/* * 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 =[| 15, 39, 57, 20, 61, 36, 41, 22, 47, 43, 29, 6, 14, 17, 18, 40, 54, 34, 42, 3, 24, 13, 10, 30 | 15, 45, 20, 19, 47, 57, 7, 46, 59, 14, 56, 17, 11, 34, 37, 62, 55, 54, 61, 16, 9, 31, 51, 2 | 45, 17, 18, 26, 29, 11, 57, 46, 23, 22, 49, 24, 20, 53, 35, 28, 19, 38, 4, 3, 0, 52, 8, 9 | 52, 51, 14, 2, 3, 45, 44, 16, 43, 39, 37, 21, 58, 0, 28, 36, 38, 7, 33, 1, 32, 63, 61, 6 | 60, 36, 24, 15, 48, 23, 47, 9, 0, 10, 32, 28, 41, 46, 2, 33, 35, 25, 12, 55, 4, 44, 40, 29 | 7, 63, 34, 16, 25, 44, 21, 39, 6, 5, 33, 30, 22, 26, 55, 41, 32, 31, 11, 18, 48, 42, 50, 27 | 38, 63, 52, 31, 56, 49, 10, 59, 48, 19, 37, 1, 62, 8, 58, 43, 25, 5, 60, 12, 27, 50, 53, 13 | 35, 4, 60, 13, 49, 8, 59, 21, 56, 62, 30, 1, 5, 23, 54, 40, 58, 50, 42, 53, 27, 26, 51, 12 |] ; % cubes: [1, 2, 8, 3, 6, 7, 5, 4] % symbols: [41, 19, 62, 4, 11, 49, 28, 38, 24, 2, 49, 20, 6, 43, 47, 61, 6, 54, 54, 23, 22, 38, 4, 37] % rotations: [9, 7, 24, 19, 19, 11, 21, 20] %% ---------- 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, 39, 17, 3, 1, 41, 24, 6, 1, 54, 29, 10, 1, 22, 57, 13, 1, 47, 42, 14, 1, 36, 40, 15, 1, 3, 39, 17, 1, 61, 43, 18, 1, 34, 30, 20, 1, 57, 13, 22, 1, 6, 41, 24, 1, 10, 54, 29, 1, 20, 34, 30, 1, 30, 20, 34, 1, 40, 15, 36, 1, 17, 3, 39, 1, 15, 36, 40, 1, 24, 6, 41, 1, 14, 47, 42, 1, 18, 61, 43, 1, 42, 14, 47, 1, 29, 10, 54, 1, 13, 22, 57, 1, 43, 18, 61, 2, 19, 54, 2, 2, 9, 17, 7, 2, 17, 7, 9, 2, 59, 61, 11, 2, 37, 47, 14, 2, 57, 62, 15, 2, 45, 34, 16, 2, 7, 9, 17, 2, 54, 2, 19, 2, 31, 46, 20, 2, 46, 20, 31, 2, 16, 45, 34, 2, 47, 14, 37, 2, 34, 16, 45, 2, 20, 31, 46, 2, 14, 37, 47, 2, 55, 56, 51, 2, 2, 19, 54, 2, 56, 51, 55, 2, 51, 55, 56, 2, 62, 15, 57, 2, 61, 11, 59, 2, 11, 59, 61, 2, 15, 57, 62, 3, 24, 57, 0, 3, 17, 53, 3, 3, 20, 23, 4, 3, 19, 49, 8, 3, 26, 38, 9, 3, 28, 45, 11, 3, 53, 3, 17, 3, 52, 46, 18, 3, 49, 8, 19, 3, 23, 4, 20, 3, 35, 29, 22, 3, 4, 20, 23, 3, 57, 0, 24, 3, 38, 9, 26, 3, 45, 11, 28, 3, 22, 35, 29, 3, 29, 22, 35, 3, 9, 26, 38, 3, 11, 28, 45, 3, 18, 52, 46, 3, 8, 19, 49, 3, 46, 18, 52, 3, 3, 17, 53, 3, 0, 24, 57, 4, 1, 51, 0, 4, 51, 0, 1, 4, 7, 6, 2, 4, 39, 28, 3, 4, 2, 7, 6, 4, 6, 2, 7, 4, 63, 16, 14, 4, 14, 63, 16, 4, 44, 32, 21, 4, 3, 39, 28, 4, 21, 44, 32, 4, 58, 43, 33, 4, 52, 45, 36, 4, 61, 38, 37, 4, 37, 61, 38, 4, 28, 3, 39, 4, 33, 58, 43, 4, 32, 21, 44, 4, 36, 52, 45, 4, 0, 1, 51, 4, 45, 36, 52, 4, 43, 33, 58, 4, 38, 37, 61, 4, 16, 14, 63, 5, 12, 41, 0, 5, 48, 10, 2, 5, 28, 47, 4, 5, 24, 44, 9, 5, 2, 48, 10, 5, 41, 0, 12, 5, 25, 29, 15, 5, 33, 60, 23, 5, 44, 9, 24, 5, 29, 15, 25, 5, 47, 4, 28, 5, 15, 25, 29, 5, 40, 35, 32, 5, 60, 23, 33, 5, 32, 40, 35, 5, 46, 55, 36, 5, 35, 32, 40, 5, 0, 12, 41, 5, 9, 24, 44, 5, 55, 36, 46, 5, 4, 28, 47, 5, 10, 2, 48, 5, 36, 46, 55, 5, 23, 33, 60, 6, 55, 25, 5, 6, 11, 22, 6, 6, 44, 41, 7, 6, 22, 6, 11, 6, 31, 27, 16, 6, 63, 26, 18, 6, 48, 30, 21, 6, 6, 11, 22, 6, 5, 55, 25, 6, 18, 63, 26, 6, 16, 31, 27, 6, 21, 48, 30, 6, 27, 16, 31, 6, 33, 50, 32, 6, 50, 32, 33, 6, 42, 39, 34, 6, 34, 42, 39, 6, 7, 44, 41, 6, 39, 34, 42, 6, 41, 7, 44, 6, 30, 21, 48, 6, 32, 33, 50, 6, 25, 5, 55, 6, 26, 18, 63, 7, 10, 27, 1, 7, 13, 31, 5, 7, 12, 63, 8, 7, 27, 1, 10, 7, 63, 8, 12, 7, 31, 5, 13, 7, 58, 56, 19, 7, 37, 53, 25, 7, 1, 10, 27, 7, 5, 13, 31, 7, 53, 25, 37, 7, 49, 43, 38, 7, 38, 49, 43, 7, 60, 62, 48, 7, 43, 38, 49, 7, 59, 52, 50, 7, 50, 59, 52, 7, 25, 37, 53, 7, 19, 58, 56, 7, 56, 19, 58, 7, 52, 50, 59, 7, 62, 48, 60, 7, 48, 60, 62, 7, 8, 12, 63, 8, 59, 27, 1, 8, 23, 53, 4, 8, 56, 42, 5, 8, 40, 35, 8, 8, 13, 50, 12, 8, 50, 12, 13, 8, 60, 26, 21, 8, 53, 4, 23, 8, 21, 60, 26, 8, 1, 59, 27, 8, 51, 58, 30, 8, 8, 40, 35, 8, 35, 8, 40, 8, 5, 56, 42, 8, 62, 54, 49, 8, 12, 13, 50, 8, 58, 30, 51, 8, 4, 23, 53, 8, 49, 62, 54, 8, 42, 5, 56, 8, 30, 51, 58, 8, 27, 1, 59, 8, 26, 21, 60, 8, 54, 49, 62]));