Problem HC $($Huffman compression$)$

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

acheahdgfdggeecadafgdeecfcdcachbfabcceegcecbcegchbeeababcbcfdceacaachb

fbdgcadgaegbfbfbbfbfccffhcccahehbffgadhdbfaaeddddceffeaabadfcdffaheecg

dehbggahbeceacedebgfacafdebdchbeehaebfcefaheegbbafdcfdhdfacedhacbeecec

begchhaefdhabcbaacbhachgefcffdgfagdbcahebfcbcaghfgchdchbbfgdfffbhgdbfb

hbcbdfecgfgcfgbhbcffebegafcfhfecfgdddegh

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.