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dekker.one
1% RUNS ON mzn20_fd
2% RUNS ON mzn-fzn_fd
3% RUNS ON mzn20_mip
4% perfsq2.mzn
5% vim: ft=zinc ts=4 sw=4 et
6%
7% Perfect squares: find a square equal to the sum of smaller, distinct squares.
8
9int: n = 100;
10
11% x[k] = 1 iff k^2 is part of the sum.
12%
13array [1..n] of var 0..1: x;
14
15% t is the sum of the first n squares, the largest value our sum can have.
16%
17int: t = ((n * (n + 1) * (2 * n + 1)) div 6);
18
19% squares is the set of square numbers less than t.
20%
21set of int: squares = {i * i | i in 1..(n * n) where i * i <= t};
22
23% k is the sum of the squares selected by the x[i].
24%
25var squares: k = sum (i in 1..n) (i * i * x[i]);
26
27solve maximize(k);
28
29output [show(k), "\n"];
30
31% output
32% [ show(k), " = sum of "
33% ] ++
34% [ if fix(x[i]) = 1 then show(i * i) ++ " " else "" endif
35% | i in 1..n
36% ] ++
37% [ "\n"
38% ];