Introduction
Constraint programming is a useful tool in formulating and solving problems that can be defined in terms of constraint among a set of variables. In fact real world problems are constraint satisfaction problems defined in terms of some variables that bear some constraints. Finding a set of variables, that are within the constraints given(or observed) is a solution to that problem.
Let us consider a problem, that can be represented by some relations of the variables x, y and z. We have a domain Dx, Dy, Dz from where the variables can take a value. The constraint is given by a set C and may have a number of constraints C1,C2,C3,etc each relating some or all of the variables x,y and z. Now a solution (or solutions) to the problem is a set dx,dy,dz such that dx Dx, dy Dy and dz Dz and all the constraints of the set C are satisfied.
Eight queens problem
Eight queens problem is a constraint satisfaction problem. The task is to place eight queens in the 64 available squares in such a way that no queen attacks eachother. So the problem can be formulated with variables x1,x2,x3,x4,x5,x6,x7,x8 and y1,y2,y3,y4,y5,y6, y7,y8; the xs represent the rows and ys the column. Now a solution for this problem is to assign values for x and for y such that the constraint is satisfied.
The problem can be formulated as
P={(x1,y1),(x2,y2),……………………..(x8,y8)}
where (x1,y1) gives the position of the first queen and so on.
So it can be clearly seen that the domains for xi and yi are
Dx = {1,2,3,4,5,6,7,8}and Dy ={1,2,3,4,5,6,7,8} respectively.
