Exercise 2.70

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The following eight-symbol alphabet with associated relative frequencies was designed to efficiently encode the lyrics of 1950s rock songs. (Note that the “symbols” of an “alphabet” need not be individual letters.)

A 	2 	NA 	16
BOOM 	1 	SHA 	3
GET 	2 	YIP 	9
JOB 	2 	WAH 	1 

Use generate-huffman-tree (exercise 2.69) to generate a corresponding Huffman tree, and use encode (exercise 2.68) to encode the following message:

Get a job

Sha na na na na na na na na

Get a job

Sha na na na na na na na na

Wah yip yip yip yip yip yip yip yip yip

Sha boom

How many bits are required for the encoding? What is the smallest number of bits that would be needed to encode this song if we used a fixed-length code for the eight-symbol alphabet?

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