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2.2. Introductory TOY(FD) Examples 27

C #+ E #+ L #+ L #+ O #= 43,

C #+ O #+ N #+ C #+ E #+ R #+ T #= 74,

F #+ L #+ U #+ T #+ E #= 30,

F #+ U #+ G #+ U #+ E #= 50,

G #+ L #+ E #+ E #= 66,

J #+ A #+ Z #+ Z #= 58,

L #+ Y #+ R #+ E #= 47,

O #+ B #+ O #+ E #= 53,

O #+ P #+ E #+ R #+ A #= 65,

P #+ O #+ L #+ K #+ A #= 59,

Q #+ U #+ A #+ R #+ T #+ E #+ T #= 50,

S #+ A #+ X #+ O #+ P #+ H #+ O #+ N #+ E #= 134,

S #+ C #+ A #+ L #+ E #= 51,

S #+ O #+ L #+ O #= 37,

S #+ O #+ N #+ G #= 61,

S #+ O #+ P #+ R #+ A #+ N #+ O #= 82,

T #+ H #+ E #+ M #+ E #= 72,

V #+ I #+ O #+ L #+ I #+ N #= 100,

W #+ A #+ L #+ T #+ Z #= 34,

labeling Label LD

Solving in the command level is shown below:

TOY(FD)> alpha [ff] L

yes

L==[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]

Elapsed time: 9735 ms.

2.2.4 Magic Sequences

We present another simple (and well-known) example, the magic series problem Van Hen-

tenryck, 1989. Let S = (s

, s

, . . . , s

N−1

) be a non-empty ﬁnite serial of non-negative

integers. As convention, we number its elements from 0. The serial S is said N-magic

if and only if there are s

occurrences of i in S, for all i in {1, . . . , N − 1}.

Below we show a possible TOY(FD) solution, included in the distribution in the

directory Examples in the ﬁle magicseq.toy, to this problem.

include "cflpfd.toy"

include "misc.toy" %% To use length/1

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

magic N L Label = true <==

length L == N,

domain L 0 (N-1), % Functional syntax (N-1)

1 2 ... 34 35 36 37 38 39 40 41 42 43 44 ... 80 81

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