Question

1. By applying Huffman’s algorithm construct an optimal binary prefix free code for the following letters A, B, I, M,S,X and Z with their corresponding frequencies.

Letter	A	B	I	M	S	X	z
Frequency	12	7	18	10	9	5	2

1. Construct Huffman Tree by showing all the necessary (5pt)
2. Give the code-word of each character using the Huffman Tree from (a) (5pt)

Answer 1

Huffman Algorithm to construct optimal binary prefix code for following letters and corresponding frequency..

It Works as follows--

1. put all letters in a Min-Priority Queue.(Q) and create n trees with one tree contain one letter.

2. remove two elements from Q with minimum frequency

, where x= letter with lowest frequency , and y = letter with 2nd lowest frequency.

3. create a new node(z) whose left child is x and right child is y.

set the frequency of z = frequency(x) + frequency(y)

4,Insert the the node z back to the Q.

5.Repeat step 2 to step 4 n-1 times)n is number of letters).

6. Mark  the left edge with binary 0 and right edge with binary 1.

answer to (b)

Now the code-word of a letter is the collection of the binary symbols from root to that letter

so

code-word of letter A is 00

code-word of letter B is 010

code-word of letter I is 10

code-word of letter M is 111

code-word of letter S is 110

code-word of letter X is 0111

code-word of letter Z is 0110