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26 CHAPTER 2. TOY(FD) Programming Examples

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more solutions (y/n/d) [y]? ; %% Do not look for more solutions

TOY(FD)>

2.2.3 A Cryptoarithmetic Problem

Alpha is a cryptoarithmetic problem where the numbers 1 - 26 are randomly assigned

to the letters of the alphabet. The numbers beside each word are the total of the

values assigned to the letters in the word. e.g for LYRE L,Y,R,E might equal 5,9,20

and 13 respectively or any other combination that add up to 47. The problem consists

of ﬁnding the value of each letter under the following equations:

BALLET = 45,

GLEE = 66,

POLKA = 59,

SONG = 61,

CELLO = 43,

JAZZ = 58,

QUARTET = 50,

SOPRANO = 82,

CONCERT = 74

LYRE = 47,

SAXOPHONE = 134,

THEME = 72,

FLUTE = 30,

OBOE = 53,

SCALE = 51,

VIOLIN = 100,

FUGUE = 50,

OPERA = 65,

SOLO = 37,

WALTZ = 34

A TOY(FD) solution, included in the distribution in the directory Examples in the

ﬁle alpha.toy, is shown below:

include "cflpfd.toy"

alpha :: [labelingType] -> [int] -> bool

alpha Label LD = true <==

LD == [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],

domain LD 1 26,

all_different LD,

B #+ A #+ L #+ L #+ E #+ T #= 45,

1 2 ... 33 34 35 36 37 38 39 40 41 42 43 ... 80 81

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Ascend FD-23R Manual do Utilizador Página 38