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dekker.one
1/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
2/*
3 * Main authors:
4 * Patrick Pekczynski <pekczynski@ps.uni-sb.de>
5 * Mikael Lagerkvist <lagerkvist@gecode.org>
6 * Christian Schulte <schulte@gecode.org>
7 *
8 * Copyright:
9 * Patrick Pekczynski, 2004
10 * Mikael Lagerkvist, 2006
11 * Christian Schulte, 2007
12 *
13 * This file is part of Gecode, the generic constraint
14 * development environment:
15 * http://www.gecode.org
16 *
17 * Permission is hereby granted, free of charge, to any person obtaining
18 * a copy of this software and associated documentation files (the
19 * "Software"), to deal in the Software without restriction, including
20 * without limitation the rights to use, copy, modify, merge, publish,
21 * distribute, sublicense, and/or sell copies of the Software, and to
22 * permit persons to whom the Software is furnished to do so, subject to
23 * the following conditions:
24 *
25 * The above copyright notice and this permission notice shall be
26 * included in all copies or substantial portions of the Software.
27 *
28 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
29 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
30 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
31 * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
32 * LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
33 * OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
34 * WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
35 *
36 */
37
38#include <gecode/driver.hh>
39#include <gecode/int.hh>
40#include <gecode/minimodel.hh>
41
42using namespace Gecode;
43
44/**
45 * \brief Options taking two additional parameters
46 *
47 * \relates LangfordNumber
48 */
49class LangfordNumberOptions : public Options {
50public:
51 int k, n; /// Parameters to be given on the command line
52 /// Initialize options for example with name \a s
53 LangfordNumberOptions(const char* s, int k0, int n0)
54 : Options(s), k(k0), n(n0) {}
55 /// Parse options from arguments \a argv (number is \a argc)
56 void parse(int& argc, char* argv[]) {
57 Options::parse(argc,argv);
58 if (argc < 3)
59 return;
60 n = atoi(argv[1]);
61 k = atoi(argv[2]);
62 }
63 /// Print help message
64 virtual void help(void) {
65 Options::help();
66 std::cerr << "\t(unsigned int) default: " << n << std::endl
67 << "\t\tparameter n" << std::endl
68 << "\t(unsigned int) default: " << k << std::endl
69 << "\t\tparameter k" << std::endl;
70 }
71};
72
73/**
74 * \brief %Example: Langford's number problem
75 *
76 * See problem 24 at http://www.csplib.org/.
77 *
78 * \ingroup Example
79 */
80class LangfordNumber : public Script {
81protected:
82 int k, n; ///< Problem parameters
83 IntVarArray y; ///< Sequence variables
84
85public:
86 /// Propagation to use for model
87 enum {
88 PROP_REIFIED, ///< Use reified constraints
89 PROP_EXTENSIONAL, ///< Use extensional constraints
90 PROP_EXTENSIONAL_CHANNEL ///< Use extensional and channel constraints
91 };
92 /// Construct model
93 LangfordNumber(const LangfordNumberOptions& opt)
94 : Script(opt), k(opt.k), n(opt.n), y(*this,k*n,1,n) {
95
96 switch (opt.propagation()) {
97 case PROP_REIFIED:
98 {
99 // Position of values in sequence
100 IntVarArgs pv(*this,k*n,0,k*n-1);
101 Matrix<IntVarArgs> p(pv,n,k);
102
103 /*
104 * The occurences of v in the Langford sequence are v numbers apart.
105 *
106 * Let \#(i, v) denote the position of the i-th occurence of
107 * value v in the Langford Sequence. Then
108 *
109 * \f$ \forall i, j \in \{1, \dots, k\}, i \neq j:
110 * \forall v \in \{1, \dots, n\}: \#(i, v) + (v + 1) = \#(j, v)\f$
111 *
112 */
113 for (int i=0; i<n; i++)
114 for (int j=0; j<k-1; j++)
115 rel(*this, p(i,j)+i+2 == p(i,j+1));
116
117 distinct(*this, pv, opt.ipl());
118
119 // Channel positions <-> values
120 for (int i=0; i<n; i++)
121 for (int j=0; j<k; j++)
122 element(*this, y, p(i,j), i+1);
123 }
124 break;
125 case PROP_EXTENSIONAL:
126 {
127 IntArgs a(n-1);
128 for (int v=2; v<=n; v++)
129 a[v-2]=v;
130 for (int v=1; v<=n; v++) {
131 // Construct regular expression for all symbols but v
132 if (v > 1)
133 a[v-2]=v-1;
134 REG ra(a), rv(v);
135 extensional(*this, y, *ra+rv+(ra(v,v)+rv)(k-1,k-1)+*ra);
136 }
137 }
138 break;
139 case PROP_EXTENSIONAL_CHANNEL:
140 {
141 // Boolean variables for channeling
142 BoolVarArgs bv(*this,k*n*n,0,1);
143 Matrix<BoolVarArgs> b(bv,k*n,n);
144
145 // Post channel constraints
146 for (int i=0; i<n*k; i++)
147 channel(*this, b.col(i), y[i], 1);
148
149 // For placing two numbers three steps apart, we construct the
150 // regular expression 0*100010*, and apply it to the projection of
151 // the sequence on the value.
152 REG r0(0), r1(1);
153 for (int v=1; v<=n; v++)
154 extensional(*this, b.row(v-1),
155 *r0 + r1 + (r0(v,v) + r1)(k-1,k-1) + *r0);
156 }
157 break;
158 }
159
160 // Symmetry breaking
161 rel(*this, y[0], IRT_LE, y[n*k-1]);
162
163 // Branching
164 branch(*this, y, INT_VAR_SIZE_MIN(), INT_VAL_MAX());
165 }
166
167 /// Print solution
168 virtual void print(std::ostream& os) const {
169 os << "\t" << y << std::endl;
170 }
171
172 /// Constructor for cloning \a l
173 LangfordNumber(LangfordNumber& l)
174 : Script(l), k(l.k), n(l.n) {
175 y.update(*this, l.y);
176
177 }
178 /// Copy during cloning
179 virtual Space*
180 copy(void) {
181 return new LangfordNumber(*this);
182 }
183};
184
185
186/** \brief Main-function
187 * \relates LangfordNumber
188 */
189int
190main(int argc, char* argv[]) {
191 LangfordNumberOptions opt("Langford Numbers",3,9);
192 opt.ipl(IPL_DOM);
193 opt.propagation(LangfordNumber::PROP_EXTENSIONAL_CHANNEL);
194 opt.propagation(LangfordNumber::PROP_REIFIED,
195 "reified");
196 opt.propagation(LangfordNumber::PROP_EXTENSIONAL,
197 "extensional");
198 opt.propagation(LangfordNumber::PROP_EXTENSIONAL_CHANNEL,
199 "extensional-channel");
200 opt.parse(argc, argv);
201 if (opt.k < 1) {
202 std::cerr << "k must be at least 1!" << std::endl;
203 return 1;
204 }
205 if (opt.k > opt.n) {
206 std::cerr << "n must be at least k!" << std::endl;
207 return 1;
208 }
209 Script::run<LangfordNumber,DFS,LangfordNumberOptions>(opt);
210 return 0;
211}
212
213// STATISTICS: example-any
214