Write efficient methods that take only a reference to the root of a binary tree, T, and compute:

a. The number of nodes in T?

b. The number of leaf nodes in T?

c. The number of internal (non-leaf) nodes in T.

d. If the tree has n nodes, for which n is it possible to arrange the nodes into a perfect binary tree (i.e. a tree in which all interior nodes have two children and the depth of all leaf nodes is identical)?