nonogram.cpp

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/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */
/*
 *  Main authors:
 *     Mikael Lagerkvist <lagerkvist@gecode.org>
 *
 *  Copyright:
 *     Mikael Lagerkvist, 2005
 *
 *  Last modified:
 *     $Date: 2010-10-07 11:52:01 +0200 (Thu, 07 Oct 2010) $ by $Author: schulte $
 *     $Revision: 11473 $
 *
 *  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;

namespace {

  extern const int* specs[];
  extern const unsigned int n_examples;

  struct Slack {
    int slack, n;
    bool row;
    bool operator<(const Slack& rhs) const { return slack < rhs.slack; }
  };
}

class Nonogram : public Script {
protected:
  const int* spec;
  BoolVarArray b;

  int width(void) const {
    return spec[0];
  }
  int height(void) const {
    return spec[1];
  }

  DFA line(int& spos) {
    REG r0(0), r1(1);
    REG border = *r0;
    REG between = +r0;
    int hints = spec[spos++];
    REG r = border;
    if (hints > 0) {
      r += r1(spec[spos],spec[spos]);
      spos++;
      for (int i=hints-1; i--; spos++)
        r += between + r1(spec[spos],spec[spos]);
    }
    return r + border;
  }

public:
  // Branching variants
  enum {
    BRANCH_NONE, 
    BRANCH_AFC,  
  };

  Nonogram(const SizeOptions& opt)
    : spec(specs[opt.size()]), b(*this,width()*height(),0,1) {
    Matrix<BoolVarArray> m(b, width(), height());

    {
      int spos = 2;
      // Post constraints for columns
      for (int w=0; w<width(); w++)
        extensional(*this, m.col(w), line(spos));
      // Post constraints for rows
      for (int h=0; h<height(); h++)
        extensional(*this, m.row(h), line(spos));
    }

    

    switch (opt.branching()) {
    case BRANCH_NONE:
      {
        /*
         * The following branches either by columns or rows, depending on
         * whether there are more hints relative to the height or width
         * for columns or rows.
         *
         * This idea is due to Pascal Van Hentenryck and has been suggested
         * to us by Hakan Kjellerstrand.
         */

        // Number of hints for columns
        int cols = 0;
        // Number of hints for rows
        int rows = 0;
        int spos = 2;
        for (int w=0; w<width(); w++) {
          int hint = spec[spos++];
          cols += hint; spos += hint;
        }
        for (int h=0; h<height(); h++) {
          int hint = spec[spos++];
          rows += hint; spos += hint;
        }
        
        if (rows*width() > cols*height()) {
          for (int w=0; w<width(); w++)
            branch(*this, m.col(w), INT_VAR_NONE, INT_VAL_MAX);
        } else {
          for (int h=0; h<height(); h++)
            branch(*this, m.row(h), INT_VAR_NONE, INT_VAL_MAX);
        }
      }
      break;
    case BRANCH_AFC:
      /*
       * The following just uses the AFC for branching. This is
       * equivalent to SIZE/AFC in this case since the variables are
       * binary.
       */
      branch(*this, b, INT_VAR_AFC_MAX, INT_VAL_MAX);
      break;
    }
  }

  Nonogram(bool share, Nonogram& s) : Script(share,s), spec(s.spec) {
    b.update(*this, share, s.b);
  }

  virtual Space*
  copy(bool share) {
    return new Nonogram(share,*this);
  }

  virtual void
  print(std::ostream& os) const {
    Matrix<BoolVarArray> m(b, width(), height());
    for (int h = 0; h < height(); ++h) {
      os << '\t';
      for (int w = 0; w < width(); ++w)
        os << ((m(w,h).val() == 1) ? '#' : ' ');
      os << std::endl;
    }
    os << std::endl;
  }
};


int
main(int argc, char* argv[]) {
  SizeOptions opt("Nonogram");
  opt.size(8);
  opt.branching(Nonogram::BRANCH_AFC);
  opt.branching(Nonogram::BRANCH_NONE, "none",
                "Branch on rows/columns in order");
  opt.branching(Nonogram::BRANCH_AFC, "afc",
                "Use AFC for branching");
  opt.parse(argc,argv);
  if (opt.size() >= n_examples) {
    std::cerr << "Error: size must be between 0 and "
              << n_examples-1 << std::endl;
    return 1;
  }
  Script::run<Nonogram,DFS,SizeOptions>(opt);
  return 0;
}

namespace {


const int heart[] =
  { 9, 9,
    // Column constraints.
    1, 3,
    2, 2, 3,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 3,
    1, 3,
    // Row constraints
    2, 2, 2,
    2, 4, 4,
    3, 1, 3, 1,
    3, 2, 1, 2,
    2, 1, 1,
    2, 2, 2,
    2, 2, 2,
    1, 3,
    1, 1
  };

const int bear[] =
  { 13, 8,
    // Column constraints
    1, 2,
    2, 2, 1,
    2, 3, 2,
    1, 6,
    2, 1, 4,
    1, 3,
    1, 4,
    1, 4,
    1, 4,
    1, 5,
    1, 4,
    2, 1, 3,
    1, 2,
    // Row constraints
    1, 1,
    1, 2,
    2, 4, 4,
    1, 12,
    1, 8,
    1, 9,
    2, 3, 4,
    2, 2, 2
  };

const int crocodile[] =
  { 15, 9,
    // Column constraints
    1, 3,
    1, 4,
    2, 2, 2,
    2, 3, 1,
    2, 2, 3,
    2, 3, 2,
    2, 2, 3,
    2, 4, 2,
    2, 3, 2,
    1, 6,
    2, 1, 3,
    2, 1, 3,
    2, 1, 4,
    1, 5,
    1, 5,
    // Row constraints
    1, 3,
    3, 2, 3, 2,
    2, 10, 3,
    1, 15,
    5, 1, 1, 1, 1, 6,
    2, 1, 7,
    2, 1, 4,
    2, 1, 4,
    1, 4
  };

const int unknown[] =
  { 10, 10,
    // Column constraints
    1, 3,
    2, 2, 1,
    2, 2, 2,
    2, 2, 1,
    3, 1, 2, 1,
    2, 1, 1,
    3, 1, 4, 1,
    3, 1, 1, 2,
    2, 3, 1,
    1, 4,
    // Row constraints
    1, 3,
    2, 2, 1,
    2, 1, 1,
    2, 1, 4,
    4, 1, 1, 1, 1,
    4, 2, 1, 1, 1,
    3, 2, 1, 1,
    2, 1, 2,
    2, 2, 3,
    1, 3
  };

const int pinwheel[] =
  { 6, 6,
    // Column constraints
    2, 1, 2,
    1, 1,
    1, 2,
    1, 2,
    1, 1,
    2, 2, 1,
    // Row constraints
    2, 2, 1,
    1, 1,
    1, 2,
    1, 2,
    1, 1,
    2, 1, 2
  };

const int difficult[] =
  { 15, 15,
    // Column constraints
    1, 3,
    1, 2,
    1, 2,
    1, 1,
    1, 2,
    1, 3,
    1, 2,
    1, 4,
    1, 3,
    1, 4,
    2, 2, 1,
    2, 1, 1,
    2, 1, 1,
    2, 1, 1,
    1, 3,
    // Row constraints
    1, 3,
    2, 1, 1,
    2, 1, 1,
    2, 1, 1,
    2, 1, 2,
    1, 5,
    1, 1,
    1, 2,
    1, 1,
    1, 1,
    2, 1, 2,
    2, 1, 2,
    2, 2, 1,
    2, 2, 2,
    1, 3
  };

const int non_unique[] =
  { 11, 15,
    // Column constraints
    1, 5,
    3, 1, 2, 4,
    3, 2, 1, 3,
    4, 2, 2, 1, 1,
    4, 1, 1, 1, 1,
    2, 1, 5,
    5, 2, 1, 1, 3, 2,
    5, 2, 1, 1, 1, 1,
    3, 1, 4, 1,
    2, 1, 1,
    1, 1,
    // Row constraints
    2, 2, 2,
    2, 2, 2,
    1, 4,
    2, 1, 1,
    2, 1, 1,
    4, 1, 1, 1, 1,
    2, 1, 1,
    2, 1, 4,
    3, 1, 1, 1,
    3, 1, 1, 4,
    2, 1, 3,
    2, 1, 2,
    1, 5,
    2, 2, 2,
    2, 3, 3
  };

  const int dragonfly[] =
    { 20, 20,
      // Column constraints.
      4, 1, 1, 1, 2,
      5, 3, 1, 2, 1, 1,
      5, 1, 4, 2, 1, 1,
      4, 1, 3, 2, 4,
      4, 1, 4, 6, 1,
      3, 1, 11, 1,
      4, 5, 1, 6, 2,
      1, 14,
      2, 7, 2,
      2, 7, 2,
      3, 6, 1, 1,
      2, 9, 2,
      4, 3, 1, 1, 1,
      3, 3, 1, 3,
      3, 2, 1, 3,
      3, 2, 1, 5,
      3, 3, 2, 2,
      3, 3, 3, 2,
      3, 2, 3, 2,
      2, 2, 6,
      // Row constraints
      2, 7, 1,
      3, 1, 1, 2,
      3, 2, 1, 2,
      3, 1, 2, 2,
      3, 4, 2, 3,
      3, 3, 1, 4,
      3, 3, 1, 3,
      3, 2, 1, 4,
      2, 2, 9,
      3, 2, 1, 5,
      2, 2, 7,
      1, 14,
      2, 8, 2,
      3, 6, 2, 2,
      4, 2, 8, 1, 3,
      4, 1, 5, 5, 2,
      5, 1, 3, 2, 4, 1,
      5, 3, 1, 2, 4, 1,
      5, 1, 1, 3, 1, 3,
      4, 2, 1, 1, 2
    };

  const int castle[]  = {
    60, 35,
    // Column constraints
    7, 2,3,1,5,1,7,1,
    7, 2,4,2,3,2,3,5,
    8, 2,6,3,1,1,5,1,5,
    10, 2,4,2,1,1,1,4,1,1,2,
    7, 2,8,2,1,5,2,5,
    7, 3,1,6,2,5,1,5,
    9, 3,3,3,1,1,6,1,1,1,
    9, 3,2,2,2,2,8,1,1,3,
    7, 1,4,4,3,7,1,1,
    7, 1,2,2,2,3,7,9,
    8, 1,2,3,1,1,5,2,2,
    7, 2,2,3,1,1,6,1,
    6, 1,3,1,5,4,1,
    8, 1,3,1,1,6,1,3,1,
    8, 3,3,4,5,1,4,2,1,
    6, 2,3,3,9,7,1,
    8, 2,3,2,2,1,1,3,5,
    8, 4,2,1,1,1,1,2,3,
    7, 4,2,2,1,4,3,2,
    4, 4,3,16,2,
    5, 1,2,5,7,1,      
    6, 4,3,2,2,7,1,      
    5, 2,3,1,10,1,      
    6, 2,4,2,1,4,1,      
    5, 1,6,7,3,1,      
    4, 3,11,3,1,      
    5, 7,1,11,2,1,      
    7, 2,2,2,2,2,2,2,      
    7, 3,1,1,1,1,2,1,      
    7, 2,2,2,2,1,1,1,      
    7, 1,1,1,1,2,1,2,      
    8, 2,2,2,2,1,1,1,1,      
    5, 4,1,1,2,2,      
    5, 5,2,17,2,1,      
    6, 9,2,3,1,4,2,      
    6, 9,4,2,1,1,1,      
    5, 5,4,2,1,4,      
    7, 11,1,2,1,4,1,2,      
    5, 3,4,2,4,4,      
    8, 2,1,4,1,2,1,5,2,      
    5, 8,4,1,1,2,      
    5, 1,1,3,2,3,      
    6, 1,3,1,8,1,6,      
    4, 2,1,7,14,      
    7, 1,2,4,4,1,2,3,      
    10, 1,1,4,2,1,1,1,1,1,4,      
    6, 3,5,3,1,1,4,      
    6, 2,4,2,2,1,2,      
    5, 4,2,3,8,4,      
    5, 4,15,2,2,4,      
    6, 4,1,10,2,1,2,      
    6, 2,12,6,1,2,4,      
    7, 3,1,3,1,3,3,4,      
    6, 3,1,2,3,4,1,      
    7, 5,2,2,2,3,3,3,      
    9, 1,2,2,2,2,4,1,1,3,      
    7, 2,1,4,2,7,1,1,      
    6, 5,2,2,3,6,3,      
    7, 3,3,2,2,3,2,3,      
    7, 4,1,2,1,1,2,1,

    // Row constraints
    4, 12,1,1,1,                                
    5, 8,6,3,1,3,                                
    6, 5,8,4,3,1,5,                                
    8, 7,3,4,1,3,5,1,7,                                
    13, 2,2,4,9,1,5,1,1,1,1,1,1,1,                                
    8, 4,5,10,2,1,8,7,1,                                
    7, 5,1,3,3,16,1,2,                                
    8, 8,5,1,2,4,9,1,3,                                
    12, 4,5,3,14,1,1,1,1,4,1,1,3,                                
    19, 3,3,2,2,2,4,1,1,1,1,1,1,1,1,3,1,1,3,2,                                
    11, 8,2,7,2,1,1,2,1,1,3,3,                                
    13, 1,5,9,12,2,1,1,3,1,1,2,2,1,                                
    17, 3,2,2,1,1,1,1,4,1,1,1,3,3,1,1,2,2,                                
    12, 5,2,2,2,2,1,5,2,1,1,2,5,                                
    12, 3,5,9,2,1,1,6,3,1,3,2,3,                                
    12, 1,4,1,1,1,4,1,5,5,3,3,3,                                
    10, 4,1,1,1,1,3,4,6,6,3,                                
    12, 3,1,3,1,1,3,3,1,1,4,6,1,                                
    11, 3,1,5,1,1,3,1,1,9,4,1,                                
    14, 2,1,1,7,1,4,1,1,1,1,1,1,3,5,                                
    11, 9,2,1,3,1,1,1,1,4,2,1,                                
    10, 1,14,1,1,2,2,2,10,1,2,                                
    10, 1,9,2,1,2,6,1,5,3,2,                                
    12, 1,9,9,1,2,2,3,1,1,4,3,1,                                
    10, 10,1,3,4,1,3,2,1,2,8,                                
    9, 9,1,3,5,1,1,1,2,7,                                
    12, 4,5,1,2,5,1,3,1,1,2,1,3,                                
    14, 1,1,1,1,2,6,2,3,2,1,1,2,3,1,                                
    11, 1,6,1,5,7,1,3,3,2,4,3,                                
    10, 1,2,1,2,9,1,5,2,6,2,                                
    8, 10,2,2,13,1,3,3,1,                                
    11, 2,2,1,6,2,3,3,2,2,2,1,                                
    12, 2,2,1,1,12,2,2,9,2,2,2,2,                                
    9, 5,1,2,4,1,5,11,2,2,                                
    3, 15,6,18,
  };

  const int p200[] =
    { 25, 25,
      // Column constraints
      4, 1,1,2,2,
      3, 5,5,7,
      4, 5,2,2,9,
      4, 3,2,3,9,
      5, 1,1,3,2,7,
      3, 3,1,5,
      5, 7,1,1,1,3,
      6, 1,2,1,1,2,1,
      3, 4,2,4,
      4, 1,2,2,2,
      3, 4,6,2,
      4, 1,2,2,1,
      4, 3,3,2,1,
      3, 4,1,15,
      6, 1,1,1,3,1,1,
      6, 2,1,1,2,2,3,
      4, 1,4,4,1,
      4, 1,4,3,2,
      4, 1,1,2,2,
      5, 7,2,3,1,1,
      5, 2,1,1,1,5,
      3, 1,2,5,
      4, 1,1,1,3,
      3, 4,2,1,
      1, 3,
      // Row constraints
      3, 2,2,3,
      5, 4,1,1,1,4,
      5, 4,1,2,1,1,
      7, 4,1,1,1,1,1,1,
      6, 2,1,1,2,3,5,
      6, 1,1,1,1,2,1,
      5, 3,1,5,1,2,
      6, 3,2,2,1,2,2,
      7, 2,1,4,1,1,1,1,
      6, 2,2,1,2,1,2,
      6, 1,1,1,3,2,3,
      5, 1,1,2,7,3,
      5, 1,2,2,1,5,
      5, 3,2,2,1,2,
      4, 3,2,1,2,
      3, 5,1,2,
      4, 2,2,1,2,
      4, 4,2,1,2,
      4, 6,2,3,2,
      4, 7,4,3,2,
      3, 7,4,4,
      3, 7,1,4,
      3, 6,1,4,
      3, 4,2,2,
      2, 2,1
    };

  // The following instances are from the http://webpbn.com site and
  // are all designed by Jan Wolter.
  // See also the survey at http://webpbn.com/survey/

  const int webpbn436[]=
    { 40, 35,
      // Column constraints
      1, 1,
      2, 3, 2,
      3, 2, 3, 3,
      3, 3, 3, 3,
      4, 3, 3, 3, 3,
      4, 4, 2, 2, 2,
      4, 3, 3, 2, 3,
      4, 3, 2, 2, 2,
      3, 3, 2, 6,
      2, 2, 9,
      3, 2, 3, 3,
      5, 4, 4, 3, 2, 4,
      5, 7, 2, 5, 2, 6,
      6, 12, 2, 3, 2, 3, 2,
      6, 3, 1, 2, 2, 2, 3,
      6, 2, 2, 3, 2, 2, 2,
      6, 6, 2, 6, 2, 2, 2,
      5, 12, 4, 3, 2, 2,
      4, 12, 2, 2, 2,
      3, 2, 6, 2,
      4, 2, 6, 5, 2,
      4, 10, 9, 2, 2,
      5, 12, 3, 3, 2, 2,
      7, 6, 2, 2, 2, 2, 2, 2,
      6, 2, 2, 3, 2, 2, 2,
      6, 4, 3, 2, 2, 2, 3,
      6, 7, 3, 3, 2, 3, 2,
      5, 5, 3, 5, 2, 6,
      5, 4, 3, 3, 3, 4,
      3, 3, 5, 3,
      2, 3, 9,
      3, 4, 2, 6,
      4, 4, 2, 2, 2,
      4, 4, 2, 2, 3,
      4, 3, 2, 2, 3,
      3, 3, 3, 3,
      3, 3, 3, 3,
      3, 4, 3, 3,
      3, 2, 3, 3,
      2, 2, 1,
      // Row constraints
      2, 2, 2,
      3, 2, 3, 2,
      4, 3, 3, 3, 2,
      4, 3, 3, 3, 3,
      6, 2, 3, 3, 3, 3, 2,
      6, 3, 3, 3, 3, 3, 3,
      6, 4, 2, 3, 2, 2, 4,
      7, 4, 2, 2, 2, 2, 3, 1,
      7, 3, 1, 2, 2, 2, 3, 3,
      7, 3, 2, 2, 2, 2, 2, 4,
      5, 3, 2, 15, 2, 4,
      3, 5, 19, 4,
      4, 6, 4, 3, 3,
      3, 6, 4, 4,
      4, 2, 4, 6, 2,
      6, 2, 2, 3, 3, 3, 2,
      6, 9, 2, 2, 2, 3, 9,
      7, 10, 2, 2, 2, 2, 2, 10,
      9, 4, 2, 3, 3, 2, 2, 3, 2, 5,
      5, 2, 5, 2, 4, 2,
      5, 5, 3, 2, 2, 5,
      5, 6, 3, 2, 3, 7,
      4, 6, 8, 9, 7,
      4, 4, 8, 7, 5,
      1, 4,
      1, 2,
      1, 2,
      1, 14,
      1, 16,
      2, 3, 3,
      2, 2, 2,
      2, 2, 2,
      2, 4, 4,
      1, 16,
      1, 12,
    };

  const int webpbn21[]=
    { 14, 25,
      // Column constraints
      1, 2,
      2, 4, 6,
      4, 9, 4, 4, 2,
      4, 1, 6, 2, 6,
    3, 1, 5, 2,
    2, 1, 6,
    2, 1, 5,
    2, 1, 4,
    2, 1, 4,
    3, 1, 4, 2,
    3, 1, 4, 6,
    5, 1, 6, 4, 4, 2,
    3, 9, 2, 6,
    2, 4, 2,
    // Row constraints
    1, 9,
    2, 1, 1,
    3, 1, 1, 1,
    3, 1, 3, 1,
    1, 13,
    1, 13,
    1, 13,
    1, 13,
    2, 2, 2,
    2, 2, 2,
    0,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
    2, 2, 2,
  };

const int webpbn27[]=
  { 27, 23,
    // Column constraints
    2, 4, 12,
    3, 6, 1, 1,
    3, 8, 1, 1,
    5, 3, 2, 2, 1, 1,
    6, 2, 1, 1, 2, 1, 6,
    4, 1, 1, 1, 1,
    6, 3, 1, 1, 2, 1, 1,
    5, 3, 2, 3, 1, 1,
    3, 10, 1, 1,
    5, 4, 2, 2, 1, 1,
    6, 3, 1, 1, 2, 1, 1,
    4, 2, 1, 1, 1,
    6, 3, 1, 1, 2, 1, 1,
    5, 3, 2, 3, 1, 6,
    3, 10, 1, 1,
    5, 4, 2, 2, 1, 1,
    6, 3, 1, 1, 2, 1, 1,
    4, 1, 1, 1, 9,
    6, 2, 1, 1, 2, 1, 1,
    5, 2, 2, 3, 1, 3,
    3, 8, 1, 5,
    3, 6, 1, 1,
    3, 4, 9, 1,
    2, 1, 1,
    2, 2, 1,
    2, 1, 1,
    1, 4,
    // Row constraints
    1, 11,
    1, 17,
    4, 3, 5, 5, 3,
    4, 2, 2, 2, 1,
    7, 2, 1, 3, 1, 3, 1, 4,
    4, 3, 3, 3, 3,
    7, 5, 1, 3, 1, 3, 1, 3,
    4, 3, 2, 2, 4,
    4, 5, 5, 5, 5,
    1, 23,
    0,
    1, 23,
    2, 1, 1,
    2, 1, 1,
    3, 1, 2, 1,
    4, 1, 1, 1, 1,
    4, 1, 1, 1, 1,
    5, 1, 10, 1, 2, 1,
    7, 1, 1, 1, 1, 1, 1, 3,
    8, 1, 1, 1, 1, 1, 1, 1, 1,
    7, 1, 1, 1, 1, 1, 1, 1,
    6, 1, 1, 1, 1, 2, 2,
    3, 5, 5, 3,
  };

  const int webpbn1[]=
  { 5, 10,
    // Column constraints
    2, 2, 1,
    3, 2, 1, 3,
    1, 7,
    2, 1, 3,
    2, 2, 1,
    // Row constraints
    1, 2,
    2, 2, 1,
    2, 1, 1,
    1, 3,
    2, 1, 1,
    2, 1, 1,
    1, 2,
    2, 1, 1,
    2, 1, 2,
    1, 2,
  };

  const int webpbn6[]=
  { 20, 20,
    // Column constraints
    1, 5,
    2, 5, 3,
    3, 2, 3, 4,
    3, 1, 7, 2,
    1, 8,
    1, 9,
    1, 9,
    1, 8,
    1, 7,
    1, 8,
    1, 9,
    1, 10,
    1, 13,
    2, 6, 2,
    1, 4,
    1, 6,
    1, 6,
    1, 5,
    1, 6,
    1, 6,
    // Row constraints
    1, 2,
    1, 2,
    1, 1,
    1, 1,
    2, 1, 3,
    2, 2, 5,
    4, 1, 7, 1, 1,
    4, 1, 8, 2, 2,
    3, 1, 9, 5,
    2, 2, 16,
    2, 1, 17,
    2, 7, 11,
    3, 5, 5, 3,
    2, 5, 4,
    2, 3, 3,
    2, 2, 2,
    2, 2, 1,
    2, 1, 1,
    2, 2, 2,
    2, 2, 2,
  };

  const int webpbn23[]=
  { 10, 11,
    // Column constraints
    1, 1,
    1, 3,
    1, 1,
    2, 2, 2,
    1, 2,
    1, 4,
    1, 1,
    1, 3,
    1, 3,
    1, 1,
    // Row constraints
    1, 1,
    1, 3,
    1, 1,
    1, 2,
    1, 1,
    1, 3,
    1, 3,
    1, 1,
    1, 2,
    1, 2,
    1, 4,
  };

const int webpbn16[]=
  { 34, 34,
    // Column constraints
    2, 1, 1,
    2, 2, 2,
    2, 3, 3,
    4, 2, 1, 1, 2,
    4, 2, 1, 1, 2,
    4, 1, 1, 1, 1,
    4, 1, 1, 1, 1,
    1, 18,
    6, 2, 1, 1, 1, 1, 2,
    6, 1, 1, 1, 1, 1, 1,
    6, 1, 1, 1, 1, 1, 1,
    1, 26,
    8, 2, 1, 1, 1, 1, 1, 1, 2,
    8, 2, 1, 1, 2, 2, 1, 1, 2,
    8, 2, 1, 1, 2, 2, 1, 1, 2,
    2, 14, 14,
    4, 1, 1, 1, 1,
    4, 1, 1, 1, 1,
    2, 14, 14,
    8, 2, 1, 1, 2, 2, 1, 1, 2,
    8, 2, 1, 1, 2, 2, 1, 1, 2,
    8, 2, 1, 1, 1, 1, 1, 1, 2,
    1, 26,
    6, 1, 1, 1, 1, 1, 1,
    6, 1, 1, 1, 1, 1, 1,
    6, 2, 1, 1, 1, 1, 2,
    1, 18,
    4, 1, 1, 1, 1,
    4, 1, 1, 1, 1,
    4, 2, 1, 1, 2,
    4, 2, 1, 1, 2,
    2, 3, 3,
    2, 2, 2,
    2, 1, 1,
    // Row constraints
    2, 1, 1,
    2, 2, 2,
    2, 3, 3,
    4, 2, 1, 1, 2,
    4, 2, 1, 1, 2,
    4, 1, 1, 1, 1,
    4, 1, 1, 1, 1,
    1, 18,
    6, 2, 1, 1, 1, 1, 2,
    6, 1, 1, 1, 1, 1, 1,
    6, 1, 1, 1, 1, 1, 1,
    1, 26,
    8, 2, 1, 1, 1, 1, 1, 1, 2,
    8, 2, 1, 1, 2, 2, 1, 1, 2,
    8, 2, 1, 1, 2, 2, 1, 1, 2,
    2, 14, 14,
    4, 1, 1, 1, 1,
    4, 1, 1, 1, 1,
    2, 14, 14,
    8, 2, 1, 1, 2, 2, 1, 1, 2,
    8, 2, 1, 1, 2, 2, 1, 1, 2,
    8, 2, 1, 1, 1, 1, 1, 1, 2,
    1, 26,
    6, 1, 1, 1, 1, 1, 1,
    6, 1, 1, 1, 1, 1, 1,
    6, 2, 1, 1, 1, 1, 2,
    1, 18,
    4, 1, 1, 1, 1,
    4, 1, 1, 1, 1,
    4, 2, 1, 1, 2,
    4, 2, 1, 1, 2,
    2, 3, 3,
    2, 2, 2,
    2, 1, 1,
  };

  const int webpbn529[]=
  { 45, 45,
    // Column constraints
    6, 7, 1, 1, 1, 1, 1,
    13, 2, 2, 4, 1, 4, 1, 5, 1, 4, 1, 4, 1, 2,
    10, 3, 1, 4, 1, 4, 1, 14, 4, 1, 2,
    8, 1, 1, 5, 1, 2, 3, 4, 1,
    4, 3, 13, 1, 10,
    3, 1, 9, 4,
    4, 6, 7, 2, 2,
    4, 8, 4, 1, 4,
    6, 2, 8, 3, 2, 5, 3,
    5, 10, 1, 3, 7, 2,
    6, 8, 6, 2, 8, 1, 2,
    7, 1, 1, 2, 2, 8, 1, 1,
    11, 2, 1, 1, 1, 2, 1, 3, 1, 3, 3, 1,
    8, 2, 1, 1, 1, 5, 4, 2, 1,
    8, 2, 1, 1, 1, 1, 7, 2, 1,
    8, 2, 1, 1, 2, 9, 1, 2, 1,
    5, 4, 6, 12, 1, 3,
    4, 16, 13, 3, 2,
    3, 12, 21, 2,
    3, 2, 13, 23,
    3, 2, 14, 19,
    4, 2, 14, 20, 2,
    6, 2, 13, 7, 2, 8, 2,
    5, 12, 8, 1, 7, 2,
    9, 5, 1, 1, 1, 2, 8, 1, 5, 2,
    8, 2, 1, 1, 1, 9, 1, 1, 4,
    8, 2, 1, 1, 1, 6, 1, 3, 5,
    6, 2, 2, 1, 5, 6, 2,
    8, 2, 1, 3, 1, 3, 7, 3, 2,
    9, 2, 3, 2, 1, 1, 2, 4, 4, 2,
    9, 2, 2, 1, 1, 2, 3, 1, 8, 2,
    5, 9, 3, 1, 7, 2,
    5, 12, 4, 1, 6, 2,
    5, 7, 4, 1, 2, 5,
    5, 2, 6, 6, 5, 6,
    4, 8, 8, 6, 3,
    5, 3, 10, 8, 4, 2,
    5, 5, 11, 9, 5, 2,
    5, 3, 1, 12, 16, 2,
    4, 3, 1, 12, 16,
    4, 5, 2, 13, 21,
    6, 6, 1, 3, 3, 1, 1,
    14, 5, 1, 3, 1, 3, 1, 1, 2, 1, 4, 1, 3, 1, 3,
    13, 5, 1, 3, 1, 3, 1, 4, 1, 4, 1, 3, 1, 3,
    6, 1, 1, 1, 1, 1, 1,
    // Row constraints
    6, 7, 1, 1, 1, 1, 1,
    13, 3, 1, 3, 1, 4, 1, 4, 1, 5, 1, 5, 1, 2,
    14, 1, 1, 1, 3, 1, 4, 1, 4, 1, 5, 1, 5, 1, 2,
    9, 2, 1, 2, 1, 1, 1, 1, 6, 2,
    4, 3, 30, 1, 5,
    9, 1, 5, 8, 1, 1, 7, 1, 1, 3,
    7, 3, 4, 8, 1, 5, 1, 2,
    4, 3, 20, 6, 6,
    6, 3, 3, 7, 2, 5, 1,
    9, 3, 3, 1, 1, 9, 1, 1, 5, 6,
    7, 2, 3, 8, 1, 3, 4, 2,
    7, 5, 3, 1, 10, 4, 5, 2,
    6, 1, 2, 3, 8, 4, 6,
    5, 2, 2, 3, 11, 10,
    5, 2, 2, 3, 10, 7,
    6, 2, 3, 1, 7, 12, 2,
    6, 2, 3, 1, 4, 11, 2,
    6, 4, 1, 2, 1, 11, 2,
    4, 9, 1, 2, 9,
    5, 6, 2, 1, 4, 11,
    6, 2, 5, 1, 2, 6, 6,
    5, 6, 2, 4, 8, 4,
    4, 4, 2, 16, 1,
    4, 2, 2, 15, 2,
    4, 3, 2, 15, 4,
    4, 3, 3, 13, 4,
    3, 4, 12, 9,
    3, 1, 9, 10,
    5, 2, 1, 17, 7, 2,
    6, 2, 2, 8, 3, 8, 2,
    6, 2, 3, 6, 3, 8, 2,
    6, 2, 4, 5, 4, 7, 2,
    5, 2, 5, 5, 4, 6,
    5, 4, 4, 5, 4, 9,
    5, 1, 4, 6, 4, 4,
    6, 4, 3, 6, 4, 3, 2,
    7, 2, 1, 2, 7, 4, 4, 2,
    7, 2, 2, 2, 9, 5, 5, 2,
    6, 2, 2, 2, 10, 6, 6,
    5, 3, 2, 1, 9, 18,
    3, 8, 4, 23,
    9, 1, 2, 1, 2, 2, 1, 1, 1, 2,
    12, 2, 1, 4, 2, 1, 4, 1, 5, 1, 3, 1, 2,
    11, 2, 1, 5, 4, 4, 1, 5, 1, 3, 1, 2,
    5, 1, 10, 1, 1, 1,
  };

  
  const int webpbn65[]=
  { 34, 40,
    // Column constraints
    1, 5,
    3, 3, 2, 1,
    4, 3, 2, 2, 1,
    5, 3, 2, 2, 2, 2,
    6, 3, 2, 2, 2, 2, 3,
    7, 1, 2, 2, 2, 2, 2, 16,
    9, 1, 2, 2, 2, 2, 2, 2, 1, 2,
    9, 1, 2, 2, 2, 2, 2, 2, 13, 1,
    10, 3, 2, 2, 2, 2, 2, 2, 4, 1, 1,
    9, 6, 5, 2, 2, 2, 2, 6, 1, 1,
    11, 1, 7, 3, 2, 2, 2, 2, 2, 1, 1, 1,
    12, 3, 4, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1,
    11, 6, 1, 2, 3, 2, 2, 2, 2, 1, 1, 1,
    6, 1, 7, 2, 16, 1, 1,
    11, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1,
    11, 1, 2, 1, 3, 1, 1, 6, 1, 1, 1, 1,
    9, 2, 7, 1, 1, 11, 1, 1, 1, 1,
    9, 2, 7, 1, 1, 11, 1, 1, 1, 1,
    11, 1, 2, 1, 3, 1, 1, 6, 1, 1, 1, 1,
    11, 1, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1,
    6, 1, 7, 2, 16, 1, 1,
    11, 6, 1, 2, 3, 2, 2, 2, 2, 1, 1, 1,
    12, 3, 4, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1,
    11, 1, 7, 3, 2, 2, 2, 2, 2, 1, 1, 1,
    9, 6, 5, 2, 2, 2, 2, 6, 1, 1,
    10, 3, 2, 2, 2, 2, 2, 2, 4, 1, 1,
    9, 1, 2, 2, 2, 2, 2, 2, 13, 1,
    9, 1, 2, 2, 2, 2, 2, 2, 1, 2,
    7, 1, 2, 2, 2, 2, 2, 16,
    6, 3, 2, 2, 2, 2, 3,
    5, 3, 2, 2, 2, 2,
    4, 3, 2, 2, 1,
    3, 3, 2, 1,
    1, 5,
    // Row constraints
    1, 12,
    3, 5, 2, 5,
    4, 5, 2, 2, 5,
    7, 1, 2, 2, 2, 2, 2, 1,
    7, 4, 2, 2, 4, 2, 2, 4,
    7, 4, 2, 2, 4, 2, 2, 4,
    7, 1, 2, 2, 2, 2, 2, 1,
    7, 6, 2, 2, 2, 2, 2, 6,
    7, 6, 2, 2, 2, 2, 2, 6,
    3, 1, 14, 1,
    2, 10, 10,
    4, 8, 3, 3, 8,
    8, 1, 1, 2, 1, 1, 2, 1, 1,
    6, 9, 2, 2, 2, 2, 9,
    2, 9, 9,
    6, 1, 1, 1, 1, 1, 1,
    3, 12, 2, 12,
    2, 12, 12,
    5, 1, 1, 4, 1, 1,
    2, 14, 14,
    2, 12, 12,
    5, 2, 1, 4, 1, 2,
    3, 9, 4, 9,
    5, 1, 7, 4, 7, 1,
    7, 1, 1, 1, 4, 1, 1, 1,
    5, 1, 7, 4, 7, 1,
    5, 1, 7, 4, 7, 1,
    7, 1, 2, 1, 2, 1, 2, 1,
    5, 1, 7, 2, 7, 1,
    7, 1, 1, 6, 2, 6, 1, 1,
    9, 1, 1, 1, 1, 2, 1, 1, 1, 1,
    7, 1, 1, 6, 2, 6, 1, 1,
    6, 1, 1, 5, 5, 1, 1,
    7, 1, 1, 1, 8, 1, 1, 1,
    6, 1, 1, 4, 4, 1, 1,
    5, 1, 2, 6, 2, 1,
    4, 2, 4, 4, 2,
    3, 2, 6, 2,
    2, 4, 4,
    1, 6,
  };


  const int *specs[] = {heart, bear, crocodile, unknown,
                        pinwheel, difficult, non_unique, dragonfly, 
                        castle, p200, 
                        // From the webpbn survey
                        webpbn1,    // 10
                        webpbn6,    // 11
                        webpbn21,   // 12
                        webpbn27,   // 13
                        webpbn23,   // 14
                        webpbn16,   // 15
                        webpbn529,  // 16
                        webpbn65,   // 17
                        webpbn436,  // 18
  };
  const unsigned n_examples = sizeof(specs)/sizeof(int*);

}

// STATISTICS: example-any