Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Suppose the letters a, b, c, d, e, f have pro...
Start Learning for Free
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?
- a)3
- b)2.1875
- c)2.25
- d)1.9375
Correct answer is option 'D'. 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 is a lossless data compression algorithm that assigns variable-length codes to characters based on their frequencies. The more frequent the character, the shorter the code.
To find the average length of Huffman codes for the given probabilities, we can follow these steps:
Step 1: Arrange the probabilities in descending order
- a: 1/2
- b: 1/4
- c: 1/8
- d: 1/16
- e: 1/32
- f: 1/32
Step 2: Build a Huffman tree
- Combine the two lowest probabilities (e and f) to create a subtree with a probability of 1/16.
- Combine the next lowest probability (d) with the subtree to create a subtree with a probability of 3/32.
- Combine the next lowest probability (c) with the subtree to create a subtree with a probability of 7/64.
- Combine the next lowest probability (b) with the subtree to create a subtree with a probability of 15/128.
- Combine the highest probability (a) with the subtree to create the root of the tree with a probability of 31/256.
The resulting Huffman tree looks like this:
```
/\
/ \
/ \
/ \
/ \
/ \
e/f d
/ \ / \
e f c b
```
Step 3: Assign codes to the characters
- Traverse the tree from the root to each leaf, assigning a 0 for a left branch and a 1 for a right branch.
- The codes for each character are as follows:
a: 0
b: 111
c: 1101
d: 1100
e: 1000
f: 1001
Step 4: Calculate the average length of the codes
- Multiply each code length by its probability and sum the results:
(0)(1/2) + (3)(1/4) + (4)(1/8) + (4)(1/16) + (4)(1/32) + (4)(1/32) = 31/16
- Therefore, the average length of the Huffman codes is 31/16 or 1.9375.
To find the average length of Huffman codes for the given probabilities, we can follow these steps:
Step 1: Arrange the probabilities in descending order
- a: 1/2
- b: 1/4
- c: 1/8
- d: 1/16
- e: 1/32
- f: 1/32
Step 2: Build a Huffman tree
- Combine the two lowest probabilities (e and f) to create a subtree with a probability of 1/16.
- Combine the next lowest probability (d) with the subtree to create a subtree with a probability of 3/32.
- Combine the next lowest probability (c) with the subtree to create a subtree with a probability of 7/64.
- Combine the next lowest probability (b) with the subtree to create a subtree with a probability of 15/128.
- Combine the highest probability (a) with the subtree to create the root of the tree with a probability of 31/256.
The resulting Huffman tree looks like this:
```
/\
/ \
/ \
/ \
/ \
/ \
e/f d
/ \ / \
e f c b
```
Step 3: Assign codes to the characters
- Traverse the tree from the root to each leaf, assigning a 0 for a left branch and a 1 for a right branch.
- The codes for each character are as follows:
a: 0
b: 111
c: 1101
d: 1100
e: 1000
f: 1001
Step 4: Calculate the average length of the codes
- Multiply each code length by its probability and sum the results:
(0)(1/2) + (3)(1/4) + (4)(1/8) + (4)(1/16) + (4)(1/32) + (4)(1/32) = 31/16
- Therefore, the average length of the Huffman codes is 31/16 or 1.9375.
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Top Courses for Computer Science Engineering (CSE)View all
Question Description
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer?.
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer?.
Solutions for Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?a)3b)2.1875c)2.25d)1.9375Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup