Construct a Huffman tree $($variable$-$length encoding$)$ for the following: $(5$ points$)$

a$.$ Encode ABACABAD using the tree you generated. $[1$ point$]$

b$.$ Decode $100010111001010$ using the tree you generated. $[1$ point$]$

c$.$ What compression gain $($percent of improvement$)$ do we get by using Huffman encoding

$($variable$-$length encoding$)$ instead of a fixed$-$length encoding scheme. Draw the tree for

the fixed$-$length encoding.