A. Tree is a data structure defined as a root node linked with zero or more sub-trees (same recursive definition as tree). Given a binary tree in which the root can have at most two subtrees, we define a new type of binary tree that further satisfies the balance condition next: for any node in such a tree, the heights of left and right subtrees can differ by 1 (left and right heights are the same or one-level different). Describe the way to compute the maximum number of nodes and minimum number of nodes respectively in such a tree with given height 20.

B. Write a short program to compute the minimum number of nodes in such a tree with height of 100. List the program and printed results on paper. This is also an exercise for you to test your programming environment and basic programming skill.

USING C++ ONLY