/* * author: Jean-Noël Monette */ include "globals.mzn"; %cubes set of int: cubes=1..8; int: ud=0; int: lr=8; int: fb=16; set of int: pos=1..24; set of int: symbols=0..4*4*4-1; array[cubes] of var cubes: cube_at; array[pos] of var symbols: symbol_at; %Each cube is placed once. constraint alldifferent(cube_at); %Party constraints on the 6 faces constraint party([symbol_at[i] | i in 1..4]); constraint party([symbol_at[i + 4] | i in 1..4]); constraint party([symbol_at[(i - 1) * 2 + 1 + lr] | i in 1..4]); constraint party([symbol_at[i * 2 + lr] | i in 1..4]); constraint party([symbol_at[if i < 3 then i else i+2 endif + fb] | i in 1..4]); constraint party([symbol_at[if i < 3 then i else i+2 endif + 2 + fb] | i in 1..4]); %Linking cubes and symbols constraint forall(i in {1,4,6,7})( link_cube_and_symbols([cube_at[i],symbol_at[i+ud],symbol_at[i+lr],symbol_at[i+fb]])); constraint forall(i in {2,3,5,8})( link_cube_and_symbols([cube_at[i],symbol_at[i+ud],symbol_at[i+fb],symbol_at[i+lr]])); %Sym break constraint cube_at[1] = 1; constraint cube_at[2] < cube_at[3]; constraint cube_at[2] < cube_at[5]; %better to search on symbol_at first rather than cube_at solve :: int_search(symbol_at, first_fail, indomain_min, complete) satisfy; %introduced because of limitation in output. array[pos] of var 0..3: color_at = [color(symbol_at[i]) |i in pos]; array[pos] of var 0..3: shape_at = [shape(symbol_at[i]) |i in pos]; array[pos] of var 0..3: fill_at = [fill(symbol_at[i]) |i in pos]; %names (for output) array[1..4] of string: colorname = ["blue","red","yellow","black"]; array[1..4] of string: fillname = ["half","plain","empty","grid"]; array[1..4] of string: shapename = ["triangle","circle","square","heart"]; output [show(cube_at), "\n", show(symbol_at), "\n"] ++ ["pos " ++ show(i) ++ ": cube " ++ show(cube_at[i]) ++ "\n" ++ "u/d:\t"++fillname[fix(fill_at[i+ud])+1]++"\t"++colorname[fix(color_at[i+ud])+1]++"\t"++shapename[fix(shape_at[i+ud])+1]++"\n" ++ "f/b:\t"++fillname[fix(fill_at[i+fb])+1]++"\t"++colorname[fix(color_at[i+fb])+1]++"\t"++shapename[fix(shape_at[i+fb])+1]++"\n" ++ "l/r:\t"++fillname[fix(fill_at[i+lr])+1]++"\t"++colorname[fix(color_at[i+lr])+1]++"\t"++shapename[fix(shape_at[i+lr])+1]++"\n" | i in 1..8];%fill predicate diff_or_equal(array[1..4] of var 0..3: x) = forall(i in 1..4,j in i+1..4)(x[i]!=x[j]) \/ forall(i in 1..4,j in i+1..4)(x[i]=x[j]); % A party is alldiff or allequal for each of the three characteristics. predicate party(array[1..4] of var 0..63: symbols) = ( diff_or_equal([color(symbols[i]) | i in 1..4]) /\ diff_or_equal([shape(symbols[i]) | i in 1..4]) /\ diff_or_equal([fill(symbols[i]) | i in 1..4]) ); %How to implement linking functions with the advantages of CSE. function array[1..3] of var 0..3: fcs(var 0..63:symbol) :: promise_total = let { var 0..3: color; var 0..3:shape;var 0..3: fill; constraint symbol = 4*4*fill+4*color+shape; } in [fill,color,shape]; function var 0..3: color_help(array[1..3] of var 0..3: fcs) :: promise_total = fcs[2]; function var 0..3: color(var int:symbol) ::promise_total = color_help(fcs(symbol)); function var 0..3: fill_help(array[1..3] of var 0..3: fcs) :: promise_total = fcs[1]; function var 0..3: fill(var int:symbol) ::promise_total = fill_help(fcs(symbol)); function var 0..3: shape_help(array[1..3] of var 0..3: fcs) :: promise_total = fcs[3]; function var 0..3: shape(var int:symbol) ::promise_total = shape_help(fcs(symbol)); %For parameters function 0..3: shape(int: symbol) = symbol mod 4; function 0..3: color(int: symbol) = symbol mod 16 div 4; function 0..3: fill(int:symbol) = symbol div 16; array[1..8,1..24] of int: data; %Which symbol positions on a cube are next to each other on the same corner. %Made by hand, I do not think there is any hope for finding a simple formula that could be used in precomputation :-) %Actually it might be divided by three and have a disjunction in link_cube_and_symbols array[1..24,1..3] of int: pp = [|21,12,7 |23,17,11 |24,4,18 |22,8,3 |1,6,16 |2,14,20 |4,18,24 |3,22,8 |7,21,12 |5,10,15 |6,16,1 |8,3,22 |16,1,6 |15,5,10 |13,9,19 |14,20,2 |18,24,4 |20,2,14 |19,13,9 |17,11,23 |12,7,21 |11,23,17 |9,19,13 |10,15,5 |]; %% ---------- DATA ---------- data =[| 10, 56, 12, 7, 39, 22, 33, 59, 21, 6, 30, 55, 27, 3, 41, 44, 57, 4, 28, 26, 60, 49, 15, 2 | 33, 22, 38, 51, 57, 10, 1, 48, 18, 0, 21, 23, 14, 8, 27, 30, 26, 34, 11, 52, 12, 40, 63, 45 | 34, 38, 12, 57, 54, 6, 61, 43, 58, 53, 20, 7, 25, 60, 33, 0, 40, 9, 37, 19, 15, 8, 30, 51 | 24, 46, 15, 16, 58, 0, 7, 53, 42, 54, 21, 5, 38, 13, 45, 55, 29, 22, 56, 50, 11, 59, 34, 17 | 39, 46, 52, 48, 41, 6, 51, 49, 32, 60, 20, 53, 2, 1, 40, 45, 13, 26, 29, 27, 50, 56, 63, 4 | 39, 5, 52, 61, 41, 19, 24, 20, 48, 23, 36, 63, 11, 13, 42, 46, 49, 54, 62, 37, 47, 31, 35, 8 | 61, 44, 43, 42, 29, 16, 37, 4, 25, 62, 32, 9, 5, 36, 10, 24, 3, 31, 14, 28, 47, 35, 17, 18 | 19, 23, 16, 14, 32, 50, 44, 18, 25, 55, 43, 1, 28, 2, 9, 58, 35, 62, 3, 59, 36, 31, 47, 17 |] ; % cubes: [4, 8, 5, 7, 2, 6, 3, 1] % symbols: [42, 58, 26, 10, 22, 54, 38, 6, 56, 50, 48, 29, 52, 8, 60, 39, 38, 19, 4, 62, 8, 61, 19, 41] % rotations: [23, 13, 17, 14, 6, 17, 6, 24] %% ---------- GENERATED TABLE ---------- include "table.mzn"; predicate link_cube_and_symbols(array [1..4] of var int: cs) = table_int(cs, array2d(1..192, index_set(cs), [1, 7, 4, 2, 1, 26, 56, 3, 1, 2, 7, 4, 1, 41, 39, 6, 1, 4, 2, 7, 1, 22, 44, 10, 1, 49, 59, 12, 1, 57, 30, 15, 1, 28, 27, 21, 1, 44, 10, 22, 1, 56, 3, 26, 1, 21, 28, 27, 1, 27, 21, 28, 1, 15, 57, 30, 1, 60, 55, 33, 1, 6, 41, 39, 1, 39, 6, 41, 1, 10, 22, 44, 1, 59, 12, 49, 1, 33, 60, 55, 1, 3, 26, 56, 1, 30, 15, 57, 1, 12, 49, 59, 1, 55, 33, 60, 2, 27, 57, 0, 2, 12, 23, 1, 2, 52, 22, 8, 2, 30, 33, 10, 2, 14, 18, 11, 2, 23, 1, 12, 2, 18, 11, 14, 2, 11, 14, 18, 2, 63, 26, 21, 2, 8, 52, 22, 2, 1, 12, 23, 2, 21, 63, 26, 2, 57, 0, 27, 2, 33, 10, 30, 2, 10, 30, 33, 2, 45, 51, 34, 2, 40, 48, 38, 2, 48, 38, 40, 2, 51, 34, 45, 2, 38, 40, 48, 2, 34, 45, 51, 2, 22, 8, 52, 2, 0, 27, 57, 2, 26, 21, 63, 3, 34, 6, 0, 3, 0, 34, 6, 3, 61, 15, 7, 3, 43, 12, 8, 3, 51, 57, 9, 3, 8, 43, 12, 3, 7, 61, 15, 3, 38, 60, 19, 3, 30, 40, 20, 3, 58, 37, 25, 3, 40, 20, 30, 3, 54, 53, 33, 3, 6, 0, 34, 3, 25, 58, 37, 3, 60, 19, 38, 3, 20, 30, 40, 3, 12, 8, 43, 3, 57, 9, 51, 3, 33, 54, 53, 3, 53, 33, 54, 3, 9, 51, 57, 3, 37, 25, 58, 3, 19, 38, 60, 3, 15, 7, 61, 4, 55, 24, 0, 4, 7, 11, 5, 4, 11, 5, 7, 4, 5, 7, 11, 4, 50, 46, 13, 4, 59, 53, 15, 4, 22, 17, 16, 4, 16, 22, 17, 4, 34, 29, 21, 4, 17, 16, 22, 4, 0, 55, 24, 4, 21, 34, 29, 4, 29, 21, 34, 4, 42, 56, 38, 4, 56, 38, 42, 4, 58, 54, 45, 4, 13, 50, 46, 4, 46, 13, 50, 4, 15, 59, 53, 4, 45, 58, 54, 4, 24, 0, 55, 4, 38, 42, 56, 4, 54, 45, 58, 4, 53, 15, 59, 5, 27, 46, 1, 5, 32, 29, 2, 5, 48, 26, 4, 5, 45, 39, 6, 5, 20, 63, 13, 5, 63, 13, 20, 5, 4, 48, 26, 5, 46, 1, 27, 5, 2, 32, 29, 5, 29, 2, 32, 5, 6, 45, 39, 5, 41, 60, 40, 5, 60, 40, 41, 5, 39, 6, 45, 5, 1, 27, 46, 5, 26, 4, 48, 5, 52, 56, 49, 5, 53, 51, 50, 5, 50, 53, 51, 5, 56, 49, 52, 5, 51, 50, 53, 5, 49, 52, 56, 5, 40, 41, 60, 5, 13, 20, 63, 6, 13, 37, 5, 6, 61, 54, 8, 6, 48, 62, 11, 6, 37, 5, 13, 6, 46, 39, 19, 6, 52, 31, 20, 6, 42, 41, 23, 6, 47, 63, 24, 6, 20, 52, 31, 6, 49, 36, 35, 6, 35, 49, 36, 6, 5, 13, 37, 6, 19, 46, 39, 6, 23, 42, 41, 6, 41, 23, 42, 6, 39, 19, 46, 6, 63, 24, 47, 6, 62, 11, 48, 6, 36, 35, 49, 6, 31, 20, 52, 6, 8, 61, 54, 6, 54, 8, 61, 6, 11, 48, 62, 6, 24, 47, 63, 7, 32, 17, 3, 7, 43, 35, 4, 7, 25, 14, 5, 7, 37, 47, 9, 7, 29, 62, 10, 7, 5, 25, 14, 7, 24, 61, 16, 7, 3, 32, 17, 7, 42, 31, 18, 7, 61, 16, 24, 7, 14, 5, 25, 7, 44, 36, 28, 7, 62, 10, 29, 7, 18, 42, 31, 7, 17, 3, 32, 7, 4, 43, 35, 7, 28, 44, 36, 7, 47, 9, 37, 7, 31, 18, 42, 7, 35, 4, 43, 7, 36, 28, 44, 7, 9, 37, 47, 7, 16, 24, 61, 7, 10, 29, 62, 8, 44, 36, 1, 8, 59, 23, 2, 8, 28, 25, 3, 8, 32, 55, 9, 8, 62, 17, 14, 8, 31, 18, 16, 8, 14, 62, 17, 8, 16, 31, 18, 8, 50, 58, 19, 8, 2, 59, 23, 8, 3, 28, 25, 8, 25, 3, 28, 8, 18, 16, 31, 8, 55, 9, 32, 8, 43, 47, 35, 8, 1, 44, 36, 8, 47, 35, 43, 8, 36, 1, 44, 8, 35, 43, 47, 8, 58, 19, 50, 8, 9, 32, 55, 8, 19, 50, 58, 8, 23, 2, 59, 8, 17, 14, 62]));