I need someone to explain this problem step by step. I need a briefe explanation to the side of the calculation to understand the problem.Thanks For the following letter frequency table, a Huffman Code was constructed as shownbelow. The associated tree is also shown below.LetterFrequencyHuffman CodeE1201L42110E037D421017910186U371000107C32111010M2411111K7111101Z2111100(a) Is there another code and a tree possible? What is (are) the difference(s)?(b) Compute the redundancy= Average Codeword Length (Lav) - Entropy (H(x)).The entropy H(x) is calculated from H(x) -Ei=1 Pilogpi-(c) Check if this redundancy is less than p₁ + 0.086, where pi is the probability ofthe most common symbol.(d) Also, check if the following inequality is satisfied:H(x) ≤ Lav ≤ H(x) + 1.Repeat parts (b), (c), (d) for a different tree you built. What conclusions can youdraw?

Answered: For the following letter frequency…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

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I need someone to explain this problem step by step. I need a briefe explanation to the side of the calculation to understand the problem. Thanks

For the following letter frequency table, a Huffman Code was constructed as shown
below. The associated tree is also shown below.
Letter
Frequency
Huffman Code
E
120
1
L
42
110
E
0
37
D
42
101
79
1
0
186
U
37
100
0
107
C
32
1110
1
0
M
24
11111
K
7
111101
Z
2
111100
(a) Is there another code and a tree possible? What is (are) the difference(s)?
(b) Compute the redundancy= Average Codeword Length (Lav) - Entropy (H(x)).
The entropy H(x) is calculated from H(x) -Ei=1 Pilogpi-
(c) Check if this redundancy is less than p₁ + 0.086, where pi is the probability of
the most common symbol.
(d) Also, check if the following inequality is satisfied:
H(x) ≤ Lav ≤ H(x) + 1.
Repeat parts (b), (c), (d) for a different tree you built. What conclusions can you
draw?

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where did you get 20/51 , 7/51 and so on? does entropy is not equal to the sumation of pilog2pi? or why is divede it by 1/pi . how do you calculate Lav

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