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dekker.one
1/***
2!Test
3expected:
4- !Result
5 solution: !Solution
6 j: 4
7 k: 10
8 objective: 4
9 s: [7, 5, 4, 3, 1, 0, 0, 0, 0, 0, 0]
10***/
11
12% perfsq.mzn
13% vim: ft=zinc ts=4 sw=4 et
14% Ralph Becket
15% Thu May 31 11:44:33 EST 2007
16%
17% Perfect squares: find a set of integers the sum of whose squares is
18% itself a square.
19
20int: z = 10;
21
22array [0..z] of 0..z*z: sq = array1d(0..z, [x*x | x in 0..z]);
23
24array [0..z] of var 0..z: s; % Decreasing indices into sq.
25
26var 0..z: k; % We are summing to sq[k];
27
28var 1..z: j; % We want this many sub-squares.
29
30
31
32 % Symmetry breaking: s is an array of indices into sq. The indices are
33 % strictly decreasing until they reach zero, whereupon the remainder are
34 % also zero.
35 %
36constraint forall ( i in 1..z ) ( s[i] > 0 -> s[i - 1] > s[i] );
37
38 % sq[k], sq[k + 1], ... can't appear in the solution.
39 %
40constraint s[0] < k;
41
42 % We want the sum of the squares to be square.
43 %
44constraint sum ( i in 0..z ) ( sq[s[i]] ) = sq[k];
45
46 % We want the longest such sequence.
47 %
48constraint s[j] > 0;
49
50solve maximize j;
51
52output [
53 "perfsq\n",
54 show(k), "^2 = ",
55 show(s[0]), "^2 + ",
56 show(s[1]), "^2 + ",
57 show(s[2]), "^2 + ",
58 show(s[3]), "^2 + ",
59 show(s[4]), "^2 + ",
60 show(s[5]), "^2 + ",
61 show(s[6]), "^2 + ",
62 show(s[7]), "^2 + ",
63 show(s[8]), "^2 + ",
64 show(s[9]), "^2 + ",
65 show(s[10]), "^2\n",
66];