In class, we analyzed the
add method for the BinaryTree class. Because each recursive call involves counting the number of nodes in each subtree (an O(N) operation) and the number of calls depends upon the height of the tree (which is O(log N) in a balanced tree), adding an item using this method will be O(N log N). Design a program that will verify this analysis experimentally using techniques similar to HW3. Provide statistics from executions of your program and a coherent argument as to why the statistics support the claim that
add is O(N log N).
Both of these properties can also be defined recursively. The height of a nonempty binary tree is the maximum of the heights of the two subtrees plus 1. The weight of a nonempty binary tree is the sum of the weights of the two subtrees plus the number of nodes in the tree.
Add methods to the BinaryTree class named
weight, that calculate and return these tree properties. Modify the main method of your
BinaryTree class so that it tests each of these methods. Part of your grade will depend upon the thoroughness of your tests. Also, don't forget to add your name to the @author comment!