% crypt
%
% Cryptomultiplication:
% Find the unique answer to:
% OEE
% EE
% ---
% EOEE
% EOE
% ----
% OOEE
%
% where E=even, O=odd.
% This program generalizes easily
% to any such problem.
% Written by Peter Van Roy
crypt(ShowResult) :-
odd(A), even(B), even(C), even(E),
mult([C, B, A], E, [I, H, G, F | X]),
lefteven(F), odd(G), even(H), even(I), zero(X), lefteven(D),
mult([C, B, A], D, [L, K, J | Y]),
lefteven(J), odd(K), even(L), zero(Y),
sum2([I, H, G, F], [0, L, K, J], [P, O, N, M | Z]),
odd(M), odd(N), even(O), even(P), zero(Z),
( ShowResult = true ->
write(' '), write(A), write(B), write(C), nl,
write(' '), write(D), write(E), nl,
write(F), write(G), write(H), write(I), nl,
write(J), write(K), write(L), nl,
write(M), write(N), write(O), write(P), nl
; true).
% In the usual source this predicate is named sum. However, sum is a
% language construct in NU-Prolog, and cannot be defined as a predicate.
% If you try, nc comes up with an obscure error message.
sum2(AL, BL, CL) :-
sum2(AL, BL, 0, CL).
sum2([A | AL], [B | BL], Carry, [C | CL]) :- !,
X is (A + B + Carry),
C is X mod 10,
NewCarry is X // 10,
sum2(AL, BL, NewCarry, CL).
sum2([], BL, 0, BL) :- !.
sum2(AL, [], 0, AL) :- !.
sum2([], [B | BL], Carry, [C | CL]) :- !,
X is B + Carry,
NewCarry is X // 10,
C is X mod 10,
sum2([], BL, NewCarry, CL).
sum2([A | AL], [], Carry, [C | CL]) :- !,
X is A + Carry,
NewCarry is X // 10,
C is X mod 10,
sum2([], AL, NewCarry, CL).
sum2([], [], Carry, [Carry]).
mult(AL, D, BL) :- mult(AL, D, 0, BL).
mult([], _, Carry, [C, Cend]) :-
C is Carry mod 10,
Cend is Carry // 10.
mult([A | AL], D, Carry, [B | BL] ) :-
X is A * D + Carry,
B is X mod 10,
NewCarry is X // 10,
mult(AL, D, NewCarry, BL).
zero([]).
zero([0 | L]) :- zero(L).
odd(1).
odd(3).
odd(5).
odd(7).
odd(9).
even(0).
even(2).
even(4).
even(6).
even(8).
lefteven(2).
lefteven(4).
lefteven(6).
lefteven(8).
% benchmark interface
benchmark(ShowResult) :-
crypt(ShowResult).
:- include(common).
