Sudoku rules :

Choco Solver :

We used Choco solver, which is a Java library made to use constraint programming easily. To use it, one only have to write the constraints.

The constraints in LP :

The sudoku solving problem can be summarized in linear programming as follows:

• ∀(i,j)∈[1,9],M(i,j) : content of the matrix at (i,j)


• ∀(i,j)∈[1,9],∀k∈[1,9] k!=i, M(k,j) != M(i,j)


• ∀(i,j)∈[1,9],∀k∈[1,9] k!=j, M(i,k) != M(i,j)


• ∀(i,j)∈[1,9],∀(k,l)∈[j/3*3+1,j/3*3 + 3]*[i/3*3+1,i/3*3+3] k!=i,l!=j, M(k,l) != M(i,j)

The constraints in Choco :

The sudoku solving problem in constraint programming can be summarized :

• mon_modele.allDifferent(ligne).post();


• mon_modele.allDifferent(colonne).post();


• mon_modele.allDifferent(carre).post();


• ligne, colonne and carre being an array containing the elements of, respectively, a line, a column and a square