I am trying to write a sudoku in clingo to learn the syntax a bit more. The part that I am satisfied with correctly represents the column/row constraints:
subgrid_size(3).
number(1..S*S) :- subgrid_size(S).
sudoku(X,Y,N) :- initial(X,Y,N).
1{sudoku(X,Y,N): number(N)}1 :- number(X), number(Y). %each coordinate has to have a unique N
1{sudoku(X,Y,N): number(X)}1 :- number(N), number(Y). %a number can only appear once per row
1{sudoku(X,Y,N): number(Y)}1 :- number(X), number(N). %a number can only appear once per col
Then I had tried to do something similar to enforce the subgrid constraint:
1{sudoku(X,Y,N): subgrid((X-1/S)*S+(Y-1)/S) }1 :- number(N),number(X), number(Y),subgrid_size(S).
This did not work, after a long time looking for solutions I found this(which works):
subgrid(X,Y,((X-1)/S)*S+(Y-1)/S):- number(X), number(Y), subgrid_size(S).
:- subgrid(X1,Y1,G), subgrid(X2,Y2,G),sudoku(X1,Y1,N), sudoku(X2,Y2,N), X1!=X2, Y1!=Y2.
Is there anyway to adapt the 1{...}1:- rule1..ruleN. line for the subgrid constraint so that it works?
Interesting approach! The immediate problem is that subgrid/1 in the choice rule is not defined anywhere. I get the error message:
info: atom does not occur in any rule head: subgrid(#Arith0)
Changing the choice rule to use subgrid/3 ...
1{sudoku(X,Y,N): subgrid(X, Y, (X-1/S)*S+(Y-1)/S ) }1 :-
number(N), number(X), number(Y), subgrid_size(S).
... and including your subgrid/3 predicate ... now doesn't return an error, but returns unsatisfiable.
Here's what worked for me:
First I changed subgrid/3 slightly -- adding +1 to the third argument, so that subgrid labels were 1-9, instead of 0-8, ie now they are numbers:
subgrid(X, Y, (((X-1)/S)*S+(Y-1)/S)+1):-
number(X),
number(Y),
subgrid_size(S).
Second, I used this choice rule:
1 { sudoku(X,Y,N):
number(X), number(Y),
subgrid(X,Y,M)
} 1 :-
number(N),
number(M).
ie for every possible (N, M) combination, there is one sudoku(X,Y,N), where (X,Y) is in subgrid M.
Does that work for you?