Algorithms | Greedy Algorithms | Question 3

A networking company uses a compression technique to encode the message before transmitting over the network. Suppose the message contains the following characters with their frequency: 

C

character   Frequency
    a             5
    b             9
    c             12
    d             13
    e             16
    f             45

Note : Each character in input message takes 1 byte. If the compression technique used is Huffman Coding, how many bits will be saved in the message?

(A)

224

(B)

800

(C)

576

(D)

324

Answer: (C)

Explanation:

Total number of characters in the message = 100. 
Each character takes 1 byte. So total number of bits needed = 800.

After Huffman Coding, the characters can be represented with:
f: 0
c: 100
d: 101
a: 1100
b: 1101
e: 111
Total number of bits needed = 224
Hence, number of bits saved = 800 - 224 = 576
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