A text is made up of the characters a, b, c, d, e each occurring with the probability 0.11, 0.40, 0.16, 0.09 and 0.24 respectively. The optimal Huffman coding technique will have the average length of :

The correct answer is option 2.

Key Points

Concept:

Huffman coding is a data compression technique. It constructs a tree by selecting the minimum frequency of available nodes. And assign the weights 1 for the left child and 0 for the right child or 0 for the left child and 1 for the right-left.

Add all the internal nodes of the tree

Average length =1 + 0.6 + 0.36 + 0.20 = 2.16

OR

Length of A = 1111 = 4 × 0.11 = 0.44
Length of B = 0 = 1 × 0.4 = 0.4
Length of C = 110 = 3 × 0.16 = 0.48
Length of D = 1110 = 4 × 0.09 = 0.36
Length of E = 10 = 2 × 0.24 = 0.48
Average length = 0.36 + 0.4 + 0.72 + 0.6 + 0.24
= 2.16
∴ Hence the correct answer is 2.16.