costas.clingo

% Raphael Finkel 10/2008, 6/2018

fullRange(1..m) . % the ruler is a permutation of numbers 1 .. m
subRange(1..m-1) . % differences in array index
diff(1.. 2*m-1) .  % differences in array value, offset by m
position(1..m) .

% #domain fullRange(Row) . % Row is index, Col is value
% #domain fullRange(Row1) . % Row is index, Col is value
% #domain fullRange(Col) . % Row is index, Col is value
% #domain fullRange(Col1) . % Row is index, Col is value
% #domain subRange(Delta) .
% #domain diff(Diff) .
% #domain position(Pos) .

% exactly one value in each index
1 {setting(Row, Col_):fullRange(Col_)} 1 :- fullRange(Row) .

% exactly one index for each value (no duplicates allowed)
1 {setting(Row_, Col):fullRange(Row_)} 1 :- fullRange(Col) .

% difference between values at Row and at Row+Delta is Diff
delta(Delta, Row, Diff) :-
    Row + Delta <= m , setting(Row, Col), Row+Delta == Row1,
    setting(Row1, Col1),
    Diff == m + Col1 - Col,
    fullRange(Row;Row1), subRange(Delta) .
:- delta(Delta, Row, Diff), Delta + Row > m . % uniqueness
% not necessary, but seems to speed up clasp:
    1 {delta(Delta, Row, Diff_):diff(Diff_)} 1 :-
        Row + Delta <= m ,
        subRange(Delta), fullRange(Row) .

% constraint on differences
0 {delta(Delta, Row_, Diff):fullRange(Row_)} 1 :-
    Delta < m-1 ,
    subRange(Delta), fullRange(Row), diff(Diff).