Homework Answers
Procedure:
1. Arrange symbols in ascending order of their probability.
2. Choose first 2 minimum probability and make them node, then add their probability, and then again arrange remaining probabilities and this sum, arrange in ascending order.
3 repeat 1st and 2nd till all symbols are covered.
Solution for given problem:-
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Problem A (1 pt). Draw a Huffman tree for the following symbols and their probabilities. Probabil...
4 [20 Points] Derive the Huffman tree for the symbols with probabilities given below. Show the...
4 [20 Points] Derive the Huffman tree for the symbols with probabilities given below. Show the codewords for the symbols and compute the average code length. A: 0.18, B: 0.2, C: 0.05, D: 0.36, E: 0.09, F: 0.12
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities...
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities (0.1,0.1,0.2 ,0.2, 0.4), respectively. For such data, two different sets of Huffman codes can result from a different tie breaking during the construction of the Huffman trees. • Construct the two Huffman trees. (8 points) Construct the Huffman codes for the given symbols for each tree. (4 points) Show that both trees will produce the same average code length. (4 points) For data transmission...
Find the optimal binary symbol code using the Huffman coding algorithm. Draw the Huffman tree (show...
Find the optimal binary symbol code using the Huffman coding algorithm. Draw the Huffman tree (show intermediate steps) and list the final prefix code for each letter. letter : { a b c d e f g } frequency: {.01, .24, .05, .20, .47, .01, .02}
3. (20 points) Draw the frequency array and a huffman tree for the following string: "dogs...
3. (20 points) Draw the frequency array and a huffman tree for the following string: "dogs do not spot hot pots or cats”. Now also show how many bits does the huffman encoding of this string take.
# 1. discuss the relevance of huffman code. give the huffman code and code tree for...
# 1. discuss the relevance of huffman code. give the huffman code and code tree for the following: Algorithm Rocks!
Consider the following symbols with their corresponding frequencies: A:1, B:1, 0:2, D:3, E:5, F:8, G :...
Consider the following symbols with their corresponding frequencies: A:1, B:1, 0:2, D:3, E:5, F:8, G : 13, H: 21 Problem 2.a. (3 points) • Construct the Huffman coding of these symbols along with its optimal coding tree. Problem 2.b. (3 points) • Use your coding tree to decode 0001001000010000000001001
Suppose we have another file with only ASCII symbols. But we decided to encode the file...
Suppose we have another file with only ASCII symbols. But we decided to encode the file in the following way using Huffman Encoding: instead of treating each character as a unique symbol, we use 2 characters together as a unique symbol. For example, if the file content is ABABCCDD. Then there are 4 total symbols (2 ABs, 1 CC, and 1 DD). Please explain how this approach to construct symbols may impact the compression process. More specifically, explain how this...
(b.) Huffman code is a way to encode information using variable-length binary strings to represent symbols depending on the frequency of each individual letter. Specifically, letters that appear more...
(b.) Huffman code is a way to encode information using variable-length binary strings to represent symbols depending on the frequency of each individual letter. Specifically, letters that appear more frequently can be encoded into strings of shorter lengths, while rarer letters can be turned into longer binary strings. On average, Huffman code is a more efficient way to encode a message as the number of bits in the output string will be shorter than if a fixed-length code was used....
9. (4) Select the best choice as Huffman code for the following symbols and their probabilities:...
9. (4) Select the best choice as Huffman code for the following symbols and their probabilities: A-0.10 C-0.17 E-0.21 B-0.21 D-0.06 F-0.25 (a) A: O, B: 10, C: 110, D: 1110, E: 11110, F: 11111 (b) A: 0,B: 10, C: 11111, D: 1110, E: 11110, F: 110 (c) A: 11110, B: 10, C: 1110, D: 11111, E: 110, F: 0 (d) A: 11111, B: 11110, C: 1110, D: 110, E: 10, F: 0 (e) A: 0,B: 01, C: 0001, D:...
I am not sure if it's 0.363 Draw a tree diagram to represent the problem. At...
I am not sure if it's 0.363
Draw a tree diagram to represent the problem. At the end of each branch use symbols to represent the event that the branch corresponds to and give the probability of the event Two cards are selected randomly without replacement from a standard deck of 52 cards. The color of each card (red or black) is recorded. Draw a tree diagram showing the possible outcomes and their probabilities for this problem. Probability Event (R...
4 [20 Points] Derive the Huffman tree for the symbols with probabilities given below. Show the codewords for the symbols and compute the average code length. A: 0.18, B: 0.2, C: 0.05, D: 0.36, E: 0.09, F: 0.12
Problem (A1) (20 points): Huffman Coding Consider a message having the 5 symbols (A,B,C,D,E) with probabilities (0.1,0.1,0.2 ,0.2, 0.4), respectively. For such data, two different sets of Huffman codes can result from a different tie breaking during the construction of the Huffman trees. • Construct the two Huffman trees. (8 points) Construct the Huffman codes for the given symbols for each tree. (4 points) Show that both trees will produce the same average code length. (4 points) For data transmission...
3. (20 points) Draw the frequency array and a huffman tree for the following string: "dogs do not spot hot pots or cats”. Now also show how many bits does the huffman encoding of this string take.
Consider the following symbols with their corresponding frequencies: A:1, B:1, 0:2, D:3, E:5, F:8, G : 13, H: 21 Problem 2.a. (3 points) • Construct the Huffman coding of these symbols along with its optimal coding tree. Problem 2.b. (3 points) • Use your coding tree to decode 0001001000010000000001001
(b.) Huffman code is a way to encode information using variable-length binary strings to represent symbols depending on the frequency of each individual letter. Specifically, letters that appear more frequently can be encoded into strings of shorter lengths, while rarer letters can be turned into longer binary strings. On average, Huffman code is a more efficient way to encode a message as the number of bits in the output string will be shorter than if a fixed-length code was used....
9. (4) Select the best choice as Huffman code for the following symbols and their probabilities: A-0.10 C-0.17 E-0.21 B-0.21 D-0.06 F-0.25 (a) A: O, B: 10, C: 110, D: 1110, E: 11110, F: 11111 (b) A: 0,B: 10, C: 11111, D: 1110, E: 11110, F: 110 (c) A: 11110, B: 10, C: 1110, D: 11111, E: 110, F: 0 (d) A: 11111, B: 11110, C: 1110, D: 110, E: 10, F: 0 (e) A: 0,B: 01, C: 0001, D:...
I am not sure if it's 0.363
Draw a tree diagram to represent the problem. At the end of each branch use symbols to represent the event that the branch corresponds to and give the probability of the event Two cards are selected randomly without replacement from a standard deck of 52 cards. The color of each card (red or black) is recorded. Draw a tree diagram showing the possible outcomes and their probabilities for this problem. Probability Event (R...
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