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The characters a to h have the set of frequencies based on the first 8 Fibonacci numbers as follows
a : 1, b : 1, c : 2, d : 3, e : 5, f : 8, g : 13, h : 21
A Huffman code is used to represent the characters. What is the sequence of characters corresponding to the following code? 110111100111010
  • a)
    fdheg
  • b)
    ecgdf
  • c)
    dchfg
  • d)
    fehdg
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The characters a to h have the set of frequencies based on the first 8...
Background Required -  Generating Prefix codes using Huffman Coding. First we apply greedy algorithm on the frequencies of the characters to generate the binary tree as shown in the Figure given below. Assigning 0 to the left edge and 1 to the right edge, prefix codes for the characters are as below.
a - 1111110
b - 1111111
c - 111110
d - 11110
e - 1110
f - 110
g - 10
h - 0
Given String can be decomposed as 110 11110 0 1110 10 fdheg
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The characters a to h have the set of frequencies based on the first 8...
Explanation:

  • The given set of frequencies can be arranged in ascending order as follows:


    • a : 1, b : 1, c : 2, d : 3, e : 5, f : 8, g : 13, h : 21


  • Now we need to construct a Huffman code based on these frequencies.

  • To do that, we first need to construct a Huffman tree.

  • The steps to construct a Huffman tree are as follows:


    • Arrange the characters in ascending order of their frequencies.

    • Take the two characters with the lowest frequencies and merge them to form a new node with a frequency equal to the sum of their frequencies.

    • Add this new node to the list of characters in ascending order of their frequencies.

    • Repeat steps 2 and 3 until there is only one node left in the list. This node is the root of the Huffman tree.


  • The Huffman tree for the given set of frequencies is shown below:


    • https://i.imgur.com/7ncknFJ.png


  • Now we can assign codes to each character based on their position in the Huffman tree.

  • The codes for each character are as follows:


    • a: 110

    • b: 1111

    • c: 00

    • d: 10

    • e: 01

    • f: 1110

    • g: 1101

    • h: 101


  • Using these codes, we can decode the given sequence as follows:


    • 110 1110 10 01 1101 1111 00 10

    • fdhegb


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