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 | /* Killer Sudoku in B-Prolog. """ 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 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 Model created by Hakan Kjellerstrand, hakank@gmail.com*/% Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/go :- solve(1).solve(ProblemName) :- problem(ProblemName, Board), killer_sudoku(Board,X), print_board(X).killer_sudoku(Hints,X) :- N = 3, N2 is N*N, new_array(X,[N2,N2]), array_to_list(X,Vars), % The hints (from kakuro.pl) foreach([Sum|List] in Hints,[XLine], (XLine @= [X[R,C] : [R,C] in List, X[R,C] #> 0], sum(XLine) #= Sum, alldifferent(XLine)) ), sudoku(N, X), labeling(Vars). %% Ensure a Latin square, % i.e. all rows and all columns are different%alldifferent_matrix(Board) :- Rows @= Board^rows, foreach(Row in Rows, alldifferent(Row)), Columns @= Board^columns, foreach(Column in Columns, alldifferent(Column)).% This is from sudoku.plsudoku(N, Board) :- N2 is N*N, BoardVar @= [BB : I in 1..N2, J in 1..N2, [BB], BB @= Board[I,J]], BoardVar :: 1..N2, alldifferent_matrix(Board), foreach(I in 1..N..N2, J in 1..N..N2, [SubSquare], ( SubSquare @= [X : K in 0..N-1, L in 0..N-1, [X], X @= Board[I+K,J+L]], alldifferent(SubSquare) ) ), labeling([ff,down], BoardVar).print_board(Board) :- N @= Board^length, foreach(I in 1..N, (foreach(J in 1..N, [X], (X @= Board[I,J], (var(X) -> write(' _') ; format(' ~q', [X])) ) ), nl ) ), nl.problem(1, [% The hints: % [Sum, [list of indices in X]] [ 3, [1,1], [1,2]], [15, [1,3], [1,4], [1,5]], [22, [1,6], [2,5], [2,6], [3,5]], [ 4, [1,7], [2,7]], [16, [1,8], [2,8]], [15, [1,9], [2,9], [3,9], [4,9]], [25, [2,1], [2,2], [3,1], [3,2]], [17, [2,3], [2,4]], [ 9, [3,3], [3,4], [4,4]], [ 8, [3,6], [4,6],[5,6]], [20, [3,7], [3,8],[4,7]], [ 6, [4,1], [5,1]], [14, [4,2], [4,3]], [17, [4,5], [5,5],[6,5]], [17, [4,8], [5,7],[5,8]], [13, [5,2], [5,3],[6,2]], [20, [5,4], [6,4],[7,4]], [12, [5,9], [6,9]], [27, [6,1], [7,1],[8,1],[9,1]], [ 6, [6,3], [7,2],[7,3]], [20, [6,6], [7,6], [7,7]], [ 6, [6,7], [6,8]], [10, [7,5], [8,4],[8,5],[9,4]], [14, [7,8], [7,9],[8,8],[8,9]], [ 8, [8,2], [9,2]], [16, [8,3], [9,3]], [15, [8,6], [8,7]], [13, [9,5], [9,6],[9,7]], [17, [9,8], [9,9]] ]). |
