BIA - L4

% tree(5, tree(3, tree(1, null, null), tree(4, null, null)), tree(7, null, null))

present(Key,tree(Key,_,_)).
present(Key,tree(_,LeftSubTree,_)) :-
	present(Key,LeftSubTree).
present(Key,tree(_,_,RightSubTree)) :-
	present(Key,RightSubTree).

inserting(Key,null,tree(Key,null,null)).
inserting(Key,tree(Root,LeftSubTree,RightSubTree), tree(Root,NewLeftSubTree,RightSubTree)) :-
	Key<Root,
	inserting(Key,LeftSubTree,NewLeftSubTree).
inserting(Key,tree(Root,LeftSubTree,RightSubTree), tree(Root,LeftSubTree,NewRightSubTree)) :-
	Key>Root,
	inserting(Key,RightSubTree,NewRightSubTree).

% 1
add(null, 0).
add(tree(Root, Left, Right), Sum) :-
	add(Left, S1),
	add(Right, S2),
	Sum is Root+S1+S2.

% 2
count_leaves(null, 0).
count_leaves(tree(_,null,null), 1) :- !.
count_leaves(tree(_,Left,Right),Count) :-
	count_leaves(Left,C1),
	count_leaves(Right,C2),
	Count is C1+C2.

% 3
compute(tree(N,null,null), N).
compute(tree(+,L,R), Rez) :-
	compute(L,R1),
	compute(R,R2),
	Rez is R1+R2.
compute(tree(-,L,R), Rez) :-
	compute(L,R1),
	compute(R,R2),
	Rez is R1-R2.
compute(tree(*,L,R), Rez) :-
	compute(L,R1),
	compute(R,R2),
	Rez is R1*R2.
compute(tree(/,L,R), Rez) :-
	compute(L,R1),
	compute(R,R2),
	Rez is R1/R2.

% 4
converting(N, tree(N,null,null)) :-
	number(N).
converting(A+B, tree(+,L,R)) :-
	converting(A,L),
	converting(B,R).
converting(A-B, tree(-,L,R)) :-
	converting(A,L),
	converting(B,R).
converting(A*B, tree(*,L,R)) :-
	converting(A,L),
	converting(B,R).
converting(A/B, tree(/,L,R)) :-
	converting(A,L),
	converting(B,R).