% ex.pl
% some example predicates that might help with assignment # 11

% uniquify a list--keep the last occurence of each element
uniq([], []).
uniq([X | R], R2) :- member(X, R), uniq(R, R2).
uniq([X | R], [X | R2]) :- \+member(X, R), uniq(R, R2).

% remove an element (which much be present) from a list...
removeOne(X,[X|R],R).
removeOne(X,[F|R],[F|S]) :- removeOne(X,R,S).


removeAll(X,[X|R],R) :- \+member(X,R).
removeAll(X,[F|R],[F|S]) :- removeAll(X,R,S), X\==F.
removeAll(X,[X|R],R2) :- removeAll(X, R, R2).

% generates permutations of the first input's list
perm([X|Y],Z) :- perm(Y,W), remove(X,Z,W).
perm([],[]).

% checks if the input list is sorted
sorted( [] ).
sorted( [_] ).
sorted( [F,S|R] ) :- sorted( [S|R] ), F < S.

% binds the second argument to a sorted version of the first
mysort( [], [] ).
mysort( L, S ) :- perm( L, S ), sorted(S).

% splits the first argument's list into subsets, i.e.,
% sublists in which the order of elements may vary
split( List, A, B ) :-
   perm( List, L2 ),
   append( A, B, L2 ).