Let T be a binary tree with n nodes, and let p be the level numbering of the nodes of T, so that the root, r, is numbered as p(r) = 1, and a node v has left child numbered 2p(v) and right child numbered 2p(v) + 1, if they exist.

a. Show that, for every node v of T , p(v) 2^(n+1)/2 - 1 b. Show an example of a binary tree with at least five nodes that attain the above upper bound on the maximum value of p(v) for some node v.

(Assume each internal node has two children)