$3.$

a$.$ Construct a Huffman tree for the following data:

b$.$ Encode ABACABAD using the tree you generated for $($a$).$

c$.$ Decode $100010111001010$ using the tree you generated for $($a$).$

d$.$ What compression gain $($percent of improvement$)$ do we get by using Huffman encoding instead of a fixed$-$length encoding scheme $($assume the fixed$-$length scheme would require $3$ bits for each character$)?$