prolog tree stuff

Frederik/README.md

@@ -5,4 +5,5 @@ AI 1 - 2019/2020
 ---
 
 * 2019-10-28: `prolog/2019-10-28-tutorial.pl` (simple prolog exercises)
-* 2019-10-31: `prolog/2019-10-31-tutorial.pl` (simple prolog exercises)
+* 2019-10-31 (substition for Katja): `prolog/2019-10-31-tutorial.pl` (simple prolog exercises)
+* 2019-11-04: `prolog/2019-11-04-trees.pl` (some simple tree exercises)

Frederik/prolog/2019-11-04-trees.pl

+% Check that a tree is indeed a binary tree
+% (as specified in the homework)
+isbinary(nil).
+isbinary(tree(N, X, Y)) :-
+    integer(N),
+    isbinary(X),
+    isbinary(Y).
+
+% Helper predicate: get the maximum of two integers
+% e.g max(2,7,X) results in X=7.
+%
+% ! is the cut operator.
+% It tells prolog not to backtrack anymore.
+% In this case, we want to ignore the second case,
+% if the first case is applicable.
+max(X,Y,X) :- X >= Y, !.
+max(_,Y,Y).
+
+% Get the largest node in a tree
+% (assuming it only contains natural numbers)
+treemax(nil, 0).
+treemax(tree(N, X, Y), Result) :-
+    treemax(X, XRes),
+    treemax(Y, YRes),
+    max(XRes, YRes, XYRes),
+    max(XYRes, N, Result).
+
+% Get the depth of a tree
+treedepth(nil, 0).
+treedepth(tree(_, X, Y), Depth) :-
+    treedepth(X, XDepth),
+    treedepth(Y, YDepth),
+    max(XDepth, YDepth, D),
+    Depth is D + 1.
+
+% helper predicate: concatenate two lists
+concatenate([], L, L).
+concatenate([H|T], L, [H|TL]) :-
+    concatenate(T, L, TL).
+
+% get the leaves of a binary tree
+leaves(nil, []).
+leaves(tree(N, nil, nil), [N]) :- !.
+leaves(tree(N, X, Y), Result) :-
+    leaves(X, XL),
+    leaves(Y, YL),
+    concatenate(XL, YL, Result).
+
+% compute the result of a formula (which you can think of as a tree).
+% Example tree: plus(times(2,6), 7)
+compute(SomeInt, SomeInt) :-
+    integer(SomeInt).
+compute(times(X, Y), R) :-
+    compute(X, XRes),
+    compute(Y, YRes),
+    R is XRes * YRes.
+compute(plus(X, Y), R) :-
+    compute(X, XRes),
+    compute(Y, YRes),
+    R is XRes + YRes.
+