# GATE | GATE IT 2006 | Question 48

• Last Updated : 28 Jun, 2021

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

Explanation:

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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

f        d     h    e     g

This solution is contributed by Pranjul Ahuja .

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