Exercise Huffman compression $(15$ points$)$

You are given a text file with the text below, which is made up of the characters I through $P.$

IIKJIKLKIKKJKILNIPIKKIIOPIJKMPJLJLLKKKKIIMKKJJLJJPIOPKIINMI

MLPKNJLIJKLPOIMLJLPILIKLPKIKJPIOLPNIKPKKKLKPKKKPPKIIIKJLJII

LLKJJIKNPMLPMIOPPKKJIPJIJNIKLNOOONIPKLMKIJPNOMPPLIKLIILLKLK

IKKNLMIIKKIKJIIKKNLONKIMPKKIPKKJLOPPIJKKKKIJPLLJLLIIPJJKKNN

KMIKKNPJJKIKKMKKINILKNNKKJLLILNOKJPNNJKLJLLPMNLOLMPLLIKNIOI

MNNIILMKKKKIIMNIKJILNKLMLKLJLLPMNLOLMPLLIKNIOIMNNIILMKKKKII

MNIKJILNKLML

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 ratio? Recall that this is the number of bits in the Huffman encoding

divided by the number of bits in the fixed$-$length encoding.