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langford-number.cpp

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00001 /* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
00002 /*
00003  *  Main authors:
00004  *     Patrick Pekczynski <pekczynski@ps.uni-sb.de>
00005  *     Mikael Lagerkvist <lagerkvist@gecode.org>
00006  *     Christian Schulte <schulte@gecode.org>
00007  *
00008  *  Copyright:
00009  *     Patrick Pekczynski, 2004
00010  *     Mikael Lagerkvist, 2006
00011  *     Christian Schulte, 2007
00012  *
00013  *  This file is part of Gecode, the generic constraint
00014  *  development environment:
00015  *     http://www.gecode.org
00016  *
00017  *  Permission is hereby granted, free of charge, to any person obtaining
00018  *  a copy of this software and associated documentation files (the
00019  *  "Software"), to deal in the Software without restriction, including
00020  *  without limitation the rights to use, copy, modify, merge, publish,
00021  *  distribute, sublicense, and/or sell copies of the Software, and to
00022  *  permit persons to whom the Software is furnished to do so, subject to
00023  *  the following conditions:
00024  *
00025  *  The above copyright notice and this permission notice shall be
00026  *  included in all copies or substantial portions of the Software.
00027  *
00028  *  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
00029  *  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
00030  *  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
00031  *  NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE
00032  *  LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
00033  *  OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
00034  *  WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
00035  *
00036  */
00037 
00038 #include <gecode/driver.hh>
00039 #include <gecode/int.hh>
00040 #include <gecode/minimodel.hh>
00041 
00042 using namespace Gecode;
00043 
00049 class LangfordNumberOptions : public Options {
00050 public:
00051   int k, n; 
00052 
00053   LangfordNumberOptions(const char* s, int k0, int n0)
00054     : Options(s), k(k0), n(n0) {}
00056   void parse(int& argc, char* argv[]) {
00057     Options::parse(argc,argv);
00058     if (argc < 3)
00059       return;
00060     n = atoi(argv[1]);
00061     k = atoi(argv[2]);
00062   }
00064   virtual void help(void) {
00065     Options::help();
00066     std::cerr << "\t(unsigned int) default: " << n << std::endl
00067               << "\t\tparameter n" << std::endl
00068               << "\t(unsigned int) default: " << k << std::endl
00069               << "\t\tparameter k" << std::endl;
00070   }
00071 };
00072 
00080 class LangfordNumber : public Script {
00081 protected:
00082   int k, n;      
00083   IntVarArray y; 
00084 
00085 public:
00087   enum {
00088     PROP_REIFIED,            
00089     PROP_EXTENSIONAL,        
00090     PROP_EXTENSIONAL_CHANNEL 
00091   };
00093   LangfordNumber(const LangfordNumberOptions& opt)
00094     : Script(opt), k(opt.k), n(opt.n), y(*this,k*n,1,n) {
00095 
00096     switch (opt.propagation()) {
00097     case PROP_REIFIED:
00098       {
00099         // Position of values in sequence
00100         IntVarArgs pv(*this,k*n,0,k*n-1);
00101         Matrix<IntVarArgs> p(pv,n,k);
00102 
00103         /*
00104          * The occurences of v in the Langford sequence are v numbers apart.
00105          *
00106          * Let \#(i, v) denote the position of the i-th occurence of
00107          * value v in the Langford Sequence. Then
00108          *
00109          * \f$ \forall i, j \in \{1, \dots, k\}, i \neq j:
00110          *     \forall v \in \{1, \dots, n\}: \#(i, v) + (v + 1) = \#(j, v)\f$
00111          *
00112          */
00113         for (int i=0; i<n; i++)
00114           for (int j=0; j<k-1; j++)
00115             rel(*this, p(i,j)+i+2 == p(i,j+1));
00116 
00117         distinct(*this, pv, opt.ipl());
00118 
00119         // Channel positions <-> values
00120         for (int i=0; i<n; i++)
00121           for (int j=0; j<k; j++)
00122             element(*this, y, p(i,j), i+1);
00123       }
00124       break;
00125     case PROP_EXTENSIONAL:
00126       {
00127         IntArgs a(n-1);
00128         for (int v=2; v<=n; v++)
00129           a[v-2]=v;
00130         for (int v=1; v<=n; v++) {
00131           // Construct regular expression for all symbols but v
00132           if (v > 1)
00133             a[v-2]=v-1;
00134           REG ra(a), rv(v);
00135           extensional(*this, y, *ra+rv+(ra(v,v)+rv)(k-1,k-1)+*ra);
00136         }
00137       }
00138       break;
00139     case PROP_EXTENSIONAL_CHANNEL:
00140       {
00141         // Boolean variables for channeling
00142         BoolVarArgs bv(*this,k*n*n,0,1);
00143         Matrix<BoolVarArgs> b(bv,k*n,n);
00144 
00145         // Post channel constraints
00146         for (int i=0; i<n*k; i++)
00147           channel(*this, b.col(i), y[i], 1);
00148 
00149         // For placing two numbers three steps apart, we construct the
00150         // regular expression 0*100010*, and apply it to the projection of
00151         // the sequence on the value.
00152         REG r0(0), r1(1);
00153         for (int v=1; v<=n; v++)
00154           extensional(*this, b.row(v-1),
00155                       *r0 + r1 + (r0(v,v) + r1)(k-1,k-1) + *r0);
00156       }
00157       break;
00158     }
00159 
00160     // Symmetry breaking
00161     rel(*this, y[0], IRT_LE, y[n*k-1]);
00162 
00163     // Branching
00164     branch(*this, y, INT_VAR_SIZE_MIN(), INT_VAL_MAX());
00165   }
00166 
00168   virtual void print(std::ostream& os) const {
00169     os << "\t" << y << std::endl;
00170   }
00171 
00173   LangfordNumber(LangfordNumber& l)
00174     : Script(l), k(l.k), n(l.n) {
00175     y.update(*this, l.y);
00176 
00177   }
00179   virtual Space*
00180   copy(void) {
00181     return new LangfordNumber(*this);
00182   }
00183 };
00184 
00185 
00189 int
00190 main(int argc, char* argv[]) {
00191   LangfordNumberOptions opt("Langford Numbers",3,9);
00192   opt.ipl(IPL_DOM);
00193   opt.propagation(LangfordNumber::PROP_EXTENSIONAL_CHANNEL);
00194   opt.propagation(LangfordNumber::PROP_REIFIED,
00195                   "reified");
00196   opt.propagation(LangfordNumber::PROP_EXTENSIONAL,
00197                   "extensional");
00198   opt.propagation(LangfordNumber::PROP_EXTENSIONAL_CHANNEL,
00199                   "extensional-channel");
00200   opt.parse(argc, argv);
00201   if (opt.k < 1) {
00202     std::cerr << "k must be at least 1!" << std::endl;
00203     return 1;
00204   }
00205   if (opt.k > opt.n) {
00206     std::cerr << "n must be at least k!" << std::endl;
00207     return 1;
00208   }
00209   Script::run<LangfordNumber,DFS,LangfordNumberOptions>(opt);
00210   return 0;
00211 }
00212 
00213 // STATISTICS: example-any
00214