Huffman Presantation

8/8/2019 Huffman Presantation

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DATA STRUCTURE

Huffman Tree : Project

S ubmitted to : S ir Abdul Wahab

S ubmitted by:

Muzmmal Hussain

Muhammad Zia S hahid

Riasat Ali



´In computer science and inf ormation theory, Huff man

coding is an entropy encoding alg orithm used f or

lossless data compressionµ

What Is Huf fman Tree . .?





Huff man tree is a eleg ant f orms of a data compressions. It is based

On minimum redundancy coding . We need represent the data in a way

that makes the data required less space.

Need O f Hu f f man Co d i n g



Huff man coding is most eff icient f orm of a binary

tree.

Adaptive Huff man coding

I S T H I S D AT A S T R U C T U R E D E R I V E F R O M

A N Y D A T A S T R U C T U R E

A R E T H E R E A N Y D S T H A T A R E D E R I V E D

F R O M I T ?



Huff man is used to compressed the f iles.

Huff man is used to minimized the binary code

Huff man is used in compression tools and also in f ax machine

Reduce storag e needed

Reduce size of data e.g . imag es audio video and text

Reduce transmission cost and band width

A d va n t a g e o f Hu f f ma n



Chang ing ensemble

If the ensemble chang es the f requencies and probabilities chang e the optimal coding chang es

e.g . in text compression symbol f requencies vary with context

Re-computing the Huff man code by running throug h the entire f ile in ad vance?!

Saving/ transmitting the code too?!

Does not consider ¶blocks of symbols·

¶ string s_of _ch· the next nine symbols are predictable ¶aracters_· ,but bits are used without con veying any new inf ormation

Disad vantag e of Huff man



The run time complexity of Huff man is 0( n),where n is number is a

symbol in the orig inal data. Each of these runs is 0 ( n) times.

The time to build the Huff man tree does not eff ect the complexity

of Huff man compress because a running time of this process

depends only on the number of diff erent symbols in the data which in

this implantation is a constant

Cost Of Huff man



On a computer: chang ing the representation of a f ile so that it takes less

space to store or/and less time to transmit. ² orig inal f ile can be reconstructed exactly f rom the

compressed representation.

diff erent than data compression in g eneral

² text compression has to be lossless.

² compare with sound and imag es: small chang es and noise is

tolerated.

Tex t C omp r e s s i o n



We can construct lossless compression by f ollowing alg orithm

Let the word ABRACADABRA

What is the most economical way to write this string in a binary

representation?

Generally speaking , if a text consists of N diff erent characters, we

need bits log[ N] bits to represent each one using a f ixed-

leng th encoding .

Co n s t r u c t i o n O f Hu f f ma n



Thus, it would require 3 bits f or each of 5

diff erent letters, or 33 bits f or 11 letters.

Can we do it better?



We can do better, provided:

² Some characters are more f requent than others.

² Characters may be diff erent bit leng ths, so that f or

example, in the Eng lish alphabet letter a may use

only one or two bits, while letter y may use several.

² We have a unique way of decoding the bit stream.

YES!!!!



U s i n g Va r i a b l e - l e n g t h En c o d i n g ( 1 )

Mag ic word: ABRACADABRA

LET A = 0

B = 100

C = 1010

D = 1011

R = 11

Thus, ABRACADABRA = 01001101010010110100110

So 11 letters demand 23 bits < 33 bits, an improvement of about

30%.



U s i n g Va r i a b l e - l e n g t h En c o d i n g ( 2 )

However, there is a serious dang er: How to ensure unique

reconstruction?

Let A -> 01 and B -> 0101

How to decode 010101?

AB?

BA?

AAA?



N o P r o b l em«««

if we use pref ix codes: no code word is a pref ix of another code

word.

Any pref ix code can be represented by a f ull binary tree.

Each leaf stores a symbol.

Each node has two children ² lef t branch means 0, rig ht means 1.

code word = path f rom the root to the leaf interpreting suitably

the lef t and rig ht branches.



P r e f i x Co d e s ( 2 )

ABRACADABRA

A = 0

B = 100

C = 1010

D = 1011

R = 11



Decoding is unique and simple!

Read the bit stream f rom lef t to rig ht and starting f rom the root,

whenever a leaf is reached,

write dow n its symbol and return to the root.





CO NS TR U CTI NG A H UFF MA N CO DE(1 )

Assume that frequencies of symbols are:

² A: 40 B: 20 C: 10 D: 10 R: 20

S mallest numbers are 10 and 10 (C and D), so connect them




C and D have already been used, and the new node above them (call it C+D)

has value 20

The smallest values are B, C+D, and R, all of which have value 20

² Connect any two of these

It is clear that the alg orithm does not construct a unique tree, but

even if we have chosen the other possible connection, the code would

be optimal too!






The smallest value is R, while A and B+C+D have value 40.

Connect R to either of the others.



CO NS TR U CTI NG A H UFF MA N CODE(4 )

Connect the final two nodes, adding 0 and 1 to each left and right branch

respectively.



A: 40 B: 20 C: 10 D: 10 R: 20

A = 0

B = 100

C = 1010

D = 1011

R = 11

20(B ) 10(C ) 10(D ) 20(R )

20

0

0

0

0

11

1

1

Date post:	09-Apr-2018
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Huffman Presantation

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