Jip J. Dekker
f2a1c4e389
git-subtree-dir: software/mza git-subtree-split: f970a59b177c13ca3dd8aaef8cc6681d83b7e813
51 lines
1.5 KiB
MiniZinc
51 lines
1.5 KiB
MiniZinc
include "alldifferent.mzn";
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predicate fzn_subcircuit(array[int] of var int: x) =
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let {
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set of int: S = index_set(x),
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int: l = min(S),
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int: u = max(S),
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int: n = card(S),
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array[S] of var 1..n: order,
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array[S] of var bool: ins = array1d(S,[ x[i] != i | i in S]),
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var l..u+1: firstin = min([ u+1 + bool2int(ins[i])*(i-u-1) | i in S]),
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var S: lastin,
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var bool: empty = (firstin > u),
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} in
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alldifferent(x) /\
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alldifferent(order) /\
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% If the subcircuit is empty then each node points at itself.
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%
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(empty -> forall(i in S)(not ins[i])) /\
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% If the subcircuit is non-empty then order numbers the subcircuit.
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%
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((not empty) ->
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% The firstin node is numbered 1.
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order[firstin] = 1 /\
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% The lastin node is greater than firstin.
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lastin > firstin /\
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% The lastin node points at firstin.
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x[lastin] = firstin /\
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% And both are in
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ins[lastin] /\ ins[firstin] /\
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% The successor of each node except where it is firstin is
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% numbered one more than the predecessor.
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forall(i in S) (
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(ins[i] /\ x[i] != firstin) -> order[x[i]] = order[i] + 1
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) /\
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% Each node that is not in is numbered after the lastin node.
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forall(i in S) (
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ins[i] \/ order[lastin] < order[i]
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)
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);
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%-----------------------------------------------------------------------------%
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