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