Struktur Data & Algoritme ( Data Structures & Algorithms ) - - PDF document

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Jan 27, 2023 549 likes •700 views

Struktur Data & Algoritme ( Data Structures & Algorithms ) Tree: application Denny ( denny@cs.ui.ac.id ) Suryana Setiawan ( setiawan@cs.ui.ac.id ) Fakultas I lm u Kom puter Universitas I ndonesia Sem ester Genap - 2 0 0 4 / 2 0 0 5

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1

Struktur Data & Algoritme ( Data Structures & Algorithms)

Denny (denny@cs.ui.ac.id) Suryana Setiawan (setiawan@cs.ui.ac.id)

Fakultas I lm u Kom puter Universitas I ndonesia Sem ester Genap - 2 0 0 4 / 2 0 0 5

Version 2 .0 - I nternal Use Only

Tree: application

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Objectives

understand one of file compression technique

(Huffman)

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Outline

Compression Huffman compression

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Compression

Process: Encoding: raw → compressed Decoding: compressed → raw Types of compression Lossy : MPEG, JPEG Lossless Compression Algorithm: RLE: Run Length Encoding Lempel-Zif Huffman Encoding Performance of compression depends on file types.

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3

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Huffman Compression

If a woodchuck could chuck wood! 32 char × 8 bit = 256 bits 13 distinct characters → 4 bit Compressed code: 128 bits Variable length string of bits to further improve

compression.

Using prefix codes

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Huffman Compression

Frequently occurring letters: short representation. Infrequent letters: long representations.

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i a u e

8 5 3 3

Huffman Encoding: comparation

a = 00 → 16 bits i = 01 → 10 bits u = 10 → 6 bits e = 11 → 6 bits Total : 4 2 bits

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Huffman Encoding: comparation

i 5 a

8

u

3

e

3 6 11 19 a = 0 → 8 bits i = 10 → 10 bits u = 110 → 9 bits e = 111 → 9 bits Total: 3 6 bits

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5

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1 1 1 1 1 1 1 1 1 1 1 1 ! a l u d k w I f h c

space

Huffman Encoding

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13 6 3 4 9 2 32 19 10 7 4 2 !:1 a:1 l:1 u:3 d:3 k:2 w :2 I :1 f:1 h:2 c:5

space:5

Huffman Encoding

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Huffman Encoding (freq)

! = 0 0 0 0 ( 1 ) I = 1 0 0 0 0 ( 1 ) a = 0 0 0 1 0 ( 1 ) f = 1 0 0 0 1 ( 1 ) l = 0 0 0 1 1 ( 1 ) h = 1 0 0 1 ( 2 ) u = 0 0 1 ( 3 ) c = 1 0 1 ( 5 ) d = 0 1 0 ( 3 ) space= 1 1 0 ( 5 ) k = 0 1 1 0 ( 2 )

= 1 1 1 ( 5 )

w = 0 1 1 1 ( 2 ) Cost: ∑ di * fi = 1 1 1 bits = 4 4 % × 2 5 6 bits

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Huffman Encoding: steps

c 5

5

u

3

d

3

w

2

k

2

a

1

l

1

f

1

I

1

h

2

!

1 2

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7

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Huffman Encoding: steps

c 5

5

u

3

d

3

w

2

k

2

f

1

I

1

h

2

!

1

a l

2 2

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Huffman Encoding: steps

c 5

5

u

3

d

3

w

2

k

2

I

1

h

2

a l

2

f !

2 3

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8

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c 5

5

u

3

d

3

w

2

k

2

h

2

a l

2

I f !

3 4

Huffman Encoding: steps

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c 5

5

u

3

d

3

k

2

a l

2

I f !

3 4

w h

4

Huffman Encoding: steps

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9

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Huffman Encoding: steps

c 5

5

u

3

d

3

I f !

3 4

w h k a l

4 6

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Huffman Encoding: steps

c 5

5

f !

3 4

w h k a l

4

u d

6

I

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10

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c 5

5

f !

3 4

w h k a l

4

u d

6

I

7

Huffman Encoding: steps

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Huffman Encoding: steps

c 5

5 4

w h u d

6

f ! k a l I

7 9

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11

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5

u d

6

f ! k a l I

7

c w h

9 10

Huffman Encoding: steps

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u d

6

f ! k a l I

7

c w h

9

13

Huffman Encoding: steps

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12

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c w h

9

u d f ! k a l I

13 19

Huffman Encoding: steps

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u d f ! k a l I

13

c w h

32

Huffman Encoding: steps

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13

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Huffman Encoding: steps

u d f ! k a l I c w h

Total: 111 bits

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Summary

Huffman encoding use frequency information to

compress file.

The most frequent character get a shorter prefix

code, and vice versa.