% Figure 4.11 Program 3 for the eight queens problem.
% solution( Ylist) if
% Ylist is a list of Y-coordinates of eight non-attacking queens
solution( Ylist) :-
sol( Ylist, % Y-coordinates of queens
[1,2,3,4,5,6,7,8], % Domain for X-coordinates
[1,2,3,4,5,6,7,8], % Domain for Y-coordinates
[-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7], % Upward diagonals
[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] ). % Downward diagonals
sol( [], [], Dy, Du, Dv).
sol( [Y | Ylist], [X | Dx1], Dy, Du, Dv) :-
del( Y, Dy, Dy1), % Choose a Y-coordinate
U is X-Y, % Corresponding upward diagonal
del( U, Du, Du1), % Remove it
V is X+Y, % Corresponding downward diagonal
del( V, Dv, Dv1), % Remove it
sol( Ylist, Dx1, Dy1, Du1, Dv1). % Use remaining values
del( Item, [Item | List], List).
del( Item, [First | List], [First | List1] ) :-
del( Item, List, List1).