Question

I’m trying to get a program to return the levels of a BT in the way of a list and I’m stuck at this:

nivel(nodo(L,Root,R)) :- nivel(nodo(L,Root,R),X),writeln(X).
nivel(vacio,[]).
nivel(nodo(L,Root,R),[Root|T]) :- nivel(L,T),nivel(R,T),writeln(T).

An example input-output of what I’m trying is:

nivel(nodo(nodo(vacio,4,vacio), t, nodo(vacio,r,vacio))
  X =[t]
  X =[4,r]

problem is I don’t know how to make the program get the new Roots.
Any ideas? Also, thanks in advance!

Answer 1

Here goes a solution, it traverses the tree once an builds a list of the items in each level.

nivel(Arbol, SubNivel):-
  nivel(Arbol, [], [], Items),
  member(SubNivel, Items),
  SubNivel \= [].

nivel(vacio, Items, SubNiveles, [Items|SubNiveles]).
nivel(nodo(Izq, Item, Der), Items, [], [[Item|Items]|NSubNiveles]):-
  nivel(Izq, [], [], [MSubItems|MSubNiveles]),
  nivel(Der, MSubItems, MSubNiveles, NSubNiveles).
nivel(nodo(Izq, Item, Der), Items, [SubItems|SubNiveles], [[Item|Items]|NSubNiveles]):-
  nivel(Izq, SubItems, SubNiveles, [MSubItems|MSubNiveles]),
  nivel(Der, MSubItems, MSubNiveles, NSubNiveles).

The second clause of nivel/4 is a hack due to the fact that the algorithm does not know in advance the height of the tree.

Test case:

?- nivel(nodo(nodo(nodo(nodo(vacio,f,vacio),e,nodo(vacio,g,vacio)),b,vacio),a,nodo(vacio,c,nodo(vacio,d,vacio))), X).
X = [a] ;     --> Root
X = [c, b] ;  --> First Level
X = [d, e] ;  --> Second Level
X = [g, f] ;  --> Third Level