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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, 11111
- b)11, 10, 011, 010, 001, 000
- c)11, 10, 01, 001, 0001, 0000
- d)110, 100, 010, 000, 001, 111
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8,...
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.
Most Upvoted Answer
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8,...
Huffman Coding
Huffman coding is a technique used for lossless data compression. It is commonly used in file compression algorithms, where it assigns variable-length codes to different characters based on their frequency of occurrence in the file. The characters with higher frequency are assigned shorter codes and vice versa.
Finding the Huffman Code
To find the Huffman codes for the given set of letters, we need to follow the steps below:
1. Arrange the letters in descending order of their probabilities:
a: 1/2
b: 1/4
c: 1/8
d: 1/16
e: 1/32
f: 1/32
2. Merge the two least probable letters and assign a new probability, which is the sum of their probabilities.
a: 1/2
b: 1/4
c: 1/8
d: 1/16
ef: 1/32 + 1/32 = 1/16
3. Repeat step 2 until all the letters are merged into a single tree.
a: 1/2
b: 1/4
c: 1/8
def: 1/16 + 1/16 = 1/8
abcdef: 1/2 + 1/4 + 1/8 + 1/8 = 1
4. Assign 0 to the left branch and 1 to the right branch at each bifurcation.
a: 0
b: 10
c: 110
d: 1110
e: 11110
f: 11111
Therefore, the correct answer is option 'A': 0, 10, 110, 1110, 11110, 11111.
Huffman coding is a technique used for lossless data compression. It is commonly used in file compression algorithms, where it assigns variable-length codes to different characters based on their frequency of occurrence in the file. The characters with higher frequency are assigned shorter codes and vice versa.
Finding the Huffman Code
To find the Huffman codes for the given set of letters, we need to follow the steps below:
1. Arrange the letters in descending order of their probabilities:
a: 1/2
b: 1/4
c: 1/8
d: 1/16
e: 1/32
f: 1/32
2. Merge the two least probable letters and assign a new probability, which is the sum of their probabilities.
a: 1/2
b: 1/4
c: 1/8
d: 1/16
ef: 1/32 + 1/32 = 1/16
3. Repeat step 2 until all the letters are merged into a single tree.
a: 1/2
b: 1/4
c: 1/8
def: 1/16 + 1/16 = 1/8
abcdef: 1/2 + 1/4 + 1/8 + 1/8 = 1
4. Assign 0 to the left branch and 1 to the right branch at each bifurcation.
a: 0
b: 10
c: 110
d: 1110
e: 11110
f: 11111
Therefore, the correct answer is option 'A': 0, 10, 110, 1110, 11110, 11111.
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