40 lines
1.5 KiB
MiniZinc
40 lines
1.5 KiB
MiniZinc
%% 奇偶排序
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%% y是x的有序版本，所有的真都在假之前
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predicate oesort(array[int] of var bool:x, array[int] of var bool:y)=
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let { int: c = card(index_set(x)) } in
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if c == 1 then x[1] == y[1]
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elseif c == 2 then comparator(x[1],x[2],y[1],y[2])
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else
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let {
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array[1..c div 2] of var bool:xf = [x[i] | i in 1..c div 2],
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array[1..c div 2] of var bool:xl = [x[i] | i in c div 2 +1..c],
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array[1..c div 2] of var bool:tf,
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array[1..c div 2] of var bool:tl } in
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oesort(xf,tf) /\ oesort(xl,tl) /\ oemerge(tf ++ tl, y)
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endif;
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%% 奇偶合并
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%% y 是 x的有序版本，所有的真都在假之前
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%% 假设 x的前一半是有序的，后一半也是
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predicate oemerge(array[int] of var bool:x, array[int] of var bool:y)=
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let { int: c = card(index_set(x)) } in
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if c == 1 then x[1] == y[1]
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elseif c == 2 then comparator(x[1],x[2],y[1],y[2])
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else
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let { array[1..c div 2] of var bool:xo =
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[ x[i] | i in 1..c where i mod 2 == 1],
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array[1..c div 2] of var bool:xe =
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[ x[i] | i in 1..c where i mod 2 == 0],
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array[1..c div 2] of var bool:to,
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array[1..c div 2] of var bool:te } in
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oemerge(xo,to) /\ oemerge(xe,te) /\
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y[1] = to[1] /\
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forall(i in 1..c div 2 -1)(
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comparator(te[i],to[i+1],y[2*i],y[2*i+1])) /\
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y[c] = te[c div 2]
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endif;
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% 比较器 o1 = max(i1,i2), o2 = min(i1,i2)
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predicate comparator(var bool:i1,var bool:i2,var bool:o1,var bool:o2)=
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(o1 = (i1 \/ i2)) /\ (o2 = (i1 /\ i2));
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