You are trying to compress a text file containing a mix of the eight letters a through h$.$ Listed below are the counts of the letters in that file.

a b c d e f g h

$3216840488424$

Carry out Huffman's algorithm based on those counts by following these steps.

a$)$ How many bits are needed to encode this file given the optimal fixed$-$length encoding?

b$)$ Compile and write down a list of the counts of each character.

c$)$ Using that list, draw the Huffman encoding tree that would result. d$)$

Write down a list of the characters and each one's Huffman variable$-$length encoding

e$)$

How many bits are needed to encode the file using the Huffman variable$-$length encoding?

f$)$

What is the compression ration? Recall that this is the number of bits in the Huffman encoding divided by the number of bits in the fixed$-$length encoding.