Jip J. Dekker
f2a1c4e389
git-subtree-dir: software/mza git-subtree-split: f970a59b177c13ca3dd8aaef8cc6681d83b7e813
50 lines
2.2 KiB
MiniZinc
50 lines
2.2 KiB
MiniZinc
%-----------------------------------------------------------------------------%
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% Requires that the array 'x' is lexicographically less than or equal to
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% array 'y'. Compares them from first to last element, regardless of indices
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%-----------------------------------------------------------------------------%
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predicate fzn_lex_lesseq_bool(array[int] of var bool: x,
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array[int] of var bool: y) =
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% if (min(card(index_set(x)), card(index_set(y))) <= 25) then
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% let { int: size = min(card(index_set(x)), card(index_set(y)));
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% } in
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% sum(i in 0..size-1)(pow(2, (size-1-i)) * bool2int(x[i+min(index_set(x))]))
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% <= sum(i in 0..size-1)(pow(2, (size-1-i)) * bool2int(y[i+min(index_set(y))]))
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% else
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% my_trace ("lex_lesseq_bool(\(x), \(y))") /\
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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 = min(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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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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% ( b[i] ->
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( x[lx + i] < y[ly + i] \/ b[i+1] ) )
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% /\ ( bool2int(b[i]) <= bool2int(x[lx + i] < y[ly + i]) + bool2int(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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%% This guy is dominated by the 1st one above but helps:
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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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% forall(i in 0..size) (
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% ( b[i] == ( x[lx + i] <= y[ly + i] ) )
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% /\
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% if i < size then
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% ( b[i] == ( x[lx + i] < y[ly + i] \/ b[i+1]
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% ) ) else true endif
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% );
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%-----------------------------------------------------------------------------%
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