Huffman coding is a data compression technique that reduces file size without losing detail by using variable length encoding based on character frequency. Developed by David Huffman, it constructs a binary tree where characters that appear more frequently receive shorter codes. The two major steps in Huffman coding involve building this tree from input characters and assigning codes based on the tree's structure.

1. Greedy Technique

2. Huffman coding
0 Huffman Coding is a technique of compressing data to
reduce its size without losing any of the details. It was
first developed by David Huffman.
0 Huffman Coding is generally useful to compress the data.
0 It uses variable length encoding.
0 It assigns variable length code to all the characters.
0 The code length of a character depends on how
frequently it occurs in the given text.
0 The character which occurs most frequently gets the
smallest code.
0 The character which occurs least frequently gets the
largest code.
0 It is also known as Huffman Encoding.

3. Encoding
• Fixed Length encoding (ASCII Encoding)
• Variable length encoding(Huffman Encoding)

4. Fixed length encoding/ASCII Encoding
• Fixed Length encoding has same length of code for all
the characters.
same length m>=Log2n
Ex: BCCADECEE message to be sent on network
In ASCII encoding, each character occupies 8 bits. There
are a total of 15 characters in the above string. Thus, a
total of 9*8=48 bits are required to send the above
string.

5. Contd.,
0 Using the Huffman Coding technique, we can
compress the string to a smaller size.
0 Because Huffman coding uses variable length
coding to generate different length code for
each character.
0 Huffman coding first creates a tree using the
frequencies of the character and then generates
code for each character.
0 There are two major steps in Huffman Coding-
1.Building a Huffman Tree from the input characters.
2.Assigning code to the characters by traversing the
Huffman Tree.

6. Huffman Tree
The steps involved in the construction of Huffman Tree are
as follows-
• Create a leaf node for each character of the text.
• Leaf node of a character contains the occurring frequency
of that character.
• Arrange all the nodes in increasing order of their frequency
value.
• Considering the first two nodes having minimum frequency
create a new internal node.
• The frequency of this new node is the sum of frequency of
those two nodes.
• Make the first node as a left child and the other node as a
right child of the newly created node.
• Keep repeating until all the nodes form a single tree.
• The tree finally obtained is the desired Huffman Tree.

7. Huffman Code
0 Now,
• We assign weight to all the edges of the constructed
Huffman Tree.
• Assign weight ‘0’ to the left edges and weight ‘1’ to the
right edges.
0 Rule
• If we assign weight ‘0’ to the left edges, then assign
weight ‘1’ to the right edges.
• If we assign weight ‘1’ to the left edges, then assign
weight ‘0’ to the right edges.
• Any of the above two conventions may be followed.
• But we must follow the same convention at the time of
decoding that is adopted at the time of encoding.

8. 0.25
0.1
B
0.15
_
0.2
C
0.2
D
0.35
A
0.2
C
0.2
D
0.35
A
0.1
B
0.15
_
0.4
0.2
C
0.2
D
0.6
0.25
0.1
B
0.15
_
0.6
1.0
0 1
0.4
0.2
C
0.2
D
0.25
0.1
B
0.15
_
0 1 0
0
1
1
0.25
0.1
B
0.15
_
0.35
A
0.4
0.2
C
0.2
D
0.35
A
0.35
A
character A B C D _
frequency 0.35 0.1 0.2 0.2 0.15
codeword 11 100 00 01 101
Average bits per character: 2.25
(0.35*2+0.1*3+02*2+0.2*2+0.15*3=2.25)/
sum(frequencies)
= 2.25/(0.35+0.1+0.2+0.2+0.15)
=2.25/ 0.8369
=2.7
Example 1:

9. Encoding and Decoding
Encode the Text: AB_CD_AB
AB_CD_AB
w.k.t codeword A=11 B=100 C=00 D=01 _= 101
Encoded msg is: 11100101000110111100
Decode the Text: 11100101000110111100
AB_CD_AB

10. Example -2
Frequency
Character

11. Final Soln:
A=111
I=00
S=01
E=10
T=11000
O=11001
U=1101

12. Example 3:
character A B C D _
frequency 0.4 0.1 0.2 0.15 0.15
codeword 1 000 011 001 010