Question

Construct two different Huffman codes for these symbols and frequencies: \({\bf{t: 0}}{\bf{.2, u: 0}}{\bf{.3, v: 0}}{\bf{.2, w: 0}}{\bf{.3}}\).

Short answer

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.

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.

Step 2:One shall find two different codes for the given set of letters with frequencies

In total there are four different possibilities to make a tree.But the \({\bf{2}}\) different codes for the letters are shown below,

The first different codes for the letters.

First way,

\(\begin{array}{l}{\bf{t - 10 }}\\{\bf{u - 00 }}\\{\bf{v - 11 }}\\{\bf{w - 01}}\end{array}\)

The second different codes for the letters

Second way,

\(\begin{array}{l}{\bf{t - 11}}\\{\bf{u - 01 }}\\{\bf{v - 10 }}\\{\bf{w - 00}}\end{array}\)

Hence, the Huffman code will be