1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
|
/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
/*
* Main authors:
* Christian Schulte <schulte@gecode.org>
*
* Copyright:
* Christian Schulte, 2001
*
* This file is part of Gecode, the generic constraint
* development environment:
* http://www.gecode.org
*
* Permission is hereby granted, free of charge, to any person obtaining
* a copy of this software and associated documentation files (the
* "Software"), to deal in the Software without restriction, including
* without limitation the rights to use, copy, modify, merge, publish,
* distribute, sublicense, and/or sell copies of the Software, and to
* permit persons to whom the Software is furnished to do so, subject to
* the following conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
* LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
* OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
* WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
*
*/
#include <gecode/driver.hh>
#include <gecode/int.hh>
#include <gecode/minimodel.hh>
using namespace Gecode;
/**
* \brief %Example: Magic squares
*
* Compute magic squares of arbitrary size
*
* See problem 19 at http://www.csplib.org/.
*
* \ingroup Example
*
*/
class MagicSquare : public Script {
private:
/// Size of magic square
const int n;
/// Fields of square
IntVarArray x;
public:
/// Branching to use for model
enum {
BRANCH_SIZE, ///< Branch by size
BRANCH_AFC_SIZE ///< Branch by size over AFC
};
/// Post constraints
MagicSquare(const SizeOptions& opt)
: Script(opt), n(opt.size()), x(*this,n*n,1,n*n) {
// Number of fields on square
const int nn = n*n;
// Sum of all a row, column, or diagonal
const int s = nn*(nn+1) / (2*n);
// Matrix-wrapper for the square
Matrix<IntVarArray> m(x, n, n);
for (int i = n; i--; ) {
linear(*this, m.row(i), IRT_EQ, s, opt.ipl());
linear(*this, m.col(i), IRT_EQ, s, opt.ipl());
}
// Both diagonals must have sum s
{
IntVarArgs d1y(n);
IntVarArgs d2y(n);
for (int i = n; i--; ) {
d1y[i] = m(i,i);
d2y[i] = m(n-i-1,i);
}
linear(*this, d1y, IRT_EQ, s, opt.ipl());
linear(*this, d2y, IRT_EQ, s, opt.ipl());
}
// All fields must be distinct
distinct(*this, x, opt.ipl());
// Break some (few) symmetries
rel(*this, m(0,0), IRT_GR, m(0,n-1));
rel(*this, m(0,0), IRT_GR, m(n-1,0));
switch (opt.branching()) {
case BRANCH_SIZE:
branch(*this, x, INT_VAR_SIZE_MIN(), INT_VAL_SPLIT_MIN());
break;
case BRANCH_AFC_SIZE:
branch(*this, x, INT_VAR_AFC_SIZE_MAX(opt.decay()), INT_VAL_SPLIT_MIN());
break;
}
}
/// Constructor for cloning \a s
MagicSquare(MagicSquare& s) : Script(s), n(s.n) {
x.update(*this, s.x);
}
/// Copy during cloning
virtual Space*
copy(void) {
return new MagicSquare(*this);
}
/// Print solution
virtual void
print(std::ostream& os) const {
// Matrix-wrapper for the square
Matrix<IntVarArray> m(x, n, n);
for (int i = 0; i<n; i++) {
os << "\t";
for (int j = 0; j<n; j++) {
os.width(2);
os << m(i,j) << " ";
}
os << std::endl;
}
}
};
/** \brief Main-function
* \relates MagicSquare
*/
int
main(int argc, char* argv[]) {
SizeOptions opt("MagicSquare");
opt.iterations(1);
opt.size(7);
opt.branching(MagicSquare::BRANCH_SIZE);
opt.branching(MagicSquare::BRANCH_SIZE, "size");
opt.branching(MagicSquare::BRANCH_AFC_SIZE, "afc-size");
opt.parse(argc,argv);
Script::run<MagicSquare,DFS,SizeOptions>(opt);
return 0;
}
// STATISTICS: example-any
|
