Question

5 pts) Huffman's greedy algorithm builds up an optimal way of representing each character as a binary string. HUFFMAN (C) 1. n=∣C∣//C is a set of n characters, c∈C 2. Q=C// initialize the min-priority queue Q 3. for i=1 to n−1// we have n−1 internal nodes 4. allocate a new node z 5. z.left=x= EXTRACT-MIN (Q) 6. z.right =y=EXTRACT−MIN(Q) 7. z. freq =x.freq +y.freq // a. freq: gives its frequency 8. INSERT (Q,z) 9. return EXTRACT-MIN (Q)// return the root of the tree What is an optimal Huffman code for the following set of frequencies, based on the first 8 Fibonacci numbers?

Answer 1

The optimal Huffman code for the set of frequencies based on the first 8 Fibonacci numbers is not explicitly provided in the given question.

Step-by-step explanation:

Huffman's greedy algorithm is used to construct an optimal prefix-free binary tree for encoding characters with variable-length codes, where the more frequent characters have shorter codes. The algorithm starts with a set of characters and their frequencies and builds a binary tree based on a priority queue.

In this context, the frequencies of characters are determined by the first 8 Fibonacci numbers. However, the actual values of these frequencies are not given, making it impossible to provide a specific optimal Huffman code without knowing the frequencies of the characters.

To obtain an optimal Huffman code, one would need the specific frequency values for each character. These frequencies would then be used in the Huffman algorithm to construct a binary tree, and the codes for each character would be derived from the tree structure.

In summary, while the algorithm and approach for constructing an optimal Huffman code are outlined, the absence of actual frequency values in the provided question prevents the calculation of the specific Huffman code for the given set of characters.