Jip J. Dekker
f2a1c4e389
git-subtree-dir: software/mza git-subtree-split: f970a59b177c13ca3dd8aaef8cc6681d83b7e813
51 lines
2.2 KiB
MiniZinc
51 lines
2.2 KiB
MiniZinc
predicate fzn_lex_lesseq_bool_reif(array[int] of var bool: x,
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array[int] of var bool: y,
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var bool: c) =
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let { int: lx = min(index_set(x)),
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int: ux = max(index_set(x)),
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int: ly = min(index_set(y)),
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int: uy = max(index_set(y)),
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int: size = max(ux - lx, uy - ly),
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array[0..size+1] of var bool: b }
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% b[i] is true if the lexicographical order holds from position i on.
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in
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(c <-> b[0])
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/\
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forall(i in 0..size) (
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( b[i] -> ( x[lx + i] <= y[ly + i] ) ) /\
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bool2int(b[i]) + bool2int(x[lx + i]) + (1-bool2int(y[ly + i])) <= 2
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/\
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( b[i] -> ( x[lx + i] < y[ly + i] \/ b[i+1] ) ) /\
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bool2int(b[i]) + (1-bool2int(x[lx + i])) + (1-bool2int(y[ly + i])) + (1-bool2int(b[i+1])) <= 3
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/\ bool2int(b[i]) + bool2int(x[lx + i]) + bool2int(y[ly + i]) + (1-bool2int(b[i+1])) <= 3
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/\ bool2int(b[i]) + bool2int(x[lx + i]) + (1-bool2int(y[ly + i])) + (1-bool2int(b[i+1])) <= 3
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)
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/\ b[size+1] = (ux-lx <= uy-ly)
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% endif
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;
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predicate fzn_lex_lesseq_bool_imp(array[int] of var bool: x,
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array[int] of var bool: y,
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var bool: c) =
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let { int: lx = min(index_set(x)),
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int: ux = max(index_set(x)),
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int: ly = min(index_set(y)),
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int: uy = max(index_set(y)),
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int: size = max(ux - lx, uy - ly),
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array[0..size+1] of var bool: b }
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% b[i] is true if the lexicographical order holds from position i on.
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in
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(c -> b[0])
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/\
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forall(i in 0..size) (
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( b[i] -> ( x[lx + i] <= y[ly + i] ) ) /\
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bool2int(b[i]) + bool2int(x[lx + i]) + (1-bool2int(y[ly + i])) <= 2
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/\
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( b[i] -> ( x[lx + i] < y[ly + i] \/ b[i+1] ) ) /\
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bool2int(b[i]) + (1-bool2int(x[lx + i])) + (1-bool2int(y[ly + i])) + (1-bool2int(b[i+1])) <= 3
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/\ bool2int(b[i]) + bool2int(x[lx + i]) + bool2int(y[ly + i]) + (1-bool2int(b[i+1])) <= 3
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/\ bool2int(b[i]) + bool2int(x[lx + i]) + (1-bool2int(y[ly + i])) + (1-bool2int(b[i+1])) <= 3
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)
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/\ b[size+1] = (ux-lx <= uy-ly)
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;
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