Kakuro Puzzle CSP Prolog

Question

Have an exam coming up and answering past paper questions to aid my revision. The question I am trying to answer is: (d) Translate the CSP into a Prolog program that computes just one way of solving this problem using finite domain constraints. [7 marks]

I have written the following code:

  kakuro(L):-
      L = [X1, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11, X12, X13, X14, X15, X16],
      L ins 1..9,       
      Z1 = [X1, X2],
      all_different(Z1),
      X1 #= 5 - X2,     
      Z2 = [X3, X4, X5, X6],
      all_different(Z2),
      X3 #= 29 - (X4+X5+X6),
      Z3 = [X7, X8],
      all_different(Z3),
      X7 #= 14 - X8,
      Z4 = [X9, X10],
      all_different(Z4),
      X9 #= 4 - X10,
      Z5 = [X11, X12, X13, X14],
      all_different(Z5),
      X11 #= 16 - (X12+X13+X14),
      Z6 = [X15, X16],
      all_different(Z6),
      X15 #= 7 - X16,

      A1 = [X3, X7],
      all_different(A1),
      X3 #= 16 - X7,
      A2 = [X1, X4, X8, X11],
      all_different(A2),
      X1 #= 18 - (X4+X8+X11),
      A3 = [X2, X5],
      all_different(A3),
      X2 #= 13 - X5,
      A4 = [X12, X15],
      all_different(A4),
      X12 #= 14 - X15,
      A5 = [X6, X9, X13, X16],
      all_different(A5),
      X6 #= 11 - (X9+X13+X16),
      A6 = [X10, X14],
      all_different(A6),
      X10 #= 3 - X14,

      labeling([], L).

I think my answer is a bit too long. Is there any way I could shorten it?

Really appreciate any help!

Answer 1

I show you a simplification up to the first empty line:

kakuro(Ls):-
      Lss = [[X1,X2],
             [X3,X4,X5,X6],
             [X7,X8],
             [X9,X10],
             [X11,X12,X13,X14],
             [X15, X16]],
      maplist(all_different, Lss),
      append(Lss, Ls),
      Ls ins 1..9,
      X1 #= 5 - X2,
      X3 #= 29 - (X4+X5+X6),
      X7 #= 14 - X8,
      X9 #= 4 - X10,
      X11 #= 16 - (X12+X13+X14),
      X15 #= 7 - X16,

Notice in particular:

• I chose a representation of the puzzle that retains more information about its structure.
• The meta-predicate maplist/2 is used to replace many individual calls of all_different/1.
• A systematic naming convention: lists end with an "-s", lists of lists end with an "s" appended to that.
• append/2 is used to remove one level of nesting.

Another change I strongly recommend: Separate the core relation from labeling/2! This simplifies testing and has many other advantages. The eventual query should look similar to:

?- kakuro(Vs), label(Vs).

or like:

?- kakuro_(Instance, Vs), label(Vs).

I leave further simplifying this, and the remainder of the program, as an exercise for you. Note that the choice of instance representation can help signficantly to shorten the code!