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 | /* Killer sudoku in Comet. """ Killer sudoku (also killer su doku, sumdoku, sum doku, addoku, or samunamupure) is a puzzle that combines elements of sudoku and kakuro. Despite the name, the simpler killer sudokus can be easier to solve than regular sudokus, depending on the solver's skill at mental arithmetic; the hardest ones, however, can take hours to crack. ... The objective is to fill the grid with numbers from 1 to 9 in a way that the following conditions are met: * Each row, column, and nonet contains each number exactly once. * The sum of all numbers in a cage must match the small number printed in its corner. * No number appears more than once in a cage. (This is the standard rule for killer sudokus, and implies that no cage can include more than 9 cells.) In 'Killer X', an additional rule is that each of the long diagonals contains each number once. """ Here we solve the problem from the Wikipedia page, also shown here Note, this model is based on the generalized KenKen model: Killer Sudoku is simpler in that the only mathematical operation is summation. The output is: 2 1 5 6 4 7 3 9 8 3 6 8 9 5 2 1 7 4 7 9 4 3 8 1 6 5 2 5 8 6 2 7 4 9 3 1 1 4 2 5 9 3 8 6 7 9 7 3 8 1 6 4 2 5 8 2 1 7 3 9 5 4 6 6 5 9 4 2 8 7 1 3 4 3 7 1 6 5 2 8 9 num_solutions: 1 time: 12 #choices = 56 #fail = 136 #propag = 3013 This Comet model was created by Hakan Kjellerstrand (hakank@gmail.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(); int n = 9; range R = 1..n; tuple cell { int r; // row int c; // column } tuple P { set {cell} cells; // cells int res; // result } // // state the problem (without the operation) // int num_p = 29; // number of cages P problem[1..num_p] = [ P({cell(1,1), cell(1,2)}, 3), P({cell(1,3), cell(1,4), cell(1,5)}, 15), P({cell(1,6), cell(2,5), cell(2,6), cell(3,5)}, 22), P({cell(1,7), cell(2,7)}, 4), P({cell(1,8), cell(2,8)}, 16), P({cell(1,9), cell(2,9), cell(3,9), cell(4,9)}, 15), P({cell(2,1), cell(2,2), cell(3,1), cell(3,2)}, 25), P({cell(2,3), cell(2,4)}, 17), P({cell(3,3), cell(3,4), cell(4,4)}, 9), P({cell(3,6), cell(4,6),cell(5,6)}, 8), P({cell(3,7), cell(3,8),cell(4,7)}, 20), P({cell(4,1), cell(5,1)},6), P({cell(4,2), cell(4,3)},14), P({cell(4,5), cell(5,5),cell(6,5)},17), P({cell(4,8), cell(5,7),cell(5,8)},17), P({cell(5,2), cell(5,3),cell(6,2)},13), P({cell(5,4), cell(6,4),cell(7,4)},20), P({cell(5,9), cell(6,9)}, 12), P({cell(6,1), cell(7,1),cell(8,1),cell(9,1)},27), P({cell(6,3), cell(7,2),cell(7,3)},6), P({cell(6,6), cell(7,6), cell(7,7)}, 20), P({cell(6,7), cell(6,8)},6), P({cell(7,5), cell(8,4),cell(8,5),cell(9,4)},10), P({cell(7,8), cell(7,9),cell(8,8),cell(8,9)},14), P({cell(8,2), cell(9,2)}, 8), P({cell(8,3), cell(9,3)},16), P({cell(8,6), cell(8,7)},15), P({cell(9,5), cell(9,6),cell(9,7)},13), P({cell(9,8), cell(9,9)},17) ]; Solver<CP> m(); var <CP>{ int } x[1..n, 1..n](m, R); // // assumption: only the segments with 2 cells can be minus or div. // function void calc(Solver<CP> m, set {cell} cc, var <CP>{ int }[,] x, int res) { m.post( sum (i in cc) x[i.r, i.c] == res); } Integer num_solutions(0); exploreall <m> { // all rows, columns, and nonets must be unique forall (i in R) m.post(alldifferent( all (j in R) x[i,j])); forall (j in R) m.post(alldifferent( all (i in R) x[i,j])); forall (i in 0..2,j in 0..2) { m.post(alldifferent( all (r in i*3+1..i*3+3,c in j*3+1..j*3+3) x[r,c])); } // solve the cages forall (i in 1..num_p) { calc(m, problem[i].cells, x, problem[i].res); } } using { // label(m); forall (i in 1..n, j in 1..n : !x[i,j].bound()) { tryall <m>(v in 1..n : x[i,j].memberOf(v)) label(x[i,j], v); } num_solutions := num_solutions + 1; forall (i in 1..n) { forall (j in 1..n) { cout << x[i,j] << " " ; } cout << endl; } cout << endl; } 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; |