Prolog Constraint Processing : Packing Squares

Question

I\'m trying to solve a constraint processing problem in prolog.

I need to pack 4 squares of 5x5,4x4,3x3 and 2x2 in a grid of 10x10. They may not overlap.

My

Answer 1

For each square, define X and Y variables that denote the upper left corner. These variable will have domains 1..10-L, where L is the length of the square. If you set the domain to 1..10, the squares may be placed partly outside your 10x10 rectangle.

Then you can post constraints for each pair of rectangles (X,Y) and (X1,Y1) that state that if they overlap on the x axis, they must not overlap on the y axis, and vice versa:

(((X  #=< X1) and (X+L   #> X1)) => ((Y+L #=< Y1) or (Y1+L1 #=< Y))),
(((X1 #=< X)  and (X1+L1 #> X))  => ((Y+L #=< Y1) or (Y1+L1 #=< Y))),
(((Y  #=< Y1) and (Y+L   #> Y1)) => ((X+L #=< X1) or (X1+L1 #=< X))),
(((Y1 #=< Y)  and (Y1+L1 #> Y))  => ((X+L #=< X1) or (X1+L1 #=< X)))

(your particular constraint syntax may vary)