/* nodoubles(L,R)  succeeds if for a given list L R is the corresponding list
which contains all the elements of L but no doubles (any more).
You may assume that you have to construct R.*/

nodoubles([],[]).
nodoubles([H |T], R) :-
	( member(H,T) ->
	    nodoubles(T,R)   % if H in T then forget H
	;
	    R = [H | R1],
	    nodoubles(T,R1)
	).
	
member(X,[X|_]).
member(X, [_Y| T]) :- member(X,T).

q1(K) :- nodoubles( [1,2,2,1,1,2,1,2],K).


/*
nodoublesacc(L,R) :- nod(L,[], R).

nod([],A,A).
nod([H |T ] , RAcc,R) :-
	(  member(H, RAcc) ->
	    nod( T, RAcc,R)  %  if H in Racc, forget it
	;
	    nod(T , [H |RAcc],R)  % else add it to Acc
	).

*/
/* 11/2006 */
/* not changing the order... */
nodoublesacc(L,R) :- nod(L,[], R).

nod([],A,[]).
nod([H |T ] , RAcc,R) :-
	(  member(H, RAcc) ->
	    nod( T, RAcc,R)  %  if H in Racc, forget it
	;
	    R = [H|R1], nod(T , [H |RAcc],R1)  % else add it to Acc
	).
/* 11/2006 */
/* make a list List which repeats Repeat times the smaller list of length Pattern */

list(Pattern, Repeat, List) :-
	generate(Pattern, List1),
	replist(Repeat,List1, List1, List).

generate(0,[]).
generate(N,[N |T]) :- N > 0, 
	N1 is N -1,
	generate(N1,T).

replist(1, _,List,List).
replist(N, Small, Acc, List) :-
	N > 1,
	append(Small, Acc, Acc1),
	N1 is N - 1,
	replist(N1, Small, Acc1, List).

append([],L,L).
append([ X| U], V, [X|W]) :- append(U,V,W).



q(P,Rep) :- list( P, Rep, List),
	time(nodoubles(List,Res1)),
	write(nodoublesfor(P,Rep,Res1)),nl,
	time(nodoublesacc(List,Res2)),
	write(nodoublesaccfor(P,Rep,Res2)),nl.

/*
?- q(100,1000).
% 10,095,151 inferences, 7.92 CPU in 7.92 seconds (100% CPU, 1274640 Lips)
nodoublesfor(100, 1000, [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])
% 5,150,002 inferences, 4.05 CPU in 4.05 seconds (100% CPU, 1271605 Lips)
nodoublesaccfor(100, 1000, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100])

Yes
?- q(100,2000).
% 20,195,151 inferences, 15.84 CPU in 15.84 seconds (100% CPU, 1274946 Lips)
nodoublesfor(100, 2000, [100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1])
% 10,300,002 inferences, 8.10 CPU in 8.10 seconds (100% CPU, 1271605 Lips)
nodoublesaccfor(100, 2000, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100])

Yes

 
*/