R O B E R T S E D G E W I C K K E V I N W A Y N E Q. Can we do better? A. Yes, if we can avoid examining the entire key, as with string sorting.

Transcription

1 .2 TRIES Rviw: umm f pfmnc f m- impmnin Fqunc f pin. impmnin pic c in d dd pin pin n k d-ck BST. g N. g N. g N cmpt() Agim F O U R T H E D I T I O N R-w i n i cc-d pin n qu() cd() und unifm ing umpin R O B E R T S E D G E W I C K K E V I N W A Y N E Q. Cn w d? A. Y, if w cn vid xmining ni k, wi ing ing. Agim, Ediin R Sdgwick nd Kvin Wn Cpig 22 2 Nvm 29, 2 ::2 AM 2 Sing m ic API Sing m impmnin c umm Sing m. Sm pciizd ing k. cc cc (pic c) ddup puic c SingST<Vu> SingST() c n mp m vid pu(sing k, Vu v) pu k-vu pi in m impmnin i mi in pc (fnc) m.x c.x d-ck BST L + c g 2 N c g 2 N c g 2 N N. 9. ing L L L N N.. Vu g(sing k) un vu pid wi givn k vid d(sing k) d k nd cpnding vu Pm N = num f ing L = ng f ing R = dix fi iz wd diinc m.x.2 MB 2 K 2 K c.x 82 MB. M 9 K G. F n ing, m fxi n BST. Cng. Efficin pfmnc f ing k.

2 Ti Ti. [fm iv, u pnuncd ""] S cc in nd (n k). Ec nd R cidn, n f c pi cc. F nw, w d n dw nu ink. ink i f k wi ink i f k wi R-w i n i cc-d pin k vu vu f in nd cpnding k cc Sc in i Sc in i Fw ink cpnding c cc in k. Sc i: nd w nd nn-nu vu. Sc mi: c nu ink nd w nd nu vu. Fw ink cpnding c cc in k. Sc i: nd w nd nn-nu vu. Sc mi: c nu ink nd w nd nu vu. g("") g("") m mind n inmdi nd (un ) un vu in nd cpnding cc (un ) 8

3 Sc in i Sc in i Fw ink cpnding c cc in k. Sc i: nd w nd nn-nu vu. Sc mi: c nu ink nd w nd nu vu. Fw ink cpnding c cc in k. Sc i: nd w nd nn-nu vu. Sc mi: c nu ink nd w nd nu vu. g("") g("") n vu in nd cpnding cc (un nu) 9 n ink (un nu) Inin in i Ti cnucin dm Fw ink cpnding c cc in k. Encun nu ink: c nw nd. Encun cc f k: vu in nd. pu("", ) 2

4 Ti pnin: Jv impmnin R-w i: Jv impmnin Nd. A vu, pu fnc R nd. piv ic c Nd piv Ojc vu; piv Nd[] nx = nw Nd[R]; u Ojc ind f Vu inc n gnic cin in Jv puic c TiST<Vu> piv ic fin in R = 2; piv Nd ; piv ic c Nd /* pviu id */ xndd ASCII puic vid pu(sing k, Vu v) = pu(, k, v, ); 2 cc impici dfind ink indx 2 c nd n f ink nd vu k n xpici d piv Nd pu(nd x, Sing k, Vu v, in d) if (x == nu) x = nw Nd(); if (d == k.ng()) x.v = v; un x; c c = k.ca(d); x.nx[c] = pu(x.nx[c], k, v, d+); un x; Ti pnin R-w i: Jv impmnin (cninud) Ti pfmnc puic n cnin(sing k) un g(k)!= nu; Sc mi. Cud v mimc n fi cc. Tpic c: xmin n fw cc (uin). puic Vu g(sing k) Nd x = g(, k, ); if (x == nu) un nu; un (Vu) x.v; c ndd Sc i. Nd xmin L cc f qui. Spc. R nu ink c f. (u uin pc pi if mn ing cmmn pfix) piv Nd g(nd x, Sing k, in d) if (x == nu) un nu; if (d == k.ng()) un x; c c = k.ca(d); un g(x.nx[c], k, d+); Bm in. F i nd vn f mi, u w pc.

5 Sing m impmnin c umm Digin: u f mm? K ug nug f nd. cc cc (pic c) ddup iud Bi G, 98 impmnin i mi in pc (fnc) m.x c.x (cmmning n mun f RAM in pn cmpu) d-ck BST L + c g 2 N c g 2 N c g 2 N N. 9. ing L L L N N.. R-w i L g R N L (R+) N.2 u f mm MB f RAM m imi pfmnc f m Windw XP fu; f, 28 MB ig i cmmndd f pfmnc. Windw XP mnu, 22 R-w i. Md f cic f m R. T muc mm f g R. i i cming dkp, i n du u. Bu p fm Pp, I cn' ink f dkp ppicin w u wud nd m n GB f pic mm, wic i w u v v in d nfi fm i cng. Rig nw, i i c. Bi G, 2 Cng. U mm,.g.,,-w i f Unicd! 8 Digin: u f mm? A md pp A (ppxim) i. mcin dd i dd mm pic cu mm PDP KB KB $K PDP KB 2 KB $M c Num f m in univ (imd) Ag f univ (imd). iin ~ 2 9 cnd 2 89 nncnd. Q. Hw mn i dd v m v xid? A. U uniqu 2-i dd f v m v im qunum. IBM S/ 9 2 MB 2 KB $M VAX 98 2 GB MB $M 2 i 89 i i m im cuin f wv Pnium 99 2 GB GB $K Xn 2 nug GB $?? fuu 28+ nug nug $ 2-i wd ug nug f nd. Kvin Wn, 99 Ex. U 2-w i mp c m cin. Rpn m 8-i c (2 i). 2-w i w 2/2 cu mm. Nd u f mm. 9 2

6 Tn i S cc nd vu in nd (n k). Ec nd cidn: m (f), qu (midd), g (ig). R-w i n i cc-d pin F Agim f Sing nd Scing Sing Jn L. Bn* R Sdgwick# Ac i cmpiiv wi m fficin ing ing W pn ic gim f ing nd pgm knwn. T cnd pgm i m ing muik d, nd div fm m pcic C impmnin i f n ing, wic i cmimpmnin f ppicin in wic k cc- mn gdd f m impmn ing. T ing gim nd Quick nd in. T m impmnin i muc m dix ; i i cmpiiv wi knwn C pc-fficin n muiw, nd upp m cd. T ing gim nd i nd in dvncd. ; i i f n ing nd cmmn In mn ppicin pgm, u Quick ud md. T ic id ind g- impmnin d n n c cmp pin, im d ck 9 u i pcic nd u ing in. T d 2 22 Tn i Sc in TST S cc nd vu in nd (n k). Ec nd cidn: m (f), qu (midd), g (ig). Fw ink cpnding c cc in k. If, k f ink; if g, k ig ink. If qu, k midd ink nd mv nx k cc. 2 u 8 ink TST f k wi f 2 ink TST f k wi u 8 Sc i. Nd w nd nn-nu vu. Sc mi. Rc nu ink nd w nd nu vu. g("") mimc: k f ig ink, d n mv nx c mc: k midd ink, mv nx c c nd ink 2 u 8 TST pnin f i un vu cid wi k cc 2 TST xmp 2

7 2-w i v. TST TST pnin in Jv 2-w i. 2 nu ink in c f. TST. nu ink in c f. 2-w i ( nu ink, n wn) TST ( nu ink) nw f ip ik dim g j n k u c mn gg fw j w j p gig w w c wd cw cu f p g jm dug nd 2 A TST nd i fiv fid: A vu. A cc c. A fnc f TST. A fnc midd TST. A fnc ig TST. ndd f ink (R = 2) u ink f k wi Ti nd pnin piv c Nd piv Vu v; piv c c; piv Nd f, mid, ig; n (TST) ink f k wi u u 2 TST: Jv impmnin TST: Jv impmnin (cninud) puic c TST<Vu> piv Nd ; puic n cnin(sing k) un g(k)!= nu; piv c Nd /* pviu id */ puic vid pu(sing k, Vu v) = pu(, k, v, ); puic Vu g(sing k) Nd x = g(, k, ); if (x == nu) un nu; un x.v; piv Nd pu(nd x, Sing k, Vu v, in d) c c = k.ca(d); if (x == nu) x = nw Nd(); x.c = c; if (c < x.c) x.f = pu(x.f, k, v, d); if (c > x.c) x.ig = pu(x.ig, k, v, d); if (d <.ng() - ) x.mid = pu(x.mid, k, v, d+); x.v = v; un x; piv Nd g(nd x, Sing k, in d) if (x == nu) un nu; c c = k.ca(d); if (c < x.c) un g(x.f, k, d); if (c > x.c) un g(x.ig, k, d); if (d < k.ng() - ) un g(x.mid, k, d+); un x; 2 28

8 Sing m impmnin c umm TST wi R 2 ncing impmnin i cc cc (pic c) mi in pc (fnc) m.x ddup c.x Hid f R-w i nd TST. D R 2 -w ncing. Ec f R 2 nd pin TST. d-ck BST L + c g 2 N c g 2 N c g 2 N N. 9. f 2 2 ing L L L N N.. R-w i L g R N L (R + ) N.2 u f mm c z zz TST L + n N n N L + n N N.2 8. TST TST TST TST TST Rmk. Cn uid ncd TST vi in civ L + g N w-c gun. Bm in. TST i f ing (f ing k), pc fficin. Q. W u n- nd w- wd? 29 Sing m impmnin c umm TST v. ing impmnin i cc cc (pic c) mi in pc (fnc) m.x ddup c.x d-ck BST L + c g 2 N c g 2 N c g 2 N N. 9. Hing. Nd xmin ni k. Sc i nd mi c u m. Nd gd funcin f v k p. D n upp dd m pin. ing L L L N N.. R-w i L g R N L (R + ) N.2 u f mm TST L + n N n N L + n N N.2 8. TST wi R 2 L + n N n N L + n N N + R TST. Wk n f ing ( digi k). On xmin ju nug k cc. Sc mi m n invv fw cc. Supp dd m pin (pu!). Bm in. TST : F n ing (pci f mi). M fxi n d-ck BST. [ und] 2

9 Sing m API Cc-d pin. T ing m API upp v ufu cc-d pin. k vu R-w i n i cc-d pin Pfix mc. K wi pfix "": "", "", nd "". Widcd mc. K mc ".": "" nd "". Lng pfix. K i ng pfix f "": "". Sing m API Din in n R-w i puic c SingST<Vu> SingST() c m wi ing k vid pu(sing k, Vu v) pu k-vu pi in m Vu g(sing k) vu pid wi k T d k-vu pi: Find nd cpnding k nd vu nu. If nd nu ink, mv nd (nd cu). d("") vid d(sing k) d k nd cpnding vu I<Sing> k() k I<Sing> kwipfix(sing ) k ving pfix I<Sing> ktmc(sing ) k mc (w. i widcd) Sing ngpfixof(sing ) ng k i pfix f Rmk. Cn dd dd ST md,.g., f() nd nk(). nu vu nd ink (d nd) vu nu

10 Odd iin Odd iin: Jv impmnin T i ug k in d d: D ind v f i; dd k ncund quu. Minin qunc f cc n p fm nd. T i ug k in d d: D ind v f i; dd k ncund quu. Minin qunc f cc n p fm nd. kwipfix(""); k q Ccing k in i (c) puic I<Sing> k() Quu<Sing> quu = nw Quu<Sing>(); cc(, "", quu); un quu; qunc f cc n p fm x piv vid cc(nd x, Sing pfix, Quu<Sing> q) if (x == nu) un; if (x.v!= nu) q.nquu(pfix); f (c c = ; c < R; c++) cc(x.nx[c], pfix + c, q); 8 Pfix mc Pfix mc Find k in m ing wi givn pfix. Find k in m ing wi givn pfix. Ex. Aucmp in c pn,, x di,. U p cc n im. Sm p mcing ing. kwipfix(""); find ui f k ginning wi "" cc k in ui k q Pfix mc in i puic I<Sing> kwipfix(sing pfix) Quu<Sing> quu = nw Quu<Sing>(); Nd x = g(, pfix, ); cc(x, pfix, quu); un quu; f ui f ing ginning wi givn pfix 9

11 Lng pfix Lng pfix Find ng k in m i pfix f qu ing. Ex. T nd pck wd dinin IP dd, u c IP dd in uing i ng pfix mc. Find ng k in m i pfix f qu ing. Sc f qu ing. Kp ck f ng k ncund. "28" "28.2" "28.2." "28.2.." "28.2." "28.2.." "28.2.." "28.222" " " pnd 2-i in num f IPv (ind f ing) ngpfixof("28.2..") = "28.2." ngpfixof("28.2..") = "28.2" ngpfixof("28..2.") = "28" "" 2 nd nd f ing vu i n nu un "" 2 nd nd f ing vu i nu un ( k n p) Piiii f ngpfixof() "" 2 nd nu ink un ( k n p) N. N m f: f("28.2..") = "28.2.." 2 Lng pfix: Jv impmnin T9 xing Find ng k in m i pfix f qu ing. Sc f qu ing. Kp ck f ng k ncund. puic Sing ngpfixof(sing qu) in ng = (, qu,, ); un qu.uing(, ng); piv in (Nd x, Sing qu, in d, in ng) if (x == nu) un ng; if (x.v!= nu) ng = d; if (d == qu.ng()) un ng; c c = qu.ca(d); un (x.nx[c], qu, d+, ng); G. Tp x mg n pn kpd. Mui-p inpu. En pd ping k uni did pp. " muc f nd m fun w n x" T9 x inpu. Find wd cpnd givn qunc f num. P cmpin pin. Ex. Mui-p: T9:

12 Cmping i A cic gim Cping -w nc m. Inn nd cc; f nd uffix ( fu k). Cping ini -w nc. Nd qunc f cc. pu("", ); pu("fi", 2); ndd i n n-w ncing Pici i. [Pcic Agim Riv Infmin Cdd in Apnumic] Cp n-w nc in in i. Td i imin muip nd p. fi 2 f i inn n-w ncing xn n-w ncing Appicin. D. P2P nwk. IP uing : find ng pfix mc. Cmpd qud- f N-d imuin. Efficin ing nd quing XML dcumn. 2 Rmving n-w ncing in i Impmnin. On p nd i cu. Suffix Sing m umm Suffix. Tdd i wi cpd -w ncing f ing uffix. A ucc in gim dign nd ni. Rd-ck BST. Pfmnc gun: g N k cmp. Supp dd m API. H. Pfmnc gun: cnn num f p. Rqui gd funcin f k p. Appicin. Lin-im ng pd uing. Cmpuin ig d (BLAST, FASTA). Impmnin. On p nd i cu. Ti. R-w, TST. Pfmnc gun: g N cc ccd. Supp cc-d pin. Bm in. Yu cn g ning xmining - i (!!!) 8