/* -*- mode: C++; c-basic-offset: 2; indent-tabs-mode: nil -*- */

/*

* Main authors:

* Mikael Zayenz Lagerkvist <lagerkvist@gecode.dev>

*

* Copyright:

* Mikael Zayenz Lagerkvist, 2005

*

* This file is part of Gecode, the generic constraint

* development environment:

* http://www.gecode.dev

*

* 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 {

/// List of specifications

extern const int* specs[];

/// Number of specifications

extern const unsigned int n_examples;

}

/**

* \brief %Example: %Nonogram

*

* This example solves nonograms. A nonogram is composed of a matrix of

* markers. For each row/column there is a specification on how many groups

* of markers (separated by one or more unmarked spots) and their length.

* The objective is to find a valid assignment, which incidentally may also

* produce a pretty picture.

*

* See problem 12 at http://www.csplib.org/.

*

* Note that "Modeling and Programming with Gecode" uses this example

* as a case study.

*

* \ingroup Example

*

*/

class Nonogram : public Script {

protected:

/// Specification to be used

const int* spec;

/// Fields of board

BoolVarArray b;

/// Return width of board

int width(void) const {

return spec[0];

}

/// Return height of board

int height(void) const {

return spec[1];

}

/// Returns next regular expression for line starting from spos

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 on rows/columns in order

BRANCH_AFC, ///< Use AFC for branching

};

/// Construction of the model.

Nonogram(const SizeOptions& opt)

: Script(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), BOOL_VAR_NONE(), BOOL_VAL_MAX());

} else {

for (int h=0; h<height(); h++)

branch(*this, m.row(h), BOOL_VAR_NONE(), BOOL_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, BOOL_VAR_AFC_MAX(opt.decay()), BOOL_VAL_MAX());

break;

}

}

/// Constructor for cloning \a s

Nonogram(Nonogram& s) : Script(s), spec(s.spec) {

b.update(*this, s.b);

}

/// Copy space during cloning

virtual Space*

copy(void) {

return new Nonogram(*this);

}

/// Print solution

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;

}

};

/** \brief Main-function

* \relates Nonogram

*/

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 {

/** \name Picture specifications

*

* A specification is given by a list of integers. The first two

* integers (w and h) specify the number of columns and rows

* respectively. Then w + h groups of integers follows. Each group is

* started by the number of integers it contains (n), followed by n integers

* specifying the sizes of the stretches of markers in that row/column.

*

* \relates Nonogram

*/

//@{

/// Specification for a heart-shaped picture.

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

};

/// Specification for a bear/bunny-shaped picture.

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

};

/// Specification for a crocodile-shaped picture

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

};

/// Specification for an unknown picture

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

};

/// Specification for a pinwheel-picture

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

};

/// Specification for a more difficult picture.

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

};

/// Specification for a non-unique picture

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

};

/** \brief Specification for a dragonfly-picture.

*

* From http://www.oberlin.edu/math/faculty/bosch/pbn-page.html, where

* it is claimed that it is hard.

*/

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

};

/// From http://www.cs.kuleuven.be/~bmd/nonogram.pl

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,

};

/** \brief Specification for a picture of cupid.

*

* From http://www.icparc.ic.ac.uk/eclipse/examples/nono.ecl.txt, the

* hardest instance.

*/

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/

/// Petro

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,

};

/// Skid

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,

};

/// Bucks

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,

};

/// Dancer

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,

};

/// Cat

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,

};

/// Edge

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,

};

/// Knot

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,