Tries. nimize. mize nimize ze. 4/18/2016 6:48 AM Tries 1

Transcription

1 Tr m nmz z mz nmz z nmz z 4/18/2016 6:48 AM Tr 1

2 Outn Stanar tr Compr tr Suffx tr Huffman nong tr 4/18/2016 6:48 AM Tr 2

3 Whr o tr om from? From th wor rtrva Introu n th /18/2016 6:48 AM Tr 3

4 Prprong Strng Prprong th pattrn p up pattrn mathng qur Aftr prprong th pattrn, KMP agorthm prform pattrn mathng n tm proportona to th txt z If th txt arg, mmuta an arh for oftn (.g., work y Shakpar), w may want to prpro th txt nta of th pattrn Thu o ttr than O(n+m) for txt of z n an pattrn of z m A tr a ompat ata trutur for rprntng a t of trng, uh a a th wor n a txt A tr upport pattrn mathng qur n tm proportona to th pattrn z (~O(m))! 4/18/2016 6:48 AM Tr 4

5 Stanar Tr Th tanar tr for a t of trng S an orr tr uh that: Eah no ut th root a wth a haratr Th hrn of a no ar aphatay orr Th path from th xtrna no to th root y th trng of S Examp: tanar tr for th t of trng S = { ar,,, u, uy,, tok, top } u t a y o r p 4/18/2016 6:48 AM Tr 5 k

6 Stanar Tr What pa o th tr u? What th maxmum hght of th tr? u t a y o r p 4/18/2016 6:48 AM Tr 6 k

7 Stanar Tr A tanar tr u O(n) pa an upport arh, nrton an ton n tm O(m), whr: n tota z of th trng n S m z of th (maxmum) trng paramtr of th opraton z of th aphat u t a y o r p 4/18/2016 6:48 AM Tr 7 k

8 Stanar Tr Whn n, an thu pa, maxmum? Whn S ont of mutuay unqu wor wth no ttr n ommon What typ of wor() prou th argt arh tm? Short wor? Long wor? Anwr: ong wor, pay tho who prfx vry ommon w o mprovmnt atr u t a y o r p 4/18/2016 6:48 AM Tr 8 k

9 Wor Mathng wth a Tr W nrt th wor of th txt nto a tr Eah af tor th ourrn of th aoat wor n th txt a a r? t o k! a u? u y t o k! t o k! t o k! h a r t h? t o p! h u t a y a o r 47, , 24 r p k 84 17, 40, 4/18/2016 6:48 AM Tr 51, 62 9

10 Stanar Tr Contruton How o you u t? u t a y o r p 4/18/2016 6:48 AM Tr 10 k

11 Stanar Tr Contruton Aumng th nput trng ar wor n th Engh anguag, how many hrn o th root no hav? u t a y o r p 4/18/2016 6:48 AM Tr 11 k

12 Stanar Tr Contruton Th numr of hrn of th root no qua to th maxmum numr of tnt frt ttr a th wor n th nput trng 2 n th xamp, maxmum of 26 n Engh u t a y o r p 4/18/2016 6:48 AM Tr 12 k

13 Stanar Tr Contruton What o th tr for ook k? 4/18/2016 6:48 AM Tr 13

14 Stanar Tr Contruton What o th tr for an ook k? 4/18/2016 6:48 AM Tr 14

15 Stanar Tr Contruton What th tr aftr ang uy an top? 4/18/2016 6:48 AM Tr 15

16 Stanar Tr Contruton What th tr aftr ang uy an top? u t y o p 4/18/2016 6:48 AM Tr 16

17 Stanar Tr Contruton What th tr aftr ang tok? u t y o p 4/18/2016 6:48 AM Tr 17

18 Stanar Tr Contruton What th tr aftr ang tok? u t y o p k 4/18/2016 6:48 AM Tr 18

19 Stanar Tr Contruton Aftr ar,,, u, uy,, tok, top u t a y o r p k 4/18/2016 6:48 AM Tr 19

20 Improvmnt What om to mn for tr?.g., th ntr tr ray nary? u t y o p 4/18/2016 6:48 AM Tr 20 k

21 Improvmnt Two typ of ompron Compr ntrna ng-hrn no qun Ao a PATRICIA Tr Why? = Prata AgorThm to Rtrv Informaton Co In Aphanumr (ao a a rax tr ) Compr xtrna ng-hrn af-no qun u t y o p 4/18/2016 6:48 AM Tr 21 k

22 Compr Tr A ompr tr ha ntrna no of gr at at two It otan from tanar tr y omprng han of runant no ar u y k to p u t a y o r p 4/18/2016 6:48 AM Tr 22 k

23 Compat Rprntaton Compat rprntaton of a ompr tr for an array of trng: Stor at th no rang of n nta of utrng Srv a an auxary nx trutur S[0] = S[1] = S[2] = S[3] = a r t o k S[4] = S[5] = S[6] = S[7] = u u y S[8] = S[9] = h a r t o p 1, 0, 0 7, 0, 3 0, 0, 0 1, 1, 1 6, 1, 2 4, 1, 1 0, 1, 1 3, 1, 2 1, 2, 3 8, 2, 3 4, 2, 3 5, 2, 2 0, 2, 2 2, 2, 3 3, 3, 4 9, 3, 3 4/18/2016 6:48 AM Tr 23

24 Mor Improvmnt W an u a tanar tr an thn ompr t But, an w u om ort of ompr tr rty? Ia? 4/18/2016 6:48 AM Tr 24

25 Suffx Tr Th uffx tr of a trng X th ompr tr of a th uffx of X m n z m m nmz z mz nmz z nmz z 4/18/2016 6:48 AM Tr 25

26 Suffx Tr Compat rprntaton of th uffx tr for a trng X of z n from an aphat of z U O(n) pa Support artrary pattrn mathng qur n X n O(m) tm, whr m th z of th pattrn Rpttv wor not tor rpttvy m n z m , 7 1, 1 0, 1 2, 7 6, 7 4, 7 2, 7 6, 7 2, 7 6, 7 4/18/2016 6:48 AM Tr 26

27 Mor Improvmnt Thr t om rptton n th tr.g., mz appar vra tm How an w furthr ompr th tr, thu rung pa an mprovng qury tm? Ia? m nmz z mz nmz z nmz z 4/18/2016 6:48 AM Tr 27

28 Enong Tr A o a mappng of ah haratr of an aphat to a nary o-wor A prfx o a nary o uh that no o-wor th prfx of anothr o-wor An nong tr rprnt a prfx o Eah af tor a haratr Th o wor of a haratr gvn y th path from th root to th af torng th haratr (0 for a ft h an 1 for a rght h) a a 4/18/2016 6:48 AM Tr 28

29 Enong Tr Gvn a txt trng X, w want to fn a prfx o for th haratr of X that y a ma nong for X Frqunt haratr hou hav hort o-wor Rar haratr hou hav ong o-wor Why? Examp X = araaara T 1 no X nto 29 t 29= T 2 no X nto how many t? 24= T 1 a r How an w u a goo nong tr? 4/18/2016 6:48 AM Tr 29 T 2 a r

30 Huffman Agorthm Gvn a trng X, Huffman agorthm ontrut a prfx o that mnmz th z of th nong of X It run n tm O(n + og ), whr n th z of X an th numr of tnt haratr of X A hap-a prorty quu u a an auxary trutur Agorthm HuffmanEnong(X) Input trng X of z n Output optma nong tr for X C tntcharatr(x) omputfrqun(c, X) Q nw mpty hap for a C T nw ng-no tr torng Q.nrt(gtFrquny(), T) wh Q.z() > 1 f 1 Q.mnKy() T 1 Q.rmovMn() f 2 Q.mnKy() T 2 Q.rmovMn() T jon(t 1, T 2 ) Q.nrt(f 1 + f 2, T) rturn Q.rmovMn() 4/18/2016 6:48 AM Tr 30

31 Examp 11 X = araaara Frqun a a r r 6 a r a r a r a r /18/2016 6:48 AM Tr 31

32 Summary of Pattrn Mathng Agorthm Sarh Tm Not Brut for Boyr-Moor KMP Stanar Tr Suffx Tr O(nm) O(nm+) O(n+m) O(m) O(m) mp, no prprong ow (goo for ma nput) O(m) prprong gnfanty fatr than prvou n prat O(m+) prprong mor ompx, ut a vry fat O(n) prprong, = z of aphat fat O(n) prprong fatr n prat au ompr Huffman-Enong Tr O(m) O(n+og) prprong fatt an mat n prat a to o ompron: ZIP 4/18/2016 6:48 AM Tr 32