Jip J. Dekker
f2a1c4e389
git-subtree-dir: software/mza git-subtree-split: f970a59b177c13ca3dd8aaef8cc6681d83b7e813
69 lines
2.1 KiB
MiniZinc
69 lines
2.1 KiB
MiniZinc
include "alldifferent.mzn";
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/** @group globals
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Constrains the elements of \a x to define a subcircuit where \a x[\p i] = \p j
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means that \p j is the successor of \p i and \a x[\p i] = \p i means that \p i
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is not in the circuit.
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*/
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%% Linear version
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predicate fzn_subcircuit(array[int] of var int: x) =
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let { 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+1),
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} in
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alldifferent(x) /\
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% NO 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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%% Another way to express minimum.
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% forall(i in l..u+1)(
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% i==firstin <-> ins[i]
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% /\ forall(j in S where j<i)( not ins[j] )
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% ) /\
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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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%%% MTZ model. Note that INTEGER order vars seem better!:
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forall (i,j in S where i!=j) (
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order[i] - order[j] + n*bool2int( x[i]==j /\ i!=lastin )
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% + (n-2)*bool2int(x[j]==i) %% the Desrochers & Laporte '91 term
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<= n-1 ) /\
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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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true
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% (not ins[i]) <-> (n == order[i])
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)
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);
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%-----------------------------------------------------------------------------%
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