serie3_aufgabe4.pl

% vim:set noet sts=0 sw=8 ts=8 ft=prolog:

n(Wert, _, _) :- integer(Wert).

tree(n(3,
	n(1,
		n(4,nil,nil),
		n(1,nil,nil)),
	n(5,
		n(9,
			n(2,nil,nil),
			nil),
		n(6,
			nil,
			n(5,nil,nil))))).

tree(n(20,
	n(31,
		nil,
		n(97,
			nil,
			n(17, nil, nil))),
	n(20,
		n(45, nil, nil),
		n(22,
			nil,
			n(7, nil, nil))))).

is_bin_tree(nil).
is_bin_tree(n(Wert, L, R)) :-
	integer(Wert),
	is_bin_tree(L),
	is_bin_tree(R).

max_value_of_tree(nil, 0).
max_value_of_tree(n(Wert, L, R), M) :-
	max_value_of_tree(L, ML),
	max_value_of_tree(R, MR),
	M1 is max(Wert, ML),
	M is max(M1, MR).

replace(nil, _, nil).
replace(n(_, L, R), New, n(New, LNew, RNew)) :-
	replace(L, New, LNew),
	replace(R, New, RNew).

max_tree(nil, nil).
max_tree(T1, T2) :-
	max_value_of_tree(T1, N),
	replace(T1, N, T2).