Question

2. A regular binary tree is a binary tree whose internal nodes all have two subtrees (left and right). In other words, all their nodes have either zero subtrees (in which case they are leaves) or two subtrees (in which case they are internal nodes). Suppose that you have a boolean function that tells you, for each node of the tree, whether it is a leaf or not (call it: leaf(n), for node n). a) Write a recursive function that computes the depth of a regular binary tree. Call it depth(n), for node n. The depth (also called the height) of a tree is the maximum (over the set of leaves) number of arcs between the root and a leaf. b) Show the trace of execution of this program on the following regular binary tree: A B с D E F G H J K

Answer 1

Solution (a):

depth(n){

if(leaf(n)) return 0;

int leftdepth = depth(node -> left);

int rightdepth = depth(node -> right);

return max(leftdepth, rightdepth) + 1;

}

Solution (b):

For node A:

depth(A) => depth (B) , depth(C)

depth(B) => max(depth (D)=0, depth(E)=0) +1 =1

Thus depth(B) = 1

depth(C) => depth(F)=0, depth(G)

depth(G) => depth(H) , depth(I)=0

depth(H) => max(depth (J)=0, depth(K)=0) +1 =1

Thus depth(H) = 1

Thus depth(G) = 2

Thus depth(C) = 3

Thus depth(A) = 4