160 lines
4.9 KiB
MiniZinc
160 lines
4.9 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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set of int: cubes=1..8;
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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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set of int: places=1..8*24;
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set of int: faces= 1..6;
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array[faces] of set of pos: face = [{1,2,3,4},{5,6,7,8},{9,10,11,12},{13,14,15,16},{17,18,19,20},{21,22,23,24}];
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set of int: chars = 0..3;
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array[cubes,pos] of var symbols: data;
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constraint global_cardinality_closed(array1d(data),symbols,[3|i in symbols])::domain;
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constraint forall(c in 7..8)(all_different([data[c,i]|i in pos])::domain);
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%redundant constraint for the previous ones
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array[cubes,symbols] of var 0..1: cnt;
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constraint forall(c in 1..8)(global_cardinality_closed([data[c,i]|i in pos],symbols,[cnt[c,i]|i in symbols])::domain);
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constraint forall(s in symbols)(sum(c in cubes)(cnt[c,s])=3);
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constraint forall(c in cubes, f in faces)(
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global_cardinality_low_up_closed([color(data[c,p])|p in face[f]],chars,[0|i in chars],[3|i in chars])::domain
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/\
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global_cardinality_low_up_closed([fill(data[c,p])|p in face[f]],chars,[0|i in chars],[3|i in chars])::domain
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/\
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global_cardinality_low_up_closed([shape(data[c,p])|p in face[f]],chars,[0|i in chars],[3|i in chars])::domain
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);
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%I believe this set of constraints is redundant with the previous one
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constraint forall(c in cubes, f in faces)(
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nvalue([color(data[c,p])|p in face[f]]) >= 2
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/\
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nvalue([fill(data[c,p])|p in face[f]]) >= 2
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/\
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nvalue([shape(data[c,p])|p in face[f]]) >= 2
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);
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solve
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::seq_search([
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int_search(cube_at,input_order,indomain_random,complete),
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int_search(symbol_at,input_order,indomain_random,complete),
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int_search(rotation,input_order,indomain_random,complete),
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int_search(array1d(data),input_order,indomain_random,complete),
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])
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satisfy;
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output ["data =",show2d(data),";\n","% cubes: ",show(cube_at),"\n% symbols: ",show(symbol_at),"\n% rotations: ",show(rotation)];
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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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int: ud=0;
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int: lr=8;
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int: fb=16;
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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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array[cubes] of var 1..24: rotation;
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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]],rotation[i],data));
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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]],rotation[i],data));
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%Note: this presolve does not change much
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predicate diff_or_equal(array[1..4] of var 0..3: x) =
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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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% Note: I never tried to (manually) presolve this one but it might be worth trying it as well...
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predicate party(array[1..4] of var 0..63: symbols) = (
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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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%Linking cube IDs with the three symbols appearing in relevant positions
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predicate link_cube_and_symbols(var int: cube, array[1..3] of var int: symbols,var 1..24: pos,array[cubes,pos] of var symbols:data) =
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forall(i in 1..3)(data[cube,pp[pos,i]]=symbols[i]);
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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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