andrews.ac.uk/~ianm/CSPLib/prob/prob021/code.html Data from This problem is 001 from http://thinks.com/crosswords/xfig.htm ("X" is the blackbox and is fixed to the value of 0) 1 2 3 4 5 6 7 8 9 --------------------------- 1 2 _ 3 X 4 _ 5 6 1 7 _ X 8 _ _ X 9 _ 2 _ X 10 _ X 11 12 X _ 3 13 14 _ _ X 15 _ 16 _ 4 X _ X X X X X _ X 5 17 _ 18 19 X 20 21 _ 22 6 _ X 23 _ X 24 _ X _ 7 25 26 X 27 _ _ X 28 _ 8 29 _ _ _ X 30 _ _ _ 9 The answer is 1608 9183 60 201 42 3 72 14 1 5360 2866 3 4 4556 1156 9 67 16 8 68 804 48 1008 7332 Solutions: MiniZinc and Gecode/fz solves the problem in about 8 seconds. ECLiPSe/ic: 35 seconds MiniZinc/fdmip in 14 seconds. Comet: 1 second.*/go :- N = 9, % Domain = 0..9999, % the max length of the numbers in this problem is 4 new_array(M,[N,N]), array_to_list(M,MVars), MVars :: 0..9, AList = [A1,A4,A7,A8,A9,A10,A11,A13,A15,A17,A20,A23,A24,A25,A27,A28,A29,A30], AList :: 0..9999, DList = [D1,D2,D3,D4,D5,D6,D10,D12,D14,D17,D18,D19,D20,D21,D22,D26,D28], DList :: 0..9999, % Set up the constraints between the matrix elements and the % clue numbers. across(M, A1, 4, 1, 1), across(M, A4, 4, 1, 6), across(M, A7, 2, 2, 1), across(M, A8, 3, 2, 4), across(M, A9, 2, 2, 8), across(M, A10, 2, 3, 3), across(M, A11, 2, 3, 6), across(M, A13, 4, 4, 1), across(M, A15, 4, 4, 6), across(M, A17, 4, 6, 1), across(M, A20, 4, 6, 6), across(M, A23, 2, 7, 3), across(M, A24, 2, 7, 6), across(M, A25, 2, 8, 1), across(M, A27, 3, 8, 4), across(M, A28, 2, 8, 8), across(M, A29, 4, 9, 1), across(M, A30, 4, 9, 6), down(M, D1, 4, 1, 1), down(M, D2, 2, 1, 2), down(M, D3, 4, 1, 4), down(M, D4, 4, 1, 6), down(M, D5, 2, 1, 8), down(M, D6, 4, 1, 9), down(M, D10, 2, 3, 3), down(M, D12, 2, 3, 7), down(M, D14, 3, 4, 2), down(M, D16, 3, 4, 8), down(M, D17, 4, 6, 1), down(M, D18, 2, 6, 3), down(M, D19, 4, 6, 4), down(M, D20, 4, 6, 6), down(M, D21, 2, 6, 7), down(M, D22, 4, 6, 9), down(M, D26, 2, 8, 2), down(M, D28, 2, 8, 8), % Set up the clue constraints. % Across % 1 27 across times two % 4 4 down plus seventy-one % 7 18 down plus four % 8 6 down divided by sixteen % 9 2 down minus eighteen % 10 Dozen in six gross % 11 5 down minus seventy % 13 26 down times 23 across % 15 6 down minus 350 % 17 25 across times 23 across % 20 A square number % 23 A prime number % 24 A square number % 25 20 across divided by seventeen % 27 6 down divided by four % 28 Four dozen % 29 Seven gross % 30 22 down plus 450 A1 #= 2 * A27, A4 #= D4 + 71, A7 #= D18 + 4, A8 #= D6 // 16, A9 #= D2 - 18, A10 #= 6 * 144 // 12, A11 #= D5 - 70, A13 #= D26 * A23, A15 #= D6 - 350, A17 #= A25 * A23, square(A20), is_prime(A23), square(A24), A25 #= A20 // 17, A27 #= D6 // 4, A28 #= 4 * 12, A29 #= 7 * 144, A30 #= D22 + 450, % Down % % 1 1 across plus twenty-seven % 2 Five dozen % 3 30 across plus 888 % 4 Two times 17 across % 5 29 across divided by twelve % 6 28 across times 23 across % 10 10 across plus four % 12 Three times 24 across % 14 13 across divided by sixteen % 16 28 down times fifteen % 17 13 across minus 399 % 18 29 across divided by eighteen % 19 22 down minus ninety-four % 20 20 across minus nine % 21 25 across minus fifty-two % 22 20 down times six % 26 Five times 24 across % 28 21 down plus twenty-seven D1 #= A1 + 27, D2 #= 5 * 12, D3 #= A30 + 888, D4 #= 2 * A17, D5 #= A29 // 12, D6 #= A28 * A23, D10 #= A10 + 4, D12 #= A24 * 3, D14 #= A13 // 16, D16 #= 15 * D28, D17 #= A13 - 399, D18 #= A29 // 18, D19 #= D22 - 94, D20 #= A20 - 9, D21 #= A25 - 52, D22 #= 6 * D20, D26 #= 5 * A24, D28 #= D21 + 27, % Fix the black boxes M[1,5] #= 0, M[2,3] #= 0, M[2,7] #= 0, M[3,2] #= 0, M[3,5] #= 0, M[3,8] #= 0, M[4,5] #= 0, M[5,1] #= 0, M[5,3] #= 0, M[5,4] #= 0, M[5,5] #= 0, M[5,6] #= 0, M[5,7] #= 0, M[5,9] #= 0, M[6,5] #= 0, M[7,2] #= 0, M[7,5] #= 0, M[7,8] #= 0, M[8,3] #= 0, M[8,7] #= 0, M[9,5] #= 0, term_variables([MVars,AList,DList], Vars), labeling(Vars), writeln(M). /* across(Matrix, Across, Len, Row, Col) Constrains 'Across' to be equal to the number represented by the 'Len' digits starting at position (Row, Col) of the array 'Matrix' and proceeding across.*/across(Matrix, Across, Len, Row, Col) :- length(Tmp,Len), Tmp :: 0..9999, toNum10(Tmp, Across), foreach(I in 0..Len-1, Matrix[Row,Col+I] #= Tmp[I+1] )./* down(Matrix, Down, Len, Row, Col): Constrains 'Down' to be equal to the number represented by the 'Len' digits starting at position (Row, Col) of the array 'Matrix' and proceeding down.*/down(Matrix, Down, Len, Row, Col) :- length(Tmp,Len), Tmp :: 0..9999, toNum10(Tmp, Down), foreach(I in 0..Len-1, Matrix[Row+I,Col] #= Tmp[I+1] )./* x is a prime*/is_prime(X) :- fd_max(X,Max), foreach(I in 2..Max // 2, I #\= X #=> X mod I #> 0 ).%% x is a square%square(X) :- fd_max(X,Max), Tmp :: 0..Max, X #= Tmp**2.toNum10(List,Num) :- toNum(List,10,Num).%% converts a number Num to/from a list of integer List given a base Base%toNum(List, Base, Num) :- length(List, Len), length(Xs, Len), exp_list(Len, Base, Xs), % calculate exponents scalar_product(List,Xs,#=,Num).%% Exponents for toNum2: [Base^(N-1), Base^(N-2), .., Base^0],% e.g. exp_list2(3, 10, ExpList) -> ExpList = [100,10,1]%exp_list(N, Base, ExpList) :- length(ExpList, N), ExpList1 @= [B : I in 0..N-1, [B], B is integer(Base**I)], reverse(ExpList1,ExpList). |