Thuat Toan Huffman

7/31/2019 Thuat Toan Huffman

1/17FIT-HCMUS

Ging vin:

Vn Ch Nam Nguyn Th Hng Nhung ng Nguyn c Tin

Gii thiu

Mt s khi nim

Gii thut nn Huffmantnh

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Cu trc d liu v gii thut - HCMUS 2011


2/17FIT-HCMUS

Thut ng:Data compression

Encoding

Decoding

Lossless data compression

Lossy data compression

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Nn d liuNhu cu xut hin ngay sau khi h thng my tnh u

tin ra i.

Hin nay, phc v cho cc dng d liu a phng tin

Tng tnh bo mt.

ng dng: Lu tr

Truyn d liu


3/17FIT-HCMUS


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Nguyn tc: Encode v decode s dng cng mt scheme.

encode decode


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T l nn (Data compression ratio) T l gia kch thc ca d liu nguyn thy v ca

d liu sau khi p dng thut ton nn.

Gi:N l kch thc ca d liu nguyn thy,

N1 l kch thc ca d liu sau khi nn. T l nn R:

V d:D liu ban u 8KB, nn cn 2 KB. T l nn: 4-1

1N

NR


4/17FIT-HCMUS


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T l nn (Data compression ratio)V kh nng tit kim khng gian: T l ca vic gim

kch thc d liu sau khi p dng thut ton nn.

Gi:N l kch thc ca d liu nguyn thy,

N1 l kch thc ca d liu sau khi nn.

T l nn R:

V d:D liu ban u 8KB, nn cn 2 KB. T l nn: 75%

N

NR

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Nn d liu khng mt mt thng tin (Lossless datacompression)

Cho php d liu nn c phc hi nguyn vn nh dliu nguyn thy (lc cha c nn).

V d: Run-length encoding

LZW

ng dng:nh PCX, GIF, PNG,.. Tp tin *. ZIP ng dng gzip (Unix)


5/17FIT-HCMUS


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Nn d liu mt mt thng tin (Lossy datacompression)

D liu nn c phc hi khng ging hon ton vi d liu nguyn thy; gn ging c th s dng c.

ng dng:Dng nn d liu a phng tin (hnh nh, m

thanh, video):nh: JPEG, DjVu;m thanh: AAC, MP2, MP3; Video: MPEG-2, MPEG-4


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6/17FIT-HCMUS


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Mong mun:Mt gii thut nn bo ton thng tin;

Khng ph thuc vo tnh cht ca d liu;

ng dng rng ri trn bt k d liu no, vi hiusut tt.


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T tng chnh: Phng php c: dng 1 dy bit c nh biu din 1 k t

David Huffman (1952): tm ra phng php xc nh m ti utrn d liu tnh : S dng vi bit biu din 1 k t (gi l m bit bit code)

di m bit cho cc k t khng ging nhau: K t xut hin nhiu ln: biu din bng m ngn; K t xut hin t : biu din bng m di

=> M ha bng m c di thay i (Variable LengthEncoding)


7/17FIT-HCMUS


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Gi s c d liu sau y:ADDAABBCCBAAABBCCCBBBCDAADDEEAA

Biu din 8 bit/k t cn:(10 + 8 + 6 + 5 + 2) * 8 = 248 bit

K t Tn s xut hin

A 10

B 8

C 6

D 5

E 2


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D liu:ADDAABBCCBAAABBCCCBBBCDAADDEEAA

Biu din bng chiu di thay i:

(10*2 + 8*2 + 6*2 + 5*3 + 2*3) = 69 bit

K t Tn s M

A 10 11

B 8 10C 6 00

D 5 011

E 2 010


8/17FIT-HCMUS


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[B1]: Duyt tp tin -> Lp bng thng k tn s xut hinca cc k t.

[B2]: Xy dng cy Huffman da vo bng thng k tn sxut hin

[B3]: Pht sinh bng m bit cho tng k t tng ng

[B4]: Duyt tp tin -> Thay th cc k t trong tp tin bngm bit tng ng.

[B5]: Lu li thng tin ca cy Huffman cho gii nn


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ADDAABBCCBAAABBCCCBBBCDAADDEEAA

11011011111110100000101111111010000

0001010100001111110110110100101111


9/17FIT-HCMUS


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D liu:ADDAABBCCBAAABBCCCBBBCDAADDEEAA

K t Tn s xut hin

A 10

B 8

C 6

D 5

E 2

Cy Huffman: cy nhphn Mi node l cha 1 k t

Mi node cha cha cc kt ca nhng node con.

Trng s ca node: Node con: tn s xut

hin ca k t tng ng

Node cha: Tng trng sca cc node con.

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10/17FIT-HCMUS 1


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E 2 D 5

ED 7C 6

CED 13

B 8 A 10

BA 18

CEDBA 31


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Pht sinh cy: Bc 1: Chn trong bng thng k hai phn t x,y c trng s

thp nht.

Bc 2: To 2 node ca cy cng vi node cha z c trng sbng tng trng s ca hai node con.

Bc 3: Loi 2 phn t x,y ra khi bng thng k.

Bc 4: Thm phn t z vo trong bng thng k.

Bc 5: Lp li Bc 1-4 cho n khi cn 1 phn t trong bngthng k.


11/17FIT-HCMUS


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Quy c:Node c trng s nh hn s nm bn nhnh tri. Node

cn li nm bn nhnh phi.

Nu 2 node c trng s bng nhauNode no c k t nh hn th nm bn tri

Node c k t ln hn nm bn phi.


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K t Tn s

A 10

B 8

C 6

D 5

E 2


12/17FIT-HCMUS 1


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K t Tn s

A 10

B 8

ED 7

C 6


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K t Tn s

CED 13

A 10

B 8


13/17FIT-HCMUS 1


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K t Tn s

BA 18

CED 13


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K t Tn s

CEDBA 31


14/17FIT-HCMUS 1


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M bit ca tng k t: ng i t node gcca cy Huffman n node l ca k t .

Cch thc: Bit 0 c to ra khi i qua nhnh tri

Bit 1 c to ra khi i qua nhnh phi


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K t M

A 11

B 10

C 00

D 011

E 010


15/17FIT-HCMUS 1


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Duyt tp tin cn nn

Thay th tt c cc k t trong tp tin bng mbit tng ng ca n.


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Phc v cho vic gii nn.

Cch thc: Cy Huffman

Bng tn s


16/17FIT-HCMUS 1


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Phc hi cy Huffman da trn thng tin lutr.

Lpi t gc cy Huffmanc tng bit t tp tin c nnNu bit 0: i qua nhnh triNu bit 1: i qua nhnh phiNu n node l: xut ra k t ti node l ny.

Cho n khi no ht d liu


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C th khng lu tr cy Huffman hoc bngthng k tn s vo trong tp tin nn haykhng?


17/17


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Thng k sn trn d liu ln v tnh ton sn cyHuffman cho b m ha v b gii m.

u im: Gim thiu kch thc ca tp tin cn nn. Gim thiu chi ph ca vic duyt tp tin lp bng thng

k

Khuyt im: Hiu qu khng cao trong trng hp khc dng d liu

thng k

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