Answer the following questions so as to justify Proposition 8.7.
a. What is the minimum number of external nodes for a proper binary tree with height h? Justify your answer.
b. What is the maximum number of external nodes for a proper binary tree with height h? Justify your answer.
c. Let T be a proper binary tree with height h and n nodes. Show that log(n+1)−1≤ h ≤ (n−1)/2.
d. For which values of n and h can the above lower and upper bounds on h be attained with equality?
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