1.1 --- /dev/null	Thu Jan 01 00:00:00 1970 +0000
     1.2 +++ b/examples/crypto.mod	Mon Dec 06 13:09:21 2010 +0100
     1.3 @@ -0,0 +1,84 @@
     1.4 +/* CRYPTO, a crypto-arithmetic puzzle */
     1.5 +
     1.6 +/* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
     1.7 +
     1.8 +/* This problem comes from the newsgroup rec.puzzle.
     1.9 +   The numbers from 1 to 26 are assigned to the letters of the alphabet.
    1.10 +   The numbers beside each word are the total of the values assigned to
    1.11 +   the letters in the word (e.g. for LYRE: L, Y, R, E might be to equal
    1.12 +   5, 9, 20 and 13, or any other combination that add up to 47).
    1.13 +   Find the value of each letter under the equations:
    1.14 +
    1.15 +   BALLET  45     GLEE  66     POLKA      59     SONG     61
    1.16 +   CELLO   43     JAZZ  58     QUARTET    50     SOPRANO  82
    1.17 +   CONCERT 74     LYRE  47     SAXOPHONE 134     THEME    72
    1.18 +   FLUTE   30     OBOE  53     SCALE      51     VIOLIN  100
    1.19 +   FUGUE   50     OPERA 65     SOLO       37     WALTZ    34
    1.20 +
    1.21 +   Solution:
    1.22 +   A, B,C, D, E,F, G, H, I, J, K,L,M, N, O, P,Q, R, S,T,U, V,W, X, Y, Z
    1.23 +   5,13,9,16,20,4,24,21,25,17,23,2,8,12,10,19,7,11,15,3,1,26,6,22,14,18
    1.24 +
    1.25 +   Reference:
    1.26 +   Koalog Constraint Solver <http://www.koalog.com/php/jcs.php>,
    1.27 +   Simple problems, the crypto-arithmetic puzzle ALPHACIPHER. */
    1.28 +
    1.29 +set LETTERS :=
    1.30 +{     'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K', 'L', 'M',
    1.31 +      'N', 'O', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X', 'Y', 'Z'
    1.32 +};
    1.33 +/* set of letters */
    1.34 +
    1.35 +set VALUES := 1..card(LETTERS);
    1.36 +/* set of values assigned to the letters */
    1.37 +
    1.38 +set WORDS;
    1.39 +/* set of words */
    1.40 +
    1.41 +param total{word in WORDS};
    1.42 +/* total[word] is the total of the values assigned to the letters in
    1.43 +   the word */
    1.44 +
    1.45 +var x{i in LETTERS, j in VALUES}, binary;
    1.46 +/* x[i,j] = 1 means that letter i is assigned value j */
    1.47 +
    1.48 +s.t. phi{i in LETTERS}: sum{j in VALUES} x[i,j] = 1;
    1.49 +
    1.50 +s.t. psi{j in VALUES}: sum{i in LETTERS} x[i,j] = 1;
    1.51 +
    1.52 +s.t. eqn{word in WORDS}: sum{k in 1..length(word), j in VALUES}
    1.53 +      j * x[substr(word,k,1), j] = total[word];
    1.54 +
    1.55 +solve;
    1.56 +
    1.57 +printf{i in LETTERS} "  %s", i;
    1.58 +printf "\n";
    1.59 +
    1.60 +printf{i in LETTERS} " %2d", sum{j in VALUES} j * x[i,j];
    1.61 +printf "\n";
    1.62 +
    1.63 +data;
    1.64 +
    1.65 +param :  WORDS :   total :=
    1.66 +         BALLET       45
    1.67 +         CELLO        43
    1.68 +         CONCERT      74
    1.69 +         FLUTE        30
    1.70 +         FUGUE        50
    1.71 +         GLEE         66
    1.72 +         JAZZ         58
    1.73 +         LYRE         47
    1.74 +         OBOE         53
    1.75 +         OPERA        65
    1.76 +         POLKA        59
    1.77 +         QUARTET      50
    1.78 +         SAXOPHONE   134
    1.79 +         SCALE        51
    1.80 +         SOLO         37
    1.81 +         SONG         61
    1.82 +         SOPRANO      82
    1.83 +         THEME        72
    1.84 +         VIOLIN      100
    1.85 +         WALTZ        34 ;
    1.86 +
    1.87 +end;