What is the average number of bits for each letter of the word "amazing" using Huffman coding algorithm? Select one:a.18/7b.19/7c.3d.20/7e.None of thesef.17/7

To answer this question, we first need to understand Huffman coding algorithm and then apply it to the word "amazing".

Huffman coding is a lossless data compression algorithm. The most frequent character gets the smallest code and the least frequent character gets the largest code.

The word "amazing" has 7 letters, and the frequency of each letter is as follows:

• a: 2
• m: 1
• z: 1
• i: 1
• n: 1
• g: 1

Now, we create a Huffman Tree based on these frequencies. The two least frequent characters 'm' and 'z' are taken and a node is created with a frequency count of 2. This process is repeated until we get a complete tree.

The Huffman codes based on this tree would be something like:

• a: 0
• m: 110
• z: 1110
• i: 1111
• n: 101
• g: 100

Now, we calculate the average number of bits per letter. This is done by multiplying the frequency of each letter by the number of bits in its Huffman code, summing these products, and then dividing by the total number of letters.

• a: 2 * 1 = 2
• m: 1 * 3 = 3
• z: 1 * 4 = 4
• i: 1 * 4 = 4
• n: 1 * 3 = 3
• g: 1 * 3 = 3

The sum of these products is 2 + 3 + 4 + 4 + 3 + 3 = 19.

The total number of letters is 7.

So, the average number of bits per letter is 19/7.

Therefore, the answer is b. 19/7.