%% df([[a,[b,c]],[d,e]],List).  
df(Tree,List) :-	
	df(Tree,[],List), !.
df([Left,Right],List1,List3) :-
	df(Left,List1,List2),df(Right,List2,List3).
df(Item,List1,List2) :-	
	append(List1,[Item],List2).

%% bf([[a,[b,c]],[d,e]],List)
bf(Tree,List) :-        
        bf(Tree,[],List), !.
bf([Left,Right],List1,List2) :-
        bf(Left,List1,List3),
	bf(Right,List2,List3).
bf(Item,List1,List2) :-
        append(List1,[Item],List2).
/**,
	append(
	append(List3,[List4],List2),
	append(List
	%%append(List3,[List4],List2)
  %%      append(List3,List5,List2).**/

%%bf2([a,[a,[a,[a]]]]
bf2([L,R],List) :-
        bf2(R,List2),
        bf2(L,List1),
	reverse(List2,List3),
	reverse(
	append(List1,List2,List),!,
bf2(A,A).

solve_breadthfirst(Node, Path) :-
     breadthfirst([[Node]], RevPath),
     reverse(RevPath, Path).

 breadthfirst([[Node|Path]|_], [Node|Path]) :-
     goal(Node).
   breadthfirst([Path|Paths], SolutionPath) :-
     expand_breadthfirst(Path, ExpPaths),
     append(Paths, ExpPaths, NewPaths),
     breadthfirst(NewPaths, SolutionPath).
goal(b).