Consider the problem of constructing a Huffman tree / code on an n-letter alphabet. (a) What is the largest possible height of a Huffman tree for n letters 21,...,? (b) For an arbitrary integer n, determine a possible pattern of letter frequencies P1, ...,Pn for which this maximum height is achieved. (Explain why the maximal height is achieved, but you don't have to write out a formal proof of that fact.)