prolog

% Question X1: Fracktorial %
fracktorial(X, Ans) :- isEven(X, Even), fracktorial(X, Ans, Even).
fracktorial(0, Ans, _) :- Ans is 1.
fracktorial(X, Ans, 1) :- X > 0, Y is X-2, fracktorial(Y, Ans2, 1), Ans is Ans2*X.
fracktorial(X, Ans, 0) :- X > 0, Y is X-1, fracktorial(Y, Ans2, 1), Ans is Ans2.
isEven(0, Ans) :- Ans is 1.
isEven(1, Ans) :- Ans is 0.
isEven(X, Ans) :- X > 1, Y is X-2, isEven(Y, Ans).


% Question X2: ReverseListHalves %
reverseListHalves(L, A) :- count(L, Count), isEven(Count, Even), reverseListHalves(L,A,Even).
reverseListHalves(L, A, 0) :- %if odd
 count(L, Count),
 End is Count-1, myFloor(End/2,Middle), Start is 0,
 MiddlePre is Middle-1, MiddlePost is Middle+1,
 sub(Start,MiddlePre,L,Half1), sub(MiddlePost,End,L,Half2),
 myReverse(Half1,Half1r), myReverse(Half2,Half2r),
 getIndexInL(Middle,L,MiddleElement),
 myAppend(Half1r,MiddleElement,Half1r2),
 myConcat(Half1r2,Half2r,A).
reverseListHalves(L, A, 1) :- %if even
 count(L, Count),
 End is Count-1, Middle is End/2, Start is 0,
 sub(Start,Middle,L,Half1), sub(Middle,End,L,Half2),
 myReverse(Half1,Half1r), myReverse(Half2,Half2r),
 myConcat(Half1r,Half2r,A).
count([], A) :- A is 0.
count([_|L1b], A) :- count(L1b, A2), A is A2+1.
sub(Start,End,L,A) :- sub(0,Start,End,L,A).
sub(_,_,_,[],A).
sub(Index,_,End,L,A) :- Index > End, A = [].
sub(Index,Start,End,L,A) :- Index < Start, Index2 is Index+1, sub(Index2,Start,End,L,A).
sub(Index,Start,End,L,[A2|A3]) :- Index >= Start, Index =< End, getIndexInL(Index,L,A2), Index2 is Index+1, sub(Index2,Start,End,L,A3).
getIndexInL(Index,L,A) :- getIndexInL(Index,0,L,A).
getIndexInL(Index,Index,[A|_],A).
getIndexInL(Index,X,[L1a|L1b],A) :- Index \= X, X2 is X+1, getIndexInL(Index,X2,L1b,A).
myReverse([],L2) :- L2 = [].
myReverse([L1a|L1b],A) :- myReverse(L1b, L2), myAppend(L2,L1a,A).
myAppend([],X,[X]).
myAppend([La|Lb],X,A) :- myAppend(Lb,X,A2), A = [La|A2].
myConcat([],A,A).
myConcat([L1a|L1b],L2,[L1a|A2]) :- myConcat(L1b,L2,A2).
myFloor(Input,Output) :- myFloor(Input,Output,0).
myFloor(Input,Index,Index) :- Index >= Input, Output is Index.
myFloor(Input,Output,Index) :- Index < Input, Index2 is Index+1, myFloor(Input,Output,Index2).