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(***********************************************************************)
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(* A Functional Constraint Library *)
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(* Nicolas Barnier, Pascal Brisset, LOG, CENA *)
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(* Copyright 2004 CENA. All rights reserved. This file is distributed *)
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(* under the terms of the GNU Lesser General Public License. *)
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(***********************************************************************)
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(* $Id: magic.ml,v 1.9 2001/06/01 14:13:09 barnier Exp $ *)
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A magic sequence is a sequence of N values (x0, x1, , xN-1) such
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that 0 will appear in the sequence x0 times, 1 will appear x1
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times,..., and N-1 will appear in the sequence xN-1 times. For example,
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for N=3, the following sequence is a solution: (1, 2, 1, 0). That is,
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0 is present once, 1 is present twice, 2 is present once, and 3 is not
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let x = Fd.array n 0 (n-1) in
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(* Constraint: cardinality constraint with x as variables and cardinals *)
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let card_vals = Array.mapi (fun i x -> (x, i)) x in
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Cstr.post (Gcc.cstr ~level:Gcc.Medium x card_vals);
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(* Redundant constraints *)
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let vals = Array.init n (fun i -> i) in
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Cstr.post (Arith.scalprod_fd vals x =~ i2e n);
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(* Search goal: first fail with min domain size *)
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Goals.Array.choose_index (fun a1 a2 -> Var.Attr.size a1 < Var.Attr.size a2) in
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let goal = Goals.Array.forall ~select:min_size Goals.indomain x in
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if Goals.solve goal then begin
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Array.iter (fun v -> Printf.printf "%a " Fd.fprint v) x; print_newline ()
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prerr_endline "No solution";;
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if Array.length Sys.argv < 2 then prerr_endline "Usage: magic <size>"
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else magic (int_of_string Sys.argv.(1));;
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examples/magic.ml
