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/*-------------------------------------------------------------------------*/
/* Benchmark (Finite Domain) */
/* */
/* Name : magsq.pl */
/* Title : Magic square problem */
/* Original Source: Daniel Diaz - INRIA France */
/* Adapted by : Daniel Diaz for GNU Prolog */
/* Date : July 1998 */
/* */
/* Fill square NxN with integers 1,2...N*N so that each line, each column */
/* and each diagonal has the same sum. */
/* threatening each other. */
/* */
/* Solution: */
/* N=3 [[4,9,2],[3,5,7],[8,1,6]] */
/*-------------------------------------------------------------------------*/
q :-
write('N ?'),
read_integer(N),
statistics(runtime, _),
magsq(N, A),
statistics(runtime, [_, Y]),
write(A),
nl,
write_array(A, '%5d', 0),
write('time : '),
write(Y),
nl.
magsq(N, A) :-
create_array(N, N, A),
N2 is N * N,
fd_set_vector_max(N2),
S is N * (N2 + 1) // 2,
g_assign(s, S),
g_assign(n, N),
g_assign(n2, N2),
array_values(A, Values),
fd_all_different(Values),
for_each_line(A, dom),
for_each_line(A, sum),
for_each_column(A, sum),
for_each_big_diagonal(A, N, sum),
array_elem(A, 1, 1, X11),
array_elem(A, 1, N, X1N),
array_elem(A, N, 1, XN1),
array_elem(A, N, N, XNN),
X11 #< X1N, % 4 symmetry breaking constraints
X11 #< XN1,
X11 #< XNN,
XN1 #> X1N,
for_each_big_diagonal(A, N, lab),
% for_each_line(A,lab).
fd_labeling(Values, [variable_method(ff), value_method(max)]).
% in practice this random is better than max
% fd_labeling(Values, [variable_method(ff), value_method(random)]).
array_prog(dom, L) :-
g_read(n2, N2),
fd_domain(L, 1, N2).
array_prog(sum, L) :-
g_read(s, S),
sum(L, S).
array_prog(lab, L) :-
fd_labeling(L, [value_method(middle)]).
/*
reorder(L,L1):-
g_read(n,N),
fd_domain(X,1,N),
findall(V,(fd_labeling(X,[value_method(middle)]),nth(X,L,V)),L1).
*/
sum([], 0).
sum([X|Xs], S) :-
S #= X + S1,
sum(Xs, S1).
:- include(array).
:- initialization(q).
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