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

Here is a solution where disjoint only takes one line:

% disjoint(+Rectangle, +Rectangle)
disjoint([XA1,XA2,YA1,YA2],[XB1,XB2,YB1,YB2]) :-
   XB1 #>= XA2 #\/ XA1 #>= XB2 #\/
   YB1 #>= YA2 #\/ YA1 #>= YB2.

The model setup and labeling works as follows:

% squares(-List)
squares(L) :-
   maplist(square, [2,3,4,5], L),
   term_variables(L, V),
   place(L),
   label(V).

% square(+Integer, -Rectangle)
square(S, [X1,X2,Y1,Y2]) :-
   X1 in 0..8,
   X2 in 1..9,
   Y1 in 0..6,
   Y2 in 1..7,
   X2 #= X1+S,
   Y2 #= Y1+S.

% place(+List)
place([]).
place([A|L]) :-
   place(L, A),
   place(L).

% place(+List, +Rectangle)
place([], _).
place([A|L], B) :-
   disjoint(A, B),
   place(L, B).

Here is an example run:

Jekejeke Prolog 3, Runtime Library 1.3.7 (May 23, 2019)

?- squares(L), show(L).
555554444
555554444
555554444
555554444
55555333.
22...333.
22...333.
L = [[0,2,5,7],[5,8,4,7],[5,9,0,4],[0,5,0,5]]