Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. Which of the following is the Huffman code for the letter a, b, c, d, e, f?a)0, 10, 110, 1110, 11110, 11111b)11, 10, 011, 010, 001, 000c)11, 10, 01, 001, 0001, 0000d)110, 100, 010, 000, 001, 111Correct answer is option 'A'. Can you explain this answer?

Question

Answer

We get the following Huffman Tree after applying Huffman Coding Algorithm. The idea is to keep the least probable characters as low as possible by picking them first.

The letters a, b, c, d, e, f have probabilities
1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively.

Answer

We get the following Huffman Tree after applying Huffman Coding Algorithm. The idea is to keep the least probable characters as low as possible by picking them first.

The letters a, b, c, d, e, f have probabilities
1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively.

Answer

Huffman Coding:

Huffman coding is a lossless data compression algorithm that is used to encode data efficiently. It is based on the idea that frequently occurring characters should have short codes, while less frequent characters should have longer codes. The algorithm constructs a binary tree of nodes, where each leaf node represents a character and its frequency. The binary code for each character is obtained by traversing the tree from the root to the corresponding leaf node.

Calculating the Huffman Codes:
To calculate the Huffman codes for the given probabilities, we need to follow these steps:

1. Create a priority queue (min heap) to store the nodes of the Huffman tree.
2. Create a leaf node for each character with its probability and add it to the priority queue.
3. While there is more than one node in the priority queue:
a. Remove the two nodes with the lowest probability from the queue.
b. Create a new internal node with these two nodes as children, and its probability as the sum of their probabilities.
c. Add the new node back to the priority queue.
4. The remaining node in the priority queue is the root of the Huffman tree.
5. Traverse the Huffman tree to assign binary codes to each character. Assign '0' to left branches and '1' to right branches.

Calculating Huffman Codes for the Given Probabilities:
Let's calculate the Huffman codes for the given probabilities:

1. Create leaf nodes for each character with their probabilities:
a: 1/2
b: 1/4
c: 1/8
d: 1/16
e: 1/32
f: 1/32

2. Create a priority queue and add the leaf nodes to it.

3. Perform the steps of the Huffman algorithm until there is only one node left in the priority queue:

- Remove the two nodes with the lowest probabilities:
f: 1/32 and e: 1/32
- Create a new internal node with these two nodes as children and their probability as the sum of their probabilities:
fe: 1/32 + 1/32 = 1/16

- Remove the two nodes with the lowest probabilities:
d: 1/16 and c: 1/8
- Create a new internal node with these two nodes as children and their probability as the sum of their probabilities:
dc: 1/16 + 1/8 = 3/16

- Remove the two nodes with the lowest probabilities:
b: 1/4 and dc: 3/16
- Create a new internal node with these two nodes as children and their probability as the sum of their probabilities:
bdc: 1/4 + 3/16 = 7/16

- Remove the two nodes with the lowest probabilities:
a: 1/2 and bdc: 7/16
- Create a new internal node with these two nodes as children and their probability as the sum of their probabilities:
abdc: 1/2 + 7/16 = 15/16

4. The remaining node in the priority queue is the root of the Huffman tree, which is abdc: 15/16.

5. Traverse the Huffman tree to assign binary codes to each

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