26 Lecture

1. Which of the following is a lossless data compression algorithm? a) Huffman encoding b) Arithmetic encoding c) Run-length encoding d) All of the above

Answer: d) All of the above

2. In Huffman encoding, the symbols to be encoded are represented as what? a) A binary tree b) A prefix code c) A suffix code d) None of the above

Answer: a) A binary tree

3. What is the goal of Huffman encoding? a) To compress data by representing frequently occurring symbols in a compressed form b) To convert data from analog to digital form c) To encrypt data for secure transmission d) None of the above

Answer: a) To compress data by representing frequently occurring symbols in a compressed form

4. How is the Huffman tree built? a) By merging the two most frequent symbols at each step b) By merging the two least frequent symbols at each step c) By randomly selecting symbols to be included d) None of the above

Answer: b) By merging the two least frequent symbols at each step

5. Which of the following is NOT a property of the Huffman code? a) Prefix-free b) Uniquely decodable c) Provides a compact representation of the original data d) Lossy compression

Answer: d) Lossy compression

6. What is a prefix code in Huffman encoding? a) A code in which no codeword is a prefix of any other codeword b) A code in which each symbol is represented by the same number of bits c) A code in which the codewords are sorted in order of frequency d) None of the above

Answer: a) A code in which no codeword is a prefix of any other codeword

7. Which of the following is a disadvantage of Huffman encoding? a) It requires the entire input to be available at once b) It is slow to encode and decode c) It cannot be used with binary data d) None of the above

Answer: a) It requires the entire input to be available at once

8. What is the time complexity of building a Huffman tree? a) O(n) b) O(n log n) c) O(n^2) d) None of the above

Answer: b) O(n log n)

9. What is the space complexity of building a Huffman tree? a) O(n) b) O(log n) c) O(n log n) d) None of the above

Answer: a) O(n)

10. Which of the following is an application of Huffman encoding? a) Lossy audio compression b) Lossless image compression c) Data encryption d) None of the above

Answer: b) Lossless image compression

1. What is Huffman encoding and how does it work? Huffman encoding is a lossless data compression algorithm that uses variable-length codes to represent characters. It works by assigning shorter codes to more frequently occurring characters and longer codes to less frequently occurring characters.

2. What is the difference between Huffman coding and Shannon-Fano coding? Huffman coding is a bottom-up approach while Shannon-Fano coding is a top-down approach. Huffman coding is more efficient than Shannon-Fano coding in terms of the length of the code words.

3. What is the optimal prefix property in Huffman coding? The optimal prefix property states that no codeword is a prefix of another codeword.

4. How do you construct a Huffman tree? To construct a Huffman tree, you start by creating a leaf node for each character and assigning a weight to each node. Then you repeatedly merge the two nodes with the smallest weights into a new parent node until there is only one node left, which is the root of the Huffman tree.

5. What is the advantage of using Huffman encoding over other compression algorithms? Huffman encoding is very efficient in terms of compression ratio because it assigns shorter codes to more frequently occurring characters. It also preserves the original data without any loss.

6. What is the role of a Huffman table in data compression? A Huffman table is a lookup table that maps each character to its corresponding Huffman code. It is used to encode and decode data during compression and decompression.

7. Can Huffman encoding be used for lossy data compression? No, Huffman encoding is a lossless data compression algorithm and cannot be used for lossy data compression.

8. How does the size of the input data affect the compression ratio in Huffman encoding? The compression ratio in Huffman encoding depends on the frequency of occurrence of each character in the input data. The larger the input data, the more accurate the frequency count, and the better the compression ratio.

9. How does the order of the input data affect the Huffman tree construction? The order of the input data does not affect the Huffman tree construction, as the algorithm only looks at the frequency of occurrence of each character.

10. How do you decode a Huffman-encoded message? To decode a Huffman-encoded message, you start at the root of the Huffman tree and follow the path corresponding to each bit in the encoded message until you reach a leaf node, which represents a character. Repeat this process until you have decoded the entire message.

Huffman encoding is a lossless data compression algorithm that encodes a message using variable-length codes based on the frequency of each character. It was invented by David A. Huffman in 1952 while he was a PhD student at MIT. The algorithm works by building a binary tree called a Huffman tree or a minimum-redundancy code. Each leaf node of the tree represents a character in the message, and the path from the root to a leaf node represents the binary code for that character. The more frequently a character appears in the message, the closer its corresponding leaf node is to the root of the tree, and the shorter its binary code. To build the Huffman tree, the algorithm first creates a leaf node for each character in the message and assigns each node a weight equal to the frequency of that character in the message. It then repeatedly combines the two nodes with the lowest weight into a new internal node, whose weight is the sum of the weights of its two children. This process continues until all the nodes are combined into a single root node, which represents the entire message. The algorithm then traverses the Huffman tree to assign a binary code to each character in the message, starting at the root and following the path to the corresponding leaf node. The binary code for each character is then stored in a lookup table or directly embedded in the compressed message. Huffman encoding is widely used in file compression software, such as gzip and PKZIP, and in various communication protocols, such as JPEG and MPEG. It is a simple yet powerful algorithm that can achieve significant compression ratios for messages with a skewed distribution of characters.