Consider the following Huffman Tree encoded with variable-length codewords.

Suppose you have a file to compress with the frequencies given in each of the subproblems below. For each subproblem, determine whether the Huffman tree gives an optimal solution. If it does, argue your case. If it doesnt, re-draw the Huffman tree such that it gives an optimal solution.

A. Input frequencies given by the following:

A: 45

B: 101

C: 25

D: 1

E: 205

F: 55

G: 28

H: 30

I: 81

J: 65

K: 108

B: Input frequencies given by the following:

A: 145

B: 101

C: 99

D: 85

E: 84

F: 55

G: 28

H: 17

I: 16

J: 6

K: 5

f g oat