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/*
Magic sequence in AMPL+CP.
http://www.dcs.st-and.ac.uk/~ianm/CSPLib/prob/prob019/spec.html
"""
A magic sequence of length n is a sequence of integers x0 . . xn-1 between
0 and n-1, such that for all i in 0 to n-1, the number i occurs exactly xi
times in the sequence. For instance, 6,2,1,0,0,0,1,0,0,0 is a magic sequence
since 0 occurs 6 times in it, 1 occurs twice, ...
"""
Model created by Hakan Kjellerstrand, hakank@gmail.com
See also my AMPL page: http://www.hakank.org/ampl/
*/
# Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/
param n;
var s{0..n-1} integer >= 0 <= n-1 integer;
#
# constraints
#
s.t. c1{i in 0..n-1}: exactly s[i] {j in 0..n-1} (s[j] = i);
s.t. c2: n = sum{i in 0..n-1} s[i];
s.t. c3: n = sum{i in 0..n-1} s[i]*i;
data;
# for{k in 10..20} {
#
# let n := k;
# printf "\nn: %d\n", n;
#
# option solver gecode;
# option gecode_options 'var_branching=size_min val_branching=min outlev=1 outfreq=1';
#
# solve;
#
# # display s;
# for{i in 0..n-1} { printf "%2d ", s[i]; }
# printf "\n\n";
# }
param n := 1000;
option solver gecode;
option gecode_options 'var_branching=size_min val_branching=min outlev=1 outfreq=1';
# option solver ilogcp;
# option ilogcp_options "optimizer=cp alldiffinferencelevel=1 debugexpr=0 logperiod=1 logverbosity=0";
solve;
for{i in 0..n-1} { printf "%2d ", s[i]; }
printf "\n\n";