Area : Computer Science

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• Area Computer Science
• Subject Algorithms
• Huffman Coding
• Report submitted by- Akash Singhal (07005016)

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Greedy Algorithms are
algorithms that follow the strategy of making the
locally optimum choice at each stage with the
hope of finding the global optimum.Huffman
Coding is an algorithm for lossless data
compression. This algorithm assign
variable-length codes to each symbol used in the
file such that no code is a prefix of the other.

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AIM PROCEDUREThe aim of this animation is to
clarify the concepts of greedy algorithms by
illustrating the problem of HUFFMAN CODING.

• This animation will use a sample file.
• The sample file will be hashed and a table will
  be created containing the frequency of each
  symbol/alphabet used in the file.
• The animation will show the construction of a
  binary tree which shows how a code is allotted to
  every symbol while compressing a data file.

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Problem Statement Given a file find a code
allotment for every symbol used in the file such
that the size of the compressed is minimum. For
well-defined interpretation of codes no code is a
prefix of another code.

• Combine the two symbols of least frequency to
  make it a single node with its frequency equal to
  the sum of the frequencies of both.

ab (5)
a (2)
b (3)
a (2)
b (3)
5

• The process continues like that until the final
  shape of the tree becomes like this

abcdef(19)
abc (9)
def (10)
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• Now the animation shows unfolding of the tree
  such that it shows the code allotment

abcdef(30)
abcdef(30)
0
1
0
1
abc (9)
abc (9)
def (21)
def (21)
0
1
c (4)
ab (5)
1
0
d (6)
ef (15)
7
abcdef(30)
0
1
abc (9)
def (21)
0
1
c (4)
1
0
ab (5)
d (6)
ef (15)
0
0
1
1
a (2)
b (3)
f (8)
e (7)
Code Allotment using Huffman Coding
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Review Questions

• Huffman coding is an example of _________
  algorithms. (ans- greedy)
• Huffman coding uses this data structure for code
  allotment (ans- binary tree)
• If the code for a is 001 then which of these
  can be a code for b
• a) 0100
• b) 0010
• c) 0011
• Ans- 0100 (because no code is a prefix of
  another)
• If there are 20 symbols in a file, how many
  leaves will the binary tree of huffman coding
  have? (Ans- 20)
• Since no code can be a prefix of another, in
  order to optimize the compression we must ensure
  that the symbol with highest frequency has
  smallest possible code and the symbol with least
  frequency has a code not smaller than others.
  Verify.

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Further Interactivity

• The user can himself upload a file and the
  animation can then return the user a table
  showing the frequency of each symbol used in the
  file and the code allotted to each symbol.
• An animation for the user uploaded file.
• We can also return the user a compressed version
  of his file. Hence this animation can act as a
  file compression tool also.

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Further Reading Links

• http//en.wikipedia.org/wiki/Huffman_coding
• http//www.cdeep.iitb.ac.in/nptel/Computer20Scien
  ce/Design20and20Analysis20of20Algorithms/TOC.h
  tm

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CREDITS