Question

I’m trying to divide a list in Prolog into 3 equal parts (…well, as equal as possible).
My algorithm is the following:

1. Find out the size of the initial list.
2. Call the procedure with two extra parameters (the size of the list and a counter that will tell me when I should stop adding elements to one list and start adding to another)

The procedure looks like this:

With 4 parameters:

div3(InitialList,FirstNewList,SecondNewList,ThirdNewList).

With 2 extra parameters:

div3(InitialList,FirstList,SecondList,ThirdList,InitialListSize,Counter).

Here’s my code:

div3([],[],[],[]).
div3([X],[X],[],[]).
div3([X,Y],[X],[Y],[]).
div3([X,Y,Z],[X],[Y],[Z]).
div3([X | Y],A,B,C) :- length([X | Y],Sz),
                       Sz1 is 0,
                       div3([X | Y],A,B,C,Sz,Sz1).

div3([X | Y],A,B,C,Sz,Sz1) :- Sz1 < Sz//3, % am I done adding to the 1st list?
                              append(X,L,A), % add to the 1st list
                              Sz2 is Sz1+1, % increment the counter
                              div3(Y,L,B,C,Sz,Sz2),!.

div3([X | Y],A,B,C,Sz,Sz1) :- Sz1 < 2*Sz//3, % am I done adding to the 2nd list?
                              append(X,L,B), % add to the 2nd list
                              Sz2 is Sz1+1, % increment the counter
                              div3(Y,A,L,C,Sz,Sz2),!.

div3([X | Y],A,B,C,Sz,Sz1) :- Sz1 < Sz, % am I done adding to the 3rd list?
                              append(X,L,C),% add to the 3rd list
                              Sz2 is Sz1+1, % increment the counter
                              div3(Y,A,B,L,Sz,Sz2),!.

Answer 1

I think the first part of your code was almost right…
What you are looking for is a recursive predicate with 3 base cases and just one recursive clause.

div3([], [], [], []).
div3([X], [X], [], []).
div3([X,Y], [X], [Y], []).
div3([X,Y,Z|Tail], [X|XTail], [Y|YTail], [Z|ZTail]):-
  div3(Tail, XTail, YTail, ZTail).