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magic-square.cpp
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1 /* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
2 /*
3  * Main authors:
4  * Christian Schulte <schulte@gecode.org>
5  *
6  * Copyright:
7  * Christian Schulte, 2001
8  *
9  * Last modified:
10  * $Date: 2015-09-11 16:29:45 +0200 (Fri, 11 Sep 2015) $ by $Author: schulte $
11  * $Revision: 14672 $
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37 
38 #include <gecode/driver.hh>
39 #include <gecode/int.hh>
40 #include <gecode/minimodel.hh>
41 
42 using namespace Gecode;
43 
54 class MagicSquare : public Script {
55 private:
57  const int n;
59  IntVarArray x;
60 
61 public:
63  enum {
65  BRANCH_AFC_SIZE
66  };
69  : Script(opt), n(opt.size()), x(*this,n*n,1,n*n) {
70  // Number of fields on square
71  const int nn = n*n;
72 
73  // Sum of all a row, column, or diagonal
74  const int s = nn*(nn+1) / (2*n);
75 
76  // Matrix-wrapper for the square
77  Matrix<IntVarArray> m(x, n, n);
78 
79  for (int i = n; i--; ) {
80  linear(*this, m.row(i), IRT_EQ, s, opt.ipl());
81  linear(*this, m.col(i), IRT_EQ, s, opt.ipl());
82  }
83  // Both diagonals must have sum s
84  {
85  IntVarArgs d1y(n);
86  IntVarArgs d2y(n);
87  for (int i = n; i--; ) {
88  d1y[i] = m(i,i);
89  d2y[i] = m(n-i-1,i);
90  }
91  linear(*this, d1y, IRT_EQ, s, opt.ipl());
92  linear(*this, d2y, IRT_EQ, s, opt.ipl());
93  }
94 
95  // All fields must be distinct
96  distinct(*this, x, opt.ipl());
97 
98  // Break some (few) symmetries
99  rel(*this, m(0,0), IRT_GR, m(0,n-1));
100  rel(*this, m(0,0), IRT_GR, m(n-1,0));
101 
102  switch (opt.branching()) {
103  case BRANCH_SIZE:
104  branch(*this, x, INT_VAR_SIZE_MIN(), INT_VAL_SPLIT_MIN());
105  break;
106  case BRANCH_AFC_SIZE:
107  branch(*this, x, INT_VAR_AFC_SIZE_MAX(opt.decay()), INT_VAL_SPLIT_MIN());
108  break;
109  }
110  }
111 
113  MagicSquare(bool share, MagicSquare& s) : Script(share,s), n(s.n) {
114  x.update(*this, share, s.x);
115  }
116 
118  virtual Space*
119  copy(bool share) {
120  return new MagicSquare(share,*this);
121  }
123  virtual void
124  print(std::ostream& os) const {
125  // Matrix-wrapper for the square
126  Matrix<IntVarArray> m(x, n, n);
127  for (int i = 0; i<n; i++) {
128  os << "\t";
129  for (int j = 0; j<n; j++) {
130  os.width(2);
131  os << m(i,j) << " ";
132  }
133  os << std::endl;
134  }
135  }
136 
137 };
138 
142 int
143 main(int argc, char* argv[]) {
144  SizeOptions opt("MagicSquare");
145  opt.iterations(1);
146  opt.size(7);
148  opt.branching(MagicSquare::BRANCH_SIZE, "size");
149  opt.branching(MagicSquare::BRANCH_AFC_SIZE, "afc-size");
150  opt.parse(argc,argv);
151  Script::run<MagicSquare,DFS,SizeOptions>(opt);
152  return 0;
153 }
154 
155 // STATISTICS: example-any
156 
void size(unsigned int s)
Set default size.
Definition: options.hpp:557
Options for scripts with additional size parameter
Definition: driver.hh:649
Slice< A > col(int c) const
Access column c.
Definition: matrix.hpp:187
virtual Space * copy(bool share)
Copy during cloning.
void branch(Home home, const FloatVarArgs &x, FloatVarBranch vars, FloatValBranch vals, FloatBranchFilter bf, FloatVarValPrint vvp)
Branch over x with variable selection vars and value selection vals.
Definition: branch.cpp:43
void parse(int &argc, char *argv[])
Parse options from arguments argv (number is argc)
Definition: options.cpp:622
void linear(Home home, const FloatVarArgs &x, FloatRelType frt, FloatVal c)
Post propagator for .
Definition: linear.cpp:45
Integer variable array.
Definition: int.hh:744
void ipl(IntPropLevel i)
Set default integer propagation level.
Definition: options.hpp:220
Greater ( )
Definition: int.hh:912
Example: Magic squares
Computation spaces.
Definition: core.hpp:1748
Parametric base-class for scripts.
Definition: driver.hh:703
void iterations(unsigned int i)
Set default number of iterations.
Definition: options.hpp:465
void decay(double d)
Set default decay factor.
Definition: options.hpp:242
Branch by size over AFC.
void update(Space &, bool share, VarArray< Var > &a)
Update array to be a clone of array a.
Definition: array.hpp:1072
IntVarBranch INT_VAR_AFC_SIZE_MAX(double d, BranchTbl tbl)
Select variable with largest accumulated failure count divided by domain size with decay factor d...
Definition: var.hpp:240
Gecode::IntArgs i(4, 1, 2, 3, 4)
int n
Number of negative literals for node type.
Definition: bool-expr.cpp:238
Equality ( )
Definition: int.hh:907
Options opt
The options.
Definition: test.cpp:101
unsigned int size(I &i)
Size of all ranges of range iterator i.
void distinct(Home home, const IntVarArgs &x, IntPropLevel ipl)
Post propagator for for all .
Definition: distinct.cpp:50
void branching(int v)
Set default branching value.
Definition: options.hpp:229
Passing integer variables.
Definition: int.hh:639
int main(int argc, char *argv[])
Main-function.
IntVarBranch INT_VAR_SIZE_MIN(BranchTbl tbl)
Select variable with smallest domain size.
Definition: var.hpp:210
Slice< A > row(int r) const
Access row r.
Definition: matrix.hpp:181
MagicSquare(const SizeOptions &opt)
Post constraints.
void rel(Home home, FloatVar x0, FloatRelType frt, FloatVal n)
Propagates .
Definition: rel.cpp:47
Post propagator for SetVar x
Definition: set.hh:784
Matrix-interface for arrays.
Definition: minimodel.hh:1923
IntValBranch INT_VAL_SPLIT_MIN(void)
Select values not greater than mean of smallest and largest value.
Definition: val.hpp:79
Gecode toplevel namespace
MagicSquare(bool share, MagicSquare &s)
Constructor for cloning s.
virtual void print(std::ostream &os) const
Print solution.