Alphabet Blocks Problem (oclpe02)

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/*          S A S   S A M P L E   L I B R A R Y                */
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/*    NAME: oclpe02                                            */
/*   TITLE: Alphabet Blocks Problem (oclpe02)                  */
/* PRODUCT: OR                                                 */
/*  SYSTEM: ALL                                                */
/*    KEYS: OR                                                 */
/*   PROCS: CLP                                                */
/*    DATA:                                                    */
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/* SUPPORT:                             UPDATE:                */
/*     REF:                                                    */
/*    MISC: Example 2 from the CLP solver chapter of the       */
/*          Mathematical Programming book.                     */
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proc optmodel;
   /* Each letter except Q and Z is represented with a variable. */
   /* The domain of each variable is the set of 4 blocks,        */
   /*   or {1, 2, 3, 4} for short.                               */
   set LETTERS = / A B C D E F G H I J K L M N O P R S T U V W X Y /;
   var Block {LETTERS} integer >= 1 <= 4;
   set BLOCKS = 1..4;

   /* There are exactly 6 letters on each alphabet block */
   con SixLettersPerBlock:
      gcc(Block, setof {b in BLOCKS} <b,6,6>);

   /* The letters in each word must be on different blocks. */
   set WORDS = / BAKE ONYX ECHO OVAL GIRD SMUG JUMP TORN LUCK VINY LUSH WRAP /;
   con CanSpell {w in WORDS}:
      gcc({k in 1..length(w)} Block[char(w,k)], setof {b in BLOCKS} <b,0,1>);

   /* Note 2: These restrictions can also be enforced by ALLDIFF constraints:
   con CanSpellv2 {w in WORDS}:
      alldiff({k in 1..length(w)} Block[char(w,k)]);
   */

   /* Breaking the symmetry that blocks can be interchanged by setting
      the block that contains the letter B as block1, the block that
      contains the letter A as block2, etc. */
   for {k in 1..length('BAKE')} fix Block[char('BAKE',k)] = k;

   solve;
   print Block;
quit;