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第4章贪心算法
赫夫曼编码
单源最短路径
1
Huffmancodes
2
Huffmancodes
DataCompressionviaHuffmanCoding
nMotivation
wLimitednetworkbandwidth.
wLimiteddiskspace.
nHumancodesareusedfordatacompression.
wReducingtimetotransmitlargefiles,and
wReducingthespacerequiredtostorethemondiskor
tape.
Huffmancodesareawidelyusedandvery
effectivetechniqueforcompressingdata,savings
of20%to90%aretypical,dependingonthe
characteristicsofthedata.3
Huffmancodes
Problem
nSupposethatyouhaveafileof100Kcharacters.Tokeepthe
examplesimple,supposethateachcharacterisoneofthe6
lettersfromathroughf.Sincewehavejust6characters,we
needjust3bitstorepresentacharacter,sothefilerequires
300Kbitstostore.Canwedobetter?
nSupposethatwehavemoreinformationaboutthefile:
wthefrequencywhicheachcharacterappears.
Solution
nTheideaisthatwewilluseavariablelengthcodeinsteadof
afixedlengthcode(3bitsforeachcharacter),withfewer
bitstostorethecommoncharacters,andmorebitstostore
therarecharacters.
4
ExampleofDataCompression
Forexample,supposethatthecharactersappearwiththe
followingfrequencies,andfollowingcodes:
Thenthevariable-lengthcodedversionwilltakenot300K
bitsbut45*1+13*3+12*3+16*3+9*4+5*4=224K
bitstostore,a25%saving.Infactthisistheoptimalway
toencodethe6characterspresent,asweshall
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