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 | /* Nonogram (Painting by numbers) in Comet """ Nonograms or Paint by Numbers are picture logic puzzles in which cells in a grid have to be colored or left blank according to numbers given at the side of the grid to reveal a hidden picture. In this puzzle type, the numbers measure how many unbroken lines of filled-in squares there are in any given row or column. For example, a clue of "4 8 3" would mean there are sets of four, eight, and three filled squares, in that order, with at least one blank square between successive groups. """ See problem 12 at http://www.csplib.org/. This model uses the built-in constraint regular and Automaton. Compare this to my own home-brewn regular constraint in Many thanks to Pascal Van Hentenryck for the improvements which reduced the running time for the P200 problem from 1:30 minutes to about 1 second. The improvements are commented below. The significant best improvement was the (re)ordering of 1..rows / 1..cols in the labeling. The developments of this model has been written in the following blog posts (sorted in reversed order of publication): * "Comet: Nonogram improved: solving problem P200 from 1:30 minutes to about 1 second" * "Comet: regular constraint, a much faster Nonogram with the regular constraint, some OPL models, and more" * "More Comet models, e.g. Nonogram, Steiner triplets, and different set covering problems" Also, compare with the following models: (older model, no regular constraint) * MiniZinc: http://www.hakank.org/minizinc/nonogram.mzn * Gecode/R: http://www.hakank.org/gecode_r/nonogram.rb (using "regexps") This Comet model was created by Hakan Kjellerstrand (hakank@bonetmail.com) Also, see my Comet page: http://www.hakank.org/comet */ // Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/ import cotfd; int t0 = System.getCPUTime(); // // Problems: // // The lambda picture /* int rows = 12; int row_rule_len = 3; int row_rules[1..rows, 1..row_rule_len] = [ [0,0,2], [0,1,2], [0,1,1], [0,0,2], [0,0,1], [0,0,3], [0,0,3], [0,2,2], [0,2,1], [2,2,1], [0,2,3], [0,2,2] ]; int cols = 10; int col_rule_len = 2; int col_rules[1..cols, 1..col_rule_len] = [ [2,1], [1,3], [2,4], [3,4], [0,4], [0,3], [0,3], [0,3], [0,2], [0,2] ]; */ // Nonogram problem from Gecode: Dragonfly // include "nonogram_dragonfly"; // Nonogram problem from Gecode: P200 // Statistics: // Before improvements suggested by Pascal Van Hentenryck: // num_solutions: 1 // time: 92726 // #choices = 142167 // #fail = 284334 // #propag = 242312778 // comet -j2 nonogram_regular.co 93,63s user 0,17s system 99% cpu 1:33,89 total // // With the improvements suggested by Pascal Van Hentenryck // and my own implementation of regular (http://www.hakank.org/comet/nonogram_regular.co ) // num_solutions: 1 // time: 607 // #choices = 520 // #fail = 1040 // #propag = 1213237 // comet -j2 nonogram_regular.co 1,66s user 0,11s system 99% cpu 1,766 total // // With this model using Automaton and the built-in regular constraint. // num_solutions: 1 // time: 437 // #choices = 520 // #fail = 794 // #propag = 693993 // comet -q nonogram_automaton.co 1,82s user 0,10s system 99% cpu 1,936 total // data files should be imported from the "data" parent directory, for example // include "../data/nonogram_p200"; // Nonogram problem from Wikipedia, soccer player // include "nonogram_soccer_player"; Solver<CP> m(); // // The grid // var <CP>{ int } board[1..rows, 1..cols](m, 0..1); Integer num_solutions(0); // explore<m> { exploreall <m> { forall (i in 1..rows) { check_rule(m, all (j in 1..row_rule_len) row_rules[i,j], all (j in 1..cols) board[i,j]); } forall (j in 1..cols) { check_rule(m, all (k in 1..col_rule_len) col_rules[j,k] , all (i in 1..rows) board[i, j]); } } using { // Slightly different labelings depending on the size of the problem. // We start with the smaller dimension. // See above for credit to Pascal Van Hentenryck. if (rows * row_rule_len < cols * col_rule_len ) { forall (i in 1..rows, j in 1..cols: !board[i,j].bound()) { tryall <m>(v in 0..1) by (-v) m.label(board[i,j], v); onFailure m.diff(board[i,j], v); } } else { forall (j in 1..cols, i in 1..rows: !board[i,j].bound()) { tryall <m>(v in 0..1) by (-v) m.label(board[i,j], v); onFailure m.diff(board[i,j], v); } } num_solutions++; cout << "#fails = " << m.getNFail() << endl; cout << "#propag = " << m.getNPropag() << endl; forall (i in 1..rows) { forall (j in 1..cols) { string s = " " ; if (board[i,j] == 1) { s = "#" ; } cout << s << "" ; } cout << endl; } cout << endl; cout << flush; } cout << "\nnum_solutions: " << num_solutions << endl; int t1 = System.getCPUTime(); cout << "time: " << (t1-t0) << endl; cout << "#choices = " << m.getNChoice() << endl; cout << "#fail = " << m.getNFail() << endl; cout << "#propag = " << m.getNPropag() << endl; // // check_rule: The main function. // function void check_rule(Solver<CP> m, int [] rules, var <CP>{ int }[] y) { int r_len = sum (i in 1..rules.getSize()) (rules[i] > 0); int rules_tmp[1..r_len]; int c = 1; forall (i in 1..rules.getSize()) { if (rules[i] > 0) { rules_tmp[c] = rules[i]; c++; } } Automaton<CP> aut = make_automaton(rules_tmp); m.post(regular(y, aut)); } // end check_rule // // Build the transition matrix for a nonogram pattern. // function Automaton<CP> make_automaton( int [] pattern) { int p_len = pattern.getSize(); int num_states = p_len + sum (i in 1..p_len) pattern[i]; Automaton<CP> aut(1..num_states+1, 0..1, 1, {num_states, num_states+1}); // convert pattern to a 0/1 pattern for easy handling of // the states int tmp[1..num_states]; int c = 1; tmp[c] = 0; forall (i in 1..p_len) { forall (j in 1..pattern[i]) { tmp[++c] = 1; } if (c < num_states) { tmp[++c] = 0; } } // create the transition states forall (i in 1..num_states) { if (tmp[i] == 0) { aut.addTransition(i,i,0); aut.addTransition(i,i+1,1); } else { if (i < num_states) { if (tmp[i+1] == 1) { aut.addTransition(i,i+1,1); } else { aut.addTransition(i,i+1,0); } } } } aut.addTransition(num_states,num_states+1,0); aut.addTransition(num_states+1,num_states+1,0); return aut; } // end make_automaton |