Chapter 7, Problem 2E

Given that a tree with a single node has a height of one, what is the maximum number of nodes that may be included in a balanced binary tree with a height of five?

Prove the equivalence of the five definitions given in the picture for a(n undirected) tree.

What is the maximum height of a an AVL tree with p nodes?

If a tree with a single node has height 1, how many nodes can there be in a binary tree that is both balanced and has a height of 5?

What is the most number of nodes that may be included in a balanced binary tree of height 5? (A tree with a single node has height 1, hence the answer is 1)

What is the minimum number of black elements in a red-black tree of height 3?

For a Binary Tree with 1023 (= 2^10 - 1) items what is the minimum height? The maximum?

Suppose a binary tree is full at every node, i.e. having the maximum possible number of nodes for that level. If a tree has tree level(height=3) then how many total number of nodes are there in the tree.

Structural Induction: Prove that a nonempty binary tree t of height h(t) has at most 2(t)+1 – 1 nodes.