Question

Using the symbols \({\bf{0, 1, and 2}}\) use ternary \(\left( {{\bf{m = 3}}} \right)\)Huffman coding to encode these letters with the givenfrequencies: \({\bf{A:0}}{\bf{.25, E:0}}{\bf{.30, N:0}}{\bf{.10, R:0}}{\bf{.05, T:0}}{\bf{.12, Z:0}}{\bf{.18}}\).

Short answer

Letters have the following codes:

A - 2

E - 1

N - 010

R - 011

T - 02

Z - 00

Step-by-step solution

Step 1:Given symbols and their frequencies, our goal is to construct a rooted binary tree where the symbols are the labels of the leaves

The algorithm begins with a forest of trees each consisting of one vertex, where each vertex has a symbol as its label and where the weight of this vertex equals the frequency of the symbol that is its label.

Step2:One shall find code of the following letters with given frequencies using three symbols

Given that,\({\bf{A :0}}{\bf{.25, E:0}}{\bf{.30, N :0}}{\bf{.10, R :0}}{\bf{.05, T:0}}{\bf{.12, Z:0}}{\bf{.18}}{\bf{.}}\)

Since,the expression is\(\left( {{\bf{N - 1 mod m - 1}}} \right){\bf{ + 1 = 2}}\).

Firstly, constructs one tree with two least weighted vertices and in following steps, 3 least weighted components are combined together to form a tree.

The codes for the letters

So, the codes for the letters are as follows as per the explanation provided in the:

A - 2

E - 1

N - 010

R - 011

T - 02

Z - 00