GATE CS 2017 Set 2 — Question 50
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Algorithms → Greedy Algorithms → Huffman Coding
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Question
A message is made up entirely of characters from the set . The table of probabilities for each of the characters is shown below:
If a message of 100 characters over is encoded using Huffman coding, then the expected length of the encoded message in bits is ___________.
| Character | Probability |
|---|---|
| 0.22 | |
| 0.34 | |
| 0.17 | |
| 0.19 | |
| 0.08 | |
| Total | 1.00 |
Correct answer
225 to 225
Solution
To find the expected length using Huffman coding, we first construct the Huffman tree by repeatedly combining the two nodes with the lowest probabilities:
1.Initial probabilities:
2.Combine and : . Remaining:
3.Combine and : . Remaining:
4.Combine and : . Remaining:
5.Combine and :
Codeword lengths ():- : 2 bits (Root )
- : 2 bits (Root )
- : 2 bits (Root )
- : 3 bits (Root )
- : 3 bits (Root )
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