Jip J. Dekker
f2a1c4e389
git-subtree-dir: software/mza git-subtree-split: f970a59b177c13ca3dd8aaef8cc6681d83b7e813
59 lines
1.4 KiB
MiniZinc
59 lines
1.4 KiB
MiniZinc
% RUNS ON mzn20_fd
|
|
% RUNS ON mzn-fzn_fd
|
|
% RUNS ON mzn20_mip
|
|
% perfsq.mzn
|
|
% vim: ft=zinc ts=4 sw=4 et
|
|
% Ralph Becket
|
|
% Thu May 31 11:44:33 EST 2007
|
|
%
|
|
% Perfect squares: find a set of integers the sum of whose squares is
|
|
% itself a square.
|
|
|
|
int: z = 10;
|
|
|
|
array [0..z] of 0..z*z: sq = array1d(0..z, [x*x | x in 0..z]);
|
|
|
|
array [0..z] of var 0..z: s; % Decreasing indices into sq.
|
|
|
|
var 0..z: k; % We are summing to sq[k];
|
|
|
|
var 1..z: j; % We want this many sub-squares.
|
|
|
|
|
|
|
|
% Symmetry breaking: s is an array of indices into sq. The indices are
|
|
% strictly decreasing until they reach zero, whereupon the remainder are
|
|
% also zero.
|
|
%
|
|
constraint forall ( i in 1..z ) ( s[i] > 0 -> s[i - 1] > s[i] );
|
|
|
|
% sq[k], sq[k + 1], ... can't appear in the solution.
|
|
%
|
|
constraint s[0] < k;
|
|
|
|
% We want the sum of the squares to be square.
|
|
%
|
|
constraint sum ( i in 0..z ) ( sq[s[i]] ) = sq[k];
|
|
|
|
% We want the longest such sequence.
|
|
%
|
|
constraint s[j] > 0;
|
|
|
|
solve maximize j;
|
|
|
|
output [
|
|
"perfsq\n",
|
|
show(k), "^2 = ",
|
|
show(s[0]), "^2 + ",
|
|
show(s[1]), "^2 + ",
|
|
show(s[2]), "^2 + ",
|
|
show(s[3]), "^2 + ",
|
|
show(s[4]), "^2 + ",
|
|
show(s[5]), "^2 + ",
|
|
show(s[6]), "^2 + ",
|
|
show(s[7]), "^2 + ",
|
|
show(s[8]), "^2 + ",
|
|
show(s[9]), "^2 + ",
|
|
show(s[10]), "^2\n",
|
|
];
|