/*

Killer Sudoko in Gecode.

http://en.wikipedia.org/wiki/Killer_Sudoku
"""
Killer sudoku (also killer su doku, sumdoku, sum doku, addoku, or
samunamupure) is a puzzle that combines elements of sudoku and kakuro.
Despite the name, the simpler killer sudokus can be easier to solve
than regular sudokus, depending on the solver's skill at mental arithmetic;
the hardest ones, however, can take hours to crack.

...

The objective is to fill the grid with numbers from 1 to 9 in a way that
the following conditions are met:

* Each row, column, and nonet contains each number exactly once.
* The sum of all numbers in a cage must match the small number printed
in its corner.
* No number appears more than once in a cage. (This is the standard rule
for killer sudokus, and implies that no cage can include more
than 9 cells.)

In 'Killer X', an additional rule is that each of the long diagonals
contains each number once.
"""

Here we solve the problem from the Wikipedia page, also shown here
http://en.wikipedia.org/wiki/File:Killersudoku_color.svg

And the solution:
http://commons.wikimedia.org/wiki/File:Killersudoku_color_solution.svg

Compare with the following models:
* Comet   : http://www.hakank.org/comet/killer_sudoku.co
* MiniZinc: http://www.hakank.org/minizinc/killer_sudoku.mzn
* SICStus: http://www.hakank.org/sicstus/killer_sudoku.pl
* ECLiPSe: http://www.hakank.org/eclipse/killer_sudoku.ecl

This Gecode model was created by Hakan Kjellerstrand, hakank@gmail.com

*/

// Licenced under CC-BY-4.0 : http://creativecommons.org/licenses/by/4.0/

#include <gecode/driver.hh>
#include <gecode/int.hh>
#include "gecode/minimodel.hh"

using namespace Gecode;

using std::cout;
using std::endl;

class KillerSudoku : public Script {
protected:

static const int n = 9;

IntVarArray x;

public:

// Actual model
KillerSudoku(const SizeOptions& opt) :
x(*this, n*n, 1, n)
{

int num_p = 29; // number of segments
int num_hints = 4; // number of hints per segment

int _P[] = {
1,1,  1,2, 0,0, 0,0,   3,
1,3,  1,4, 1,5, 0,0,  15,
1,6,  2,5, 2,6, 3,5,  22,
1,7,  2,7, 0,0, 0,0,   4,
1,8,  2,8, 0,0, 0,0,  16,
1,9,  2,9, 3,9, 4,9,  15,
2,1,  2,2, 3,1, 3,2,  25,
2,3,  2,4, 0,0, 0,0,  17,
3,3,  3,4, 4,4, 0,0,   9,
3,6,  4,6, 5,6, 0,0,   8,
3,7,  3,8, 4,7, 0,0,  20,
4,1,  5,1, 0,0, 0,0,   6,
4,2,  4,3, 0,0, 0,0,  14,
4,5,  5,5, 6,5, 0,0,  17,
4,8,  5,7, 5,8, 0,0,  17,
5,2,  5,3, 6,2, 0,0,  13,
5,4,  6,4, 7,4, 0,0,  20,
5,9,  6,9, 0,0, 0,0,  12,
6,1,  7,1, 8,1, 9,1,  27,
6,3,  7,2, 7,3, 0,0,   6,
6,6,  7,6, 7,7, 0,0,  20,
6,7,  6,8, 0,0, 0,0,   6,
7,5,  8,4, 8,5, 9,4,  10,
7,8,  7,9, 8,8, 8,9,  14,
8,2,  9,2, 0,0, 0,0,   8,
8,3,  9,3, 0,0, 0,0,  16,
8,6,  8,7, 0,0, 0,0,  15,
9,5,  9,6, 9,7, 0,0,  13,
9,8,  9,9, 0,0, 0,0,  17
};

IntArgs P(num_p*(2*num_hints+1), _P);

// The usual Sudoku constraints
// rows and columns
Matrix<IntVarArray> m(x, n, n);
for(int i = 0; i < n; i++) {
distinct(*this, m.row(i), opt.icl());
distinct(*this, m.col(i), opt.icl());
}
// and the squares
int nn = 3;
for (int i=0; i < n; i+=n) {
for (int j=0; j < n; j+=n) {
distinct(*this, m.slice(i, i+nn, j, j+nn), opt.icl());
}
}

// calculate the hints
for(int p = 0; p < num_p; p++) {
IntVarArgs p_tmp;
for(int i = 0; i < num_hints; i++) {
int p_test = P[p*9 + 2*i+0];
if (p_test > 0) {
int p1 = P[p*9+2*i+0]-1;
int p2 = P[p*9+2*i+1]-1;
p_tmp << expr(*this, x[p1*n+p2]);
}
}
int p_sum = P[p*9+2*num_hints];
rel(*this, sum(p_tmp) == p_sum, opt.icl());
}

branch(*this, x, INT_VAR_SIZE_MIN(), INT_VAL_MIN());

}

// Constructor for cloning s
KillerSudoku(bool share, KillerSudoku& s) : Script(share,s) {
x.update(*this, share, s.x);
}

// Copy during cloning
virtual Space*
copy(bool share) {
return new KillerSudoku(share,*this);
}

// Print solution
virtual void
print(std::ostream& os) const {
os << "Solution: " << endl;
for(int i = 0; i < n; i++) {
for(int j = 0; j < n; j++) {
os << x[i*n+j] << " ";
}
os << endl;
}
os << endl;
}

};

/**
*  main
*/
int
main(int argc, char* argv[]) {
SizeOptions opt("KillerSudoku");
opt.solutions(0);
opt.icl(ICL_DOM);

opt.parse(argc,argv);

Script::run<KillerSudoku,DFS,SizeOptions>(opt);

return 0;
}