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dekker.one
1/***
2!Test
3expected:
4- !Result
5 solution: !Solution
6 q:
7 - [0, 0, 0, 0, 0, 0, 0, 1]
8 - [0, 0, 0, 1, 0, 0, 0, 0]
9 - [1, 0, 0, 0, 0, 0, 0, 0]
10 - [0, 0, 1, 0, 0, 0, 0, 0]
11 - [0, 0, 0, 0, 0, 1, 0, 0]
12 - [0, 1, 0, 0, 0, 0, 0, 0]
13 - [0, 0, 0, 0, 0, 0, 1, 0]
14 - [0, 0, 0, 0, 1, 0, 0, 0]
15- !Result
16 solution: !Solution
17 q:
18 - [0, 0, 0, 1, 0, 0, 0, 0]
19 - [0, 0, 0, 0, 0, 1, 0, 0]
20 - [0, 0, 0, 0, 0, 0, 0, 1]
21 - [0, 0, 1, 0, 0, 0, 0, 0]
22 - [1, 0, 0, 0, 0, 0, 0, 0]
23 - [0, 0, 0, 0, 0, 0, 1, 0]
24 - [0, 0, 0, 0, 1, 0, 0, 0]
25 - [0, 1, 0, 0, 0, 0, 0, 0]
26- !Result
27 solution: !Solution
28 q:
29 - [0, 0, 0, 0, 1, 0, 0, 0]
30 - [0, 0, 0, 0, 0, 0, 0, 1]
31 - [0, 0, 0, 1, 0, 0, 0, 0]
32 - [1, 0, 0, 0, 0, 0, 0, 0]
33 - [0, 0, 0, 0, 0, 0, 1, 0]
34 - [0, 1, 0, 0, 0, 0, 0, 0]
35 - [0, 0, 0, 0, 0, 1, 0, 0]
36 - [0, 0, 1, 0, 0, 0, 0, 0]
37***/
38
39% n-queens example in Zinc using IP techniques
40% By Ralph Becket
41
42% MiniZinc version
43% Peter Stuckey September 30 2006
44
45int: n = 8;
46
47set of int: rg = 0 .. n-1;
48
49array [rg, rg] of var 0 .. 1: q :: add_to_output;
50
51%
52% Every row and column has exactly one queen.
53% Every diagonal has at most one queen.
54%
55
56constraint forall (i in rg) (
57 ( sum (j in rg) (q[i, j]) = 1 )
58/\ ( sum (j in rg) (q[j, i]) = 1 )
59/\ ( sum (j, k in rg where j - k = i) (q[j, k]) <= 1 )
60/\ ( sum (j, k in rg where j - k = - i) (q[j, k]) <= 1 )
61/\ ( sum (j, k in rg where j - k = i) (q[n - 1 - j, k]) <= 1 )
62/\ ( sum (j, k in rg where j - k = - i) (q[n - 1 - j, k]) <= 1 )
63);
64
65%
66% Find the first solution.
67%
68
69solve ::
70 int_search(
71 array1d(1..n*n, q),
72 first_fail,
73 indomain_min,
74 complete
75 )
76 satisfy;
77
78output ["8 queens, IP version:"] ++
79 [ if j = 0 then "\n" else "" endif ++
80 if fix(q[i, j]) = 1 then "Q " else ". " endif
81 | i, j in rg
82 ] ++
83 [ "\n" ];