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Praktikum3.pl

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+% Präfix-Prädikat aus Übungsaufgabe 20 b)
+prefix([], _).
+prefix([H|T], [H|Ys]) :- prefix(T, Ys).
+
+% Reverse-Prädikat des Prolog-Systems
+reverse([], []).
+reverse([H|T], R) :- reverse(T, RT), append(RT, [H], R).
+
+% Postfix-Prädikat
+postfix(Xs, Ys) :-
+    reverse(Xs, RXs),
+    reverse(Ys, RYs),
+    prefix(RXs, RYs).
+
+% Postfix mit append
+postfix(Xs, Ys) :-
+    append(_, Xs, Ys).
+
+% ----------------------------------------------------%
+
+% Definition eines Binärbaums
+% Ein leerer Baum ist ein leerer Baum
+tree(empty).
+tree(node(_, Left, Right)) :- tree(Left), tree(Right).
+
+% Überprüfung, ob ein Element im Baum enthalten ist
+membertree(X, node(X, _, _)).
+membertree(X, node(_, Left, _)) :- membertree(X, Left).
+membertree(X, node(_, _, Right)) :- membertree(X, Right).
+
+% ----------------------------------------------------%
+
+% Preorder
+preorder(empty, []).
+preorder(node(X, Left, Right), Ys) :-
+    preorder(Left, Ls),
+    preorder(Right, Rs),
+    append([X|Ls], Rs, Ys).
+
+% Postorder
+postorder(empty, []).
+postorder(node(X, Left, Right), Ys) :-
+    postorder(Left, Ls),
+    postorder(Right, Rs),
+    append(Ls, Rs, Temp),
+    append(Temp, [X], Ys).
+
+% Roots
+roots([], []).
+roots([empty|Xbs], Ys) :- roots(Xbs, Ys).
+roots([node(X, _, _)|Xbs], [X|Ys]) :- roots(Xbs, Ys).