/* bst.pl
 *
 * CS 313 example
 *
 * binary search trees of integers
 */

/* example trees */

mytree1(node(5, node(3, nil, nil),
	        node(8, node(7, nil, nil),
		        node(9, nil, nil)))).
mytree2(node(2, node(1, nil, nil), T)) :-
	mytree1(T).

/* printing */

show(T) :- show1(T, 0).

show1(nil, _).
show1(node(N, L, R), Indent) :-
	Indent2 is Indent + 4,
	show1(R, Indent2),
	tab(Indent),
	write_ln(N),
	show1(L, Indent2).

/* testing for membership */

find(X, node(X, _, _)).
find(X, node(N, L, _)) :-
	X<N,
	find(X, L).
find(X, node(N, _, R)) :-
	X>N,
	find(X, R).

/* sample output:

?- show(node(6, node(3, nil, nil), node(7, nil, nil))).
    7
6
    3

?- mytree1(T), show(T).
        9
    8
        7
5
    3

T = node(5, node(3, nil, nil), node(8, node(7, nil, nil), node(9, nil, nil))) 

?- mytree2(T), show(T).
            9
        8
            7
    5
        3
2
    1

T = node(2, node(1, nil, nil), node(5, node(3, nil, nil), node(8, node(7, nil, nil), node(9, nil, nil)))) 

?- mytree1(T), find(7, T).

T = node(5, node(3, nil, nil), node(8, node(7, nil, nil), node(9, nil, nil))) 

Yes

?- mytree2(T), find(4, T).

No

*/