Algorithms. Algorithms 5.2 TRIES. R-way tries ternary search tries character-based operations ROBERT SEDGEWICK KEVIN WAYNE

Size: px
Start display at page:

Download "Algorithms. Algorithms 5.2 TRIES. R-way tries ternary search tries character-based operations ROBERT SEDGEWICK KEVIN WAYNE"

Transcription

1 Agoritm ROBERT SEDGEWICK KEVIN WAYNE 5.2 TRIES Agoritm F O U R T H E D I T I O N R-wy tri trnry rc tri crctr-bd oprtion ROBERT SEDGEWICK KEVIN WAYNE ttp://g4.c.princton.du Lt updtd on 11/12/15 7:45 AM

2 Summry of t prformnc of ymbo-tb impmnttion Ordr of growt of t frquncy of oprtion. impmnttion Q. Cn w do bttr? typic c rc inrt dt ordrd oprtion oprtion on ky rd-bck BST og N og N og N comprto() tb qu() Cod() undr uniform ing umption A. Y, if w cn void xmining t ntir ky, wit tring orting. 2

3 String ymbo tb bic API String ymbo tb. Symbo tb pciizd to tring ky. pubic c StringST<Vu> StringST() crt n mpty ymbo tb void put(string ky, Vu v) put ky-vu pir into t ymbo tb Vu gt(string ky) rturn vu pird wit givn ky void dt(string ky) dt ky nd corrponding vu Go. Ftr tn ing, mor fxib tn BST. 3

4 String ymbo tb impmnttion cot ummry crctr cc (typic c) ddup impmnttion rc it rc mi inrt pc (rfrnc) moby.txt ctor.txt rd-bck BST L + c g 2 N c g 2 N c g 2 N 4 N ing (inr probing) L L L 4 N to 16 N Prmtr N = numbr of tring L = ngt of tring fi iz word ditinct moby.txt 1.2 MB 210 K 32 K ctor.txt 82 MB 11.4 M 900 K Cng. Efficint prformnc for tring ky. 4

5 5.2 TRIES Agoritm R-wy tri trnry rc tri crctr-bd oprtion ROBERT SEDGEWICK KEVIN WAYNE ttp://g4.c.princton.du

6 Tri 6

7 Tri Tri. [from rtriv, but pronouncd "try"] Stor crctr in nod (not ky). Ec nod R cidrn, on for c poib crctr. (for now, w do not drw nu ink) root ink to tri for ky tt trt wit ink to tri for ky tt trt wit b t y 4 ky vu by o r vu for in nod corrponding to t crctr in ky or 7 t 5 3 7

8 Src in tri Foow ink corrponding to c crctr in t ky. Src it: nod wr rc nd non-nu vu. Src mi: rc nu ink or nod wr rc nd nu vu. gt("") b t y o 5 r rturn vu in nod corrponding to t crctr in ky (rturn 3) 8

9 Src in tri Foow ink corrponding to c crctr in t ky. Src it: nod wr rc nd non-nu vu. Src mi: rc nu ink or nod wr rc nd nu vu. gt("") b t y o 5 r rc my trmintd t n intrmdit nod (rturn 0)

10 Src in tri Foow ink corrponding to c crctr in t ky. Src it: nod wr rc nd non-nu vu. Src mi: rc nu ink or nod wr rc nd nu vu. gt("") b t y o 5 r no vu ocitd nod corrponding to t crctr in ky (rturn nu) 10

11 Src in tri Foow ink corrponding to c crctr in t ky. Src it: nod wr rc nd non-nu vu. Src mi: rc nu ink or nod wr rc nd nu vu. gt("tr") b t y o 5 r no ink to t (rturn nu) 11

12 Foow ink corrponding to c crctr in t ky. Encountr nu ink: crt nw nod. Encountr t t crctr of t ky: t vu in tt nod. 12 Inrtion into tri r put("or", 7) b y o t

13 Tri contruction dmo tri b t y o 5 r 1 7 3

14 Tri contruction dmo tri

15 Tri contruction dmo put("", 0) 0 ky i qunc of crctr from root to vu vu i in nod corrponding to t crctr

16 Tri contruction dmo tri 0

17 Tri contruction dmo tri 0

18 Tri contruction dmo put("", 1) 0 1

19 Tri contruction dmo tri 0 1

20 Tri contruction dmo tri 0 1

21 Tri contruction dmo put("", 2) 2 0 1

22 Tri contruction dmo tri 2 0 1

23 Tri contruction dmo put("", 3)

24 Tri contruction dmo tri

25 Tri contruction dmo put("by", 4) b y

26 Tri contruction dmo tri b y

27 Tri contruction dmo put("t", 5) b t y

28 Tri contruction dmo tri b t y

29 Tri contruction dmo put("", 6) b t y ovrwrit od vu wit nw vu 1 3

30 Tri contruction dmo tri b t y

31 Tri contruction dmo tri b t y

32 Tri contruction dmo put("or", 7) b t y o 5 r 1 7 3

33 Tri contruction dmo tri b t y o 5 r 1 7 3

34 Tri rprnttion: Jv impmnttion Nod. A vu, pu rfrnc to R nod. privt ttic c Nod { } privt Objct v; // no gnric rry crtion privt Nod[] nxt = nw Nod[R]; crctr r impicity dfind by ink indx Tri rprnttion c nod n rry of ink nd vu Rmrk. Nitr ky nor crctr r tord xpicity

35 R-wy tri: Jv impmnttion pubic c TriST<Vu> { privt ttic fin int R = 256; privt Nod root = nw Nod(); privt ttic c Nod { /* prviou id */ } xtndd ASCII pubic void put(string ky, Vu v) { root = put(root, ky, v, 0); } privt Nod put(nod x, String ky, Vu v, int d) { if (x == nu) x = nw Nod(); if (d == ky.ngt()) { x.v = v; rturn x; } cr c = ky.crat(d); x.nxt[c] = put(x.nxt[c], ky, v, d+1); rturn x; } 35

36 R-wy tri: Jv impmnttion (continud) pubic Vu gt(string ky) { } Nod x = gt(root, ky, 0); if (x == nu) rturn nu; rturn (Vu) x.v; // ct ndd privt Nod gt(nod x, String ky, int d) { } if (x == nu) rturn nu; if (d == ky.ngt()) rturn x; cr c = ky.crat(d); rturn gt(x.nxt[c], ky, d+1); } 36

37 Tri prformnc Src it. Nd to xmin L crctr for quity. Src mi. Coud v mimtc on firt crctr. Typic c: xmin ony fw crctr (ubinr). Spc. R nu ink t c f. (but ubinr pc poib if mny tring r ong common prfix) rctr r impicity dfind by ink indx 2 c nod n rry of in nd vu Bottom in. Ft rc it nd vn ftr rc mi, but wt pc

38 To dt ky-vu pir: Find t nod corrponding to ky nd t vu to nu. If nod nu vu nd nu ink, rmov tt nod (nd rcur) Dtion in n R-wy tri r b y o t dt("") t vu to nu

39 Dtion in n R-wy tri To dt ky-vu pir: Find t nod corrponding to ky nd t vu to nu. If nod nu vu nd nu ink, rmov tt nod (nd rcur). dt("") b t y o 5 r 1 7 nu vu nd ink (dt nod) 39

40 String ymbo tb impmnttion cot ummry impmnttion R-wy tri. rc it Mtod of coic for m R. Work w for mdium R. Too muc mmory for rg R. crctr cc (typic c) rc mi inrt pc (rfrnc) Cng. U mmory,.g., wy tri for Unicod! moby.txt ddup ctor.txt rd-bck BST L + c g 2 N c g 2 N c g 2 N 4 N ing (inr probing) L L L 4 N to 16 N R-wy tri L og R N R + L (R+1) N 1.12 out of mmory 40

41 5.2 TRIES Agoritm R-wy tri trnry rc tri crctr-bd oprtion ROBERT SEDGEWICK KEVIN WAYNE ttp://g4.c.princton.du

42 Trnry rc tri Stor crctr nd vu in nod (not ky). Ec nod 3 cidrn: mr (ft), qu (midd), rgr (rigt). Ft Agoritm for Sorting nd Srcing String Jon L. Bnty* Robrt Sdgwick# Abtrct W prnt tortic goritm for orting nd rcing mutiky dt, nd driv from tm prctic C impmnttion for ppiction in wic ky r crctr tring. T orting goritm bnd Quickort nd rdix ort; it i comptitiv wit t bt known C ort cod. T rcing goritm bnd tri nd binry rc tr; it i ftr tn ing nd otr commony ud rc mtod. T bic id bind t go- tt i comptitiv wit t mot fficint tring orting progrm known. T cond progrm i ymbo tb impmnttion tt i ftr tn ing, wic i commony rgrdd t ftt ymbo tb impmnttion. T ymbo tb impmnttion i muc mor pc-fficint tn mutiwy tr, nd upport mor dvncd rc. In mny ppiction progrm, ort u Quickort impmnttion bd on n btrct compr oprtion, 42

43 Stor crctr nd vu in nod (not ky). Ec nod 3 cidrn: mr (ft), qu (midd), rgr (rigt). 43 Trnry rc tri c nod 3 ink ink to TST for ky tt trt wit crctr tn ink to TST for ky tt trt wit b y o r t r 1 r y u 1 r b y o r r y u t btrct tri TST

44 Src it in TST gt("") b t y o r rturn vu in nod corrponding to t crctr in ky

45 Src mi in TST gt("tr") b t y o r no ink to t (rturn nu) 45

46 Src in TST Foow ink corrponding to c crctr in t ky. If, tk ft ink; if grtr, tk rigt ink. If qu, tk t midd ink nd mov to t nxt ky crctr. Src it. Nod wr rc nd non-nu vu. Src mi. Rc nu ink or nod wr rc nd nu vu. gt("") mimtc: tk ft or rigt ink, do not mov to nxt cr b mtc: tk midd ink, mov to nxt cr t r y 4 u o r 8 r rturn vu ocitd wit t ky crctr y 13 46

47 Trnry rc tri contruction dmo trnry rc tri b t y o r

48 Trnry rc tri contruction dmo trnry rc tri 48

49 Trnry rc tri contruction dmo put("", 0) 0 ky i qunc of crctr from root to vu uing midd ink vu i in nod corrponding to t crctr 49

50 Trnry rc tri contruction dmo put("", 0) 0 50

51 Trnry rc tri contruction dmo put("", 1)

52 Trnry rc tri contruction dmo trnry rc tri

53 Trnry rc tri contruction dmo put("", 2)

54 Trnry rc tri contruction dmo trnry rc tri

55 Trnry rc tri contruction dmo put("", 3)

56 Trnry rc tri contruction dmo trnry rc tri

57 Trnry rc tri contruction dmo put("by", 4) b y

58 Trnry rc tri contruction dmo trnry rc tri b y

59 Trnry rc tri contruction dmo put("t", 5) b t y

60 Trnry rc tri contruction dmo trnry rc tri b t y

61 Trnry rc tri contruction dmo put("", 6) b t y ovrwrit od vu wit nw vu

62 Trnry rc tri contruction dmo trnry rc tri b t y

63 Trnry rc tri contruction dmo put("or", 7) b t y o r

64 Trnry rc tri contruction dmo trnry rc tri b t y o r

65 Trnry rc tri contruction dmo trnry rc tri b t y o r

66 26-wy tri v. TST 26-wy tri. 26 nu ink in c f. TST. 3 nu ink in c f. 26-wy tri (1035 nu ink, not own) TST (155 nu ink) now for tip ik dim tg jot ob nob ky ut c bt mn gg fw jy ow joy rp gig w w cb wd cw cu f tp go tr jm dug nd 66

67 TST rprnttion in Jv A TST nod i fiv fid: A vu. A crctr c. A rfrnc to ft TST. A rfrnc to midd TST. A rfrnc to rigt TST. privt c Nod { privt Vu v; privt cr c; privt Nod ft, mid, rigt; } tndrd rry of ink (R = 26) trnry rc tr (TST) u ink for ky tt trt wit Tri nod rprnttion ink for ky tt trt wit u u 67

68 TST: Jv impmnttion pubic c TST<Vu> { privt Nod root; privt c Nod { /* prviou id */ } pubic Vu gt(string ky) { Nod x = gt(root, ky, 0); if (x == nu) rturn nu; rturn x.v; } privt Nod gt(nod x, String ky, int d) { if (x == nu) rturn nu; cr c = ky.crat(d); if (c < x.c) rturn gt(x.ft, ky, d); if (c > x.c) rturn gt(x.rigt, ky, d); if (d < ky.ngt() - 1) rturn gt(x.mid, ky, d+1); rturn x; } } pubic void put(string Ky, Vu v) { /* imir, book or bookit */ } 68

69 String ymbo tb impmnttion cot ummry impmnttion rc it Rmrk. Cn buid bncd TST vi rottion to civ L + og N wort-c gurnt. crctr cc (typic c) rc mi inrt pc (rfrnc) moby.txt ddup Bottom in. TST i ft ing (for tring ky), pc fficint. ctor.txt rd-bck BST L + c g 2 N c g 2 N c g 2 N 4 N ing (inr probing) L L L 4 N to 16 N R-wy tri L og R N R + L (R+1) N 1.12 out of mmory TST L + n N n N L + n N 4 N

70 TST wit R 2 brncing t root Hybrid of R-wy tri nd TST. Do R 2 -wy brncing t root. Ec of R 2 root nod point to TST. rry of 26 2 root b c zy zz TST TST TST TST TST Q. Wt bout on- nd two-ttr word? 70

71 String ymbo tb impmnttion cot ummry crctr cc (typic c) ddup impmnttion rc it rc mi inrt pc (rfrnc) moby.txt ctor.txt rd-bck BST L + c g 2 N c g 2 N c g 2 N 4N ing (inr probing) L L L 4N to 16N R-wy tri L og R N R + L (R+1) N 1.12 out of mmory TST L + n N n N L + n N 4 N TST wit R 2 L + n N n N L + n N 4 N + R Bottom in. Ftr tn ing for our bncmrk cint. 71

72 TST v. ing Hing. Nd to xmin ntir ky. Src it nd mi cot bout t m. Prformnc ri on function. Do not upport ordrd ymbo tb oprtion. TST. Work ony for tring (or digit) ky. Src mi my invov ony fw crctr. Support ordrd ymbo tb oprtion (pu xtr!). Bottom in. TST r: Ftr tn ing (pciy for rc mi). Mor fxib tn rd-bck BST. [ty tund] 72

73 5.2 TRIES Agoritm R-wy tri trnry rc tri crctr-bd oprtion ROBERT SEDGEWICK KEVIN WAYNE ttp://g4.c.princton.du

74 String ymbo tb API Crctr-bd oprtion. T tring ymbo tb API upport vr ufu crctr-bd oprtion. ky vu by or 7 t 5 Prfix mtc. Ky wit prfix :,, nd or. Widcrd mtc. Ky tt mtc.: nd t. Longt prfix. Ky tt i t ongt prfix of ort:. 74

75 String ymbo tb API pubic c StringST<Vu> StringST() crt ymbo tb wit tring ky void put(string ky, Vu v) put ky-vu pir into t ymbo tb Vu gt(string ky) vu pird wit ky void dt(string ky) dt ky nd corrponding vu Itrb<String> ky() ky Itrb<String> kywitprfix(string ) ky ving prfix Itrb<String> kyttmtc(string ) ky tt mtc (wr. i widcrd) String ongtprfixof(string ) ongt ky tt i prfix of Rmrk. Cn o dd otr ordrd ST mtod,.g., foor() nd rnk(). 75

76 Wrmup: ordrd itrtion To itrt troug ky in ortd ordr: Do inordr trvr of tri; dd ky ncountrd to quu. Mintin qunc of crctr on pt from root to nod. kywitprfix(""); ky() ky b by o or or t t t q by by by by b y by by or by or t o r 7 t 5 Cocting t ky in tri (trc) 76

77 Ordrd itrtion: Jv impmnttion To itrt troug ky in ortd ordr: Do inordr trvr of tri; dd ky ncountrd to quu. Mintin qunc of crctr on pt from root to nod. pubic Itrb<String> ky() { } Quu<String> quu = nw Quu<String>(); coct(root, "", quu); rturn quu; qunc of crctr on pt from root to x privt void coct(nod x, String prfix, Quu<String> quu) { } if (x == nu) rturn; if (x.v!= nu) quu.nquu(prfix); for (cr c = 0; c < R; c++) coct(x.nxt[c], prfix + c, quu); or u StringBuidr 77

78 Prfix mtc Find ky in ymbo tb trting wit givn prfix. Ex. Autocompt in c pon, rc br, txt ditor, or. Ur typ crctr on t tim. Sytm rport mtcing tring. 78

79 Prfix mtc in n R-wy tri Find ky in ymbo tb trting wit givn prfix. kywitprfix(""); b y 4 6 find ubtri for ky bginning wit "" o r 7 t 5 b y o r 7 t 5 coct ky in tt ubtri Prfix mtc in tri pubic Itrb<String> kywitprfix(string prfix) { } Quu<String> quu = nw Quu<String>(); Nod x = gt(root, prfix, 0); coct(x, prfix, quu); rturn quu; root of ubtri for tring bginning wit givn prfix ky o or or quu or 79

80 Longt prfix Find ongt ky in ymbo tb tt i prfix of qury tring. Ex. To nd pckt towrd dtintion IP ddr, routr coo IP ddr in routing tb tt i ongt prfix mtc. "128" " " " " " " " " " " " " " " " " rprntd 32-bit binry numbr for IPv4 (intd of tring) ongtprfixof(" ") = " " ongtprfixof(" ") = " " ongtprfixof(" ") = "128" Not. Not t m foor: foor(" ") = " " 80

81 Longt prfix in n R-wy tri Find ongt ky in ymbo tb tt i prfix of qury tring. Src for qury tring. Kp trck of ongt ky ncountrd. "" "" "ort" rc nd t nd of tring vu i not nu rturn rc nd t nd of tring vu i nu rturn (t ky on pt) Poibiiti for ongtprfixof() xof() rc nd t nu ink rturn (t ky on pt) 81

82 Longt prfix in n R-wy tri: Jv impmnttion Find ongt ky in ymbo tb tt i prfix of qury tring. Src for qury tring. Kp trck of ongt ky ncountrd. pubic String ongtprfixof(string qury) { int ngt = rc(root, qury, 0, 0); rturn qury.ubtring(0, ngt); } privt int rc(nod x, String qury, int d, int ngt) { } if (x == nu) rturn ngt; if (x.v!= nu) ngt = d; if (d == qury.ngt()) rturn ngt; cr c = qury.crat(d); rturn rc(x.nxt[c], qury, d+1, ngt); 82

83 T9 txting (prdictiv txting) Go. Typ txt mg on pon kypd. Muti-tp input. Entr ttr by rptdy pring ky. Ex. good: T9 txt input. " muc ftr nd mor fun wy to ntr txt" Find word tt corrpond to givn qunc of numbr. 4663: good, om, gon, oof. txtonym Pr * to ct nxt option. Pr 0 to comption option. Sytm dpt to ur' tndnci. ttp:// 83

84 Ptrici tri Ptrici tri. [Prctic Agoritm to Rtriv Informtion Codd in Apnumric] Rmov on-wy brncing. Ec nod rprnt qunc of crctr. Impmnttion: on tp byond ti cour. Appiction. put("", 1); put("fi", 2); tndrd tri no on-wy brncing fi 1 2 Dtb rc. P2P ntwork rc. IP routing tb: find ongt prfix mtc. Comprd qud-tr for N-body imution. Efficinty toring nd qurying XML documnt. 1 f intrn on-wy brncing i xtrn on-wy brncing Ao known : crit-bit tr, rdix tr. 2 84

85 Suffix tr Suffix tr. Ptrici tri of uffix of tring. Linr-tim contruction: w byond cop of ti cour. uffix tr for BANANAS Appiction. BANANAS A NA S NAS NA S S NAS Linr-tim: ongt rptd ubtring, ongt common ubtring, ongt pindromic ubtring, ubtring rc, tndm rpt,. Computtion bioogy dtb (BLAST, FASTA). S 85

86 String ymbo tb ummry A ucc tory in goritm dign nd nyi. Rd-bck BST. Prformnc gurnt: og N ky compr. Support ordrd ymbo tb API. H tb. Prformnc gurnt: contnt numbr of prob. Rquir good function for ky typ. Tri. R-wy, TST. Prformnc gurnt: og N crctr ccd. Support crctr-bd oprtion. 86

Algorithms. Algorithms 5.2 TRIES. R-way tries ternary search tries character-based operations ROBERT SEDGEWICK KEVIN WAYNE

Algorithms. Algorithms 5.2 TRIES. R-way tries ternary search tries character-based operations ROBERT SEDGEWICK KEVIN WAYNE Agoritm ROBERT SEDGEWICK KEVIN WAYNE 5.2 TRIES Agoritm F O U R T H E D I T I O N R-way tri trnary arc tri caractr-bad opration ROBERT SEDGEWICK KEVIN WAYNE ttp://ag4.c.princton.du Lat updatd on 12/4/18

More information

Algorithms. Algorithms 5.2 TRIES. R-way tries ternary search tries character-based operations ROBERT SEDGEWICK KEVIN WAYNE

Algorithms. Algorithms 5.2 TRIES. R-way tries ternary search tries character-based operations ROBERT SEDGEWICK KEVIN WAYNE Agoritm ROBERT SEDGEWICK KEVIN WAYNE 5.2 TRIES Agoritm F O U R T H E D I T I O N R-way tri trnary arc tri caractr-bad opration ROBERT SEDGEWICK KEVIN WAYNE ttp://ag4.c.princton.du Summary of t prformanc

More information

TRIES BBM ALGORITHMS DEPT. OF COMPUTER ENGINEERING ERKUT ERDEM. Apr. 21, 2015

TRIES BBM ALGORITHMS DEPT. OF COMPUTER ENGINEERING ERKUT ERDEM. Apr. 21, 2015 BBM 202 - ALGORITHMS DEPT. OF COMPUTER ENGINEERING ERKUT ERDEM TRIES Apr. 21, 2015 Acknowdgmnt: T cour id ar adaptd from t id prpard by R. Sdgwick and K. Wayn of Princton Univrity. Tri R-way tri Trnary

More information

Tries and Suffix Trees. Inge Li Gørtz

Tries and Suffix Trees. Inge Li Gørtz Tri nd Suffix Tr Ing Li Gørtz String indxing prom String mtcing prom. Givn tring T (txt) nd P (pttrn) ovr n pt Σ, rport trting poition of occurrnc of P in T. Finit utomton: O(mΣ + n) tim nd pc KMP: O(m+n)

More information

Algorithms. Algorithms 5.2 TRIES. R-way tries ternary search tries character-based operations

Algorithms. Algorithms 5.2 TRIES. R-way tries ternary search tries character-based operations Agim ROBERT SEDGEWICK KEVIN WAYNE Summ f pfmnc f m- impmnin Od f gw f fqunc f pin..2 TRIES impmnin pic c c in d dd pin pin n k Agim F O U R T H E D I T I O N R-w i n c i cc-d pin d-ck BST g N g N g N cmpt()

More information

CS 103 BFS Alorithm. Mark Redekopp

CS 103 BFS Alorithm. Mark Redekopp CS 3 BFS Aloritm Mrk Rkopp Brt-First Sr (BFS) HIGHLIGHTED ALGORITHM 3 Pt Plnnin W'v sn BFS in t ontxt o inin t sortst pt trou mz? S?? 4 Pt Plnnin W xplor t 4 niors s on irtion 3 3 3 S 3 3 3 3 3 F I you

More information

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.

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. .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

More information

CPE702 Algorithm Analysis and Design Week 11 String Processing

CPE702 Algorithm Analysis and Design Week 11 String Processing CPE702 Agorithm Anaysis and Dsign Wk 11 String Procssing Prut Boonma prut@ng.cmu.ac.th Dpartmnt of Computr Enginring Facuty of Enginring, Chiang Mai Univrsity Basd on Sids by M.T. Goodrich and R. Tamassia

More information

Applications of trees

Applications of trees Trs Apptons o trs Orgnzton rts Attk trs to syst Anyss o tr ntworks Prsng xprssons Trs (rtrv o norton) Don-n strutur Mutstng Dstnton-s orwrng Trnsprnt swts Forwrng ts o prxs t routrs Struturs or nt pntton

More information

Indexed Search Tree (Trie)

Indexed Search Tree (Trie) Indxd Sarch Tr (Tri) Fawzi Emad Chau-Wn Tsng Dpartmnt of Computr Scinc Univrsity of Maryand, Cog Park Indxd Sarch Tr (Tri) Spcia cas of tr Appicab whn Ky C can b dcomposd into a squnc of subkys C 1, C

More information

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016

Winter 2016 COMP-250: Introduction to Computer Science. Lecture 23, April 5, 2016 Wintr 2016 COMP-250: Introduction to Computr Scinc Lctur 23, April 5, 2016 Commnt out input siz 2) Writ ny lgorithm tht runs in tim Θ(n 2 log 2 n) in wors cs. Explin why this is its running tim. I don

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

Functions and Graphs 1. (a) (b) (c) (f) (e) (d) 2. (a) (b) (c) (d)

Functions and Graphs 1. (a) (b) (c) (f) (e) (d) 2. (a) (b) (c) (d) Functions nd Grps. () () (c) - - - O - - - O - - - O - - - - (d) () (f) - - O - 7 6 - - O - -7-6 - - - - - O. () () (c) (d) - - - O - O - O - - O - -. () G() f() + f( ), G(-) f( ) + f(), G() G( ) nd G()

More information

Some Terminologies. Some Terminologies. Trees. Example: UNIX Directory. Trees. Binary Trees, Binary Search Trees 1/9/2014

Some Terminologies. Some Terminologies. Trees. Example: UNIX Directory. Trees. Binary Trees, Binary Search Trees 1/9/2014 // Som Trminoogis Binry Trs, Binry Srch Trs www.cs.ust.hk/~humin/comp /st.ppt Chid nd prnt Evry nod xcpt th root hs on prnt A nod cn hv n ritrry numr of chidrn Lvs Nods with no chidrn Siing nods with sm

More information

I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o

I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o I M P O R T A N T S A F E T Y I N S T R U C T I O N S W h e n u s i n g t h i s e l e c t r o n i c d e v i c e, b a s i c p r e c a u t i o n s s h o u l d a l w a y s b e t a k e n, i n c l u d f o l

More information

d e c b a d c b a d e c b a a c a d c c e b

d e c b a d c b a d e c b a a c a d c c e b FLAT PEYOTE STITCH Bin y mkin stoppr -- sw trou n pull it lon t tr until it is out 6 rom t n. Sw trou t in witout splittin t tr. You soul l to sli it up n own t tr ut it will sty in pl wn lt lon. Evn-Count

More information

shhgs@wgqqh.com chinapub 2002 7 Bruc Eckl 1000 7 Bruc Eckl 1000 Th gnsis of th computr rvolution was in a machin. Th gnsis of our programming languags thus tnds to look lik that Bruc machin. 10 7 www.wgqqh.com/shhgs/tij.html

More information

FL/VAL ~RA1::1. Professor INTERVI of. Professor It Fr recru. sor Social,, first of all, was. Sys SDC? Yes, as a. was a. assumee.

FL/VAL ~RA1::1. Professor INTERVI of. Professor It Fr recru. sor Social,, first of all, was. Sys SDC? Yes, as a. was a. assumee. B Pror NTERV FL/VAL ~RA1::1 1 21,, 1989 i n or Socil,, fir ll, Pror Fr rcru Sy Ar you lir SDC? Y, om um SM: corr n 'd m vry ummr yr. Now, y n y, f pr my ry for ummr my 1 yr Un So vr ummr cour d rr o l

More information

Minimum Spanning Trees

Minimum Spanning Trees Minimum Spnning Trs Minimum Spnning Trs Problm A town hs st of houss nd st of rods A rod conncts nd only houss A rod conncting houss u nd v hs rpir cost w(u, v) Gol: Rpir nough (nd no mor) rods such tht:

More information

The Z transform techniques

The Z transform techniques h Z trnfor tchniqu h Z trnfor h th rol in dicrt yt tht th Lplc trnfor h in nlyi of continuou yt. h Z trnfor i th principl nlyticl tool for ingl-loop dicrt-ti yt. h Z trnfor h Z trnfor i to dicrt-ti yt

More information

Planar convex hulls (I)

Planar convex hulls (I) Covx Hu Covxty Gv st P o ots 2D, tr ovx u s t sst ovx oyo tt ots ots o P A oyo P s ovx or y, P, t st s try P. Pr ovx us (I) Coutto Gotry [s 3250] Lur To Bowo Co ovx o-ovx 1 2 3 Covx Hu Covx Hu Covx Hu

More information

Trade Patterns, Production networks, and Trade and employment in the Asia-US region

Trade Patterns, Production networks, and Trade and employment in the Asia-US region Trade Patterns, Production networks, and Trade and employment in the Asia-U region atoshi Inomata Institute of Developing Economies ETRO Development of cross-national production linkages, 1985-2005 1985

More information

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018

CSE 373: More on graphs; DFS and BFS. Michael Lee Wednesday, Feb 14, 2018 CSE 373: Mor on grphs; DFS n BFS Mihl L Wnsy, F 14, 2018 1 Wrmup Wrmup: Disuss with your nighor: Rmin your nighor: wht is simpl grph? Suppos w hv simpl, irt grph with x nos. Wht is th mximum numr of gs

More information

Case Study 1 PHA 5127 Fall 2006 Revised 9/19/06

Case Study 1 PHA 5127 Fall 2006 Revised 9/19/06 Cas Study Qustion. A 3 yar old, 5 kg patint was brougt in for surgry and was givn a /kg iv bolus injction of a muscl rlaxant. T plasma concntrations wr masurd post injction and notd in t tabl blow: Tim

More information

3-2-1 ANN Architecture

3-2-1 ANN Architecture ARTIFICIAL NEURAL NETWORKS (ANNs) Profssor Tom Fomby Dpartmnt of Economics Soutrn Mtodist Univrsity Marc 008 Artificial Nural Ntworks (raftr ANNs) can b usd for itr prdiction or classification problms.

More information

Trigonometric functions

Trigonometric functions Robrto s Nots on Diffrntial Calculus Captr 5: Drivativs of transcndntal functions Sction 5 Drivativs of Trigonomtric functions Wat you nd to know alrady: Basic trigonomtric limits, t dfinition of drivativ,

More information

Bayesian belief networks: Inference

Bayesian belief networks: Inference C 740 Knowd rprntton ctur 0 n f ntwork: nfrnc o ukrcht o@c.ptt.du 539 nnott qur C 750 chn rnn n f ntwork. 1. Drctd ccc rph Nod rndo vr nk n nk ncod ndpndnc. urr rthquk r ohnc rc C 750 chn rnn n f ntwork.

More information

Wireless & Hybrid Fire Solutions

Wireless & Hybrid Fire Solutions ic b 8 c b u i N5 b 4o 25 ii p f i b p r p ri u o iv p i o c v p c i b A i r v Hri F N R L L T L RK N R L L rr F F r P o F i c b T F c c A vri r of op oc F r P, u icoc b ric, i fxib r i i ribi c c A K

More information

1 Review: Volumes of Solids (Stewart )

1 Review: Volumes of Solids (Stewart ) Lecture : Some Bic Appliction of Te Integrl (Stewrt 6.,6.,.,.) ul Krin eview: Volume of Solid (Stewrt 6.-6.) ecll: we d provided two metod for determining te volume of olid of revolution. Te rt w by dic

More information

Multiple patterns. Why? Algorithms. Aho Corasick (AC) Text Algorithms (4AP) Lecture 3.2: Multiple pattern matching. Jaak Vilo 2008 fall

Multiple patterns. Why? Algorithms. Aho Corasick (AC) Text Algorithms (4AP) Lecture 3.2: Multiple pattern matching. Jaak Vilo 2008 fall Multipl pattrn Txt Algoritm (AP) Lctur.: Multipl pattrn matcing Jaak Vilo 8 fall S {P} Jaak Vilo MTAT..9 Txt Algoritm Wy? Multipl pattrn Higligt multipl diffrnt arc word on t pag Viru dtction filtr for

More information

n r t d n :4 T P bl D n, l d t z d th tr t. r pd l

n r t d n :4 T P bl D n, l d t z d   th tr t. r pd l n r t d n 20 20 :4 T P bl D n, l d t z d http:.h th tr t. r pd l 2 0 x pt n f t v t, f f d, b th n nd th P r n h h, th r h v n t b n p d f r nt r. Th t v v d pr n, h v r, p n th pl v t r, d b p t r b R

More information

Lecture 20: Minimum Spanning Trees (CLRS 23)

Lecture 20: Minimum Spanning Trees (CLRS 23) Ltur 0: Mnmum Spnnn Trs (CLRS 3) Jun, 00 Grps Lst tm w n (wt) rps (unrt/rt) n ntrou s rp voulry (vrtx,, r, pt, onnt omponnts,... ) W lso suss jny lst n jny mtrx rprsntton W wll us jny lst rprsntton unlss

More information

D t r l f r th n t d t t pr p r d b th t ff f th l t tt n N tr t n nd H n N d, n t d t t n t. n t d t t. h n t n :.. vt. Pr nt. ff.,. http://hdl.handle.net/2027/uiug.30112023368936 P bl D n, l d t z d

More information

Who is this Great Team? Nickname. Strangest Gift/Friend. Hometown. Best Teacher. Hobby. Travel Destination. 8 G People, Places & Possibilities

Who is this Great Team? Nickname. Strangest Gift/Friend. Hometown. Best Teacher. Hobby. Travel Destination. 8 G People, Places & Possibilities Who i thi Gt Tm? Exi Sh th foowing i of infomtion bot of with o tb o tm mt. Yo o not hv to wit n of it own. Yo wi b givn on 5 mint to omih thi tk. Stngt Gift/Fin Niknm Homtown Bt Th Hobb Tv Dtintion Robt

More information

CSC Design and Analysis of Algorithms. Example: Change-Making Problem

CSC Design and Analysis of Algorithms. Example: Change-Making Problem CSC 801- Dsign n Anlysis of Algorithms Ltur 11 Gry Thniqu Exmpl: Chng-Mking Prolm Givn unlimit mounts of oins of nomintions 1 > > m, giv hng for mount n with th lst numr of oins Exmpl: 1 = 25, 2 =10, =

More information

and the ANAVETS Unit Portage Ave, Winnipeg, Manitoba, Canada May 23 to May E L IBSF

and the ANAVETS Unit Portage Ave, Winnipeg, Manitoba, Canada May 23 to May E L IBSF t NVET Uit 283 IR FO RE VET ER N N N I MY NVY & R 3584 Pt, Wii, Mitb, IN O RPORTE E IL L I GU VET IF N ENG R H LI E My 23 t My 28-2015 R LE YOUR ONE TOP HOP FOR QULITY POOL UE & ILLIR EORIE GMEROOM 204-783-2666

More information

Graphs Breadth First Search

Graphs Breadth First Search Grp Brdt Frt Sr SFO ORD LAX DFW - 1 - Outo Ø By undrtndn t tur, you oud to: q L rp ordn to t ordr n w vrt r dovrd n rdt-rt r. q Idnty t urrnt tt o rdt-rt r n tr o vrt tt r prvouy dovrd, ut dovrd or undovrd.

More information

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9 OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at

More information

dy 1. If fx ( ) is continuous at x = 3, then 13. If y x ) for x 0, then f (g(x)) = g (f (x)) when x = a. ½ b. ½ c. 1 b. 4x a. 3 b. 3 c.

dy 1. If fx ( ) is continuous at x = 3, then 13. If y x ) for x 0, then f (g(x)) = g (f (x)) when x = a. ½ b. ½ c. 1 b. 4x a. 3 b. 3 c. AP CALCULUS BC SUMMER ASSIGNMENT DO NOT SHOW YOUR WORK ON THIS! Complt ts problms during t last two wks of August. SHOW ALL WORK. Know ow to do ALL of ts problms, so do tm wll. Itms markd wit a * dnot

More information

Graph Search (6A) Young Won Lim 5/18/18

Graph Search (6A) Young Won Lim 5/18/18 Grp Sr (6A) Youn Won Lm Copyrt () 2015 2018 Youn W. Lm. Prmon rnt to opy, trut n/or moy t oumnt unr t trm o t GNU Fr Doumntton Ln, Vron 1.2 or ny ltr vron pul y t Fr Sotwr Founton; wt no Invrnt Ston, no

More information

Ash Wednesday. First Introit thing. * Dómi- nos. di- di- nos, tú- ré- spi- Ps. ne. Dó- mi- Sál- vum. intra-vé-runt. Gló- ri-

Ash Wednesday. First Introit thing. * Dómi- nos. di- di- nos, tú- ré- spi- Ps. ne. Dó- mi- Sál- vum. intra-vé-runt. Gló- ri- sh Wdsdy 7 gn mult- tú- st Frst Intrt thng X-áud m. ns ní- m-sr-cór- Ps. -qu Ptr - m- Sál- vum m * usqu 1 d fc á-rum sp- m-sr-t- ó- num Gló- r- Fí- l- Sp-rí- : quó-n- m ntr-vé-runt á- n-mm c * m- quó-n-

More information

4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd

4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n, h r th ff r d nd n r t d n 20 20 0 : 0 T P bl D n, l d t z d http:.h th tr t. r pd l 4 4 N v b r t, 20 xpr n f th ll f th p p l t n p pr d. H ndr d nd th nd f t v L th n n f th pr v n f V ln, r dn nd l r thr n nt pr n,

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

More information

Roadmap. XML Indexing. DataGuide example. DataGuides. Strong DataGuides. Multiple DataGuides for same data. CPS Topics in Database Systems

Roadmap. XML Indexing. DataGuide example. DataGuides. Strong DataGuides. Multiple DataGuides for same data. CPS Topics in Database Systems Roadmap XML Indxing CPS 296.1 Topics in Databas Systms Indx fabric Coopr t al. A Fast Indx for Smistructurd Data. VLDB, 2001 DataGuid Goldman and Widom. DataGuids: Enabling Qury Formulation and Optimization

More information

Keeping Up with Mephibosheth

Keeping Up with Mephibosheth 252 Grp Nvmbr 2016, Wk 3 Smll Grp, K-1 Kping Up wit Mpibt Bibl Str: Kping Up wit Mpibt (Dvid nd Mpibt) 2 Sml 9:1-13 Bttm Lin: Hnr tr b kping r prmi. Mmr Vr: Lv n ntr dpl. Hnr tr mr tn rlv. Rmn 12:10, NIrV

More information

TUESDAY JULY Concerning an Upcoming Change Order for the Clearwell Project. Pages 28 SALLISAW MUNICIPAL AUTHORITY SPECIAL MEETING

TUESDAY JULY Concerning an Upcoming Change Order for the Clearwell Project. Pages 28 SALLISAW MUNICIPAL AUTHORITY SPECIAL MEETING SSW MUCP UTHOT SPEC MEETG TUESD U 2 200 0 00M SSW WTE TETMET PT COEECE OOM EPPE OD GED Mg Cd T Od 2 Dc Quum 3 c B P m B P h H W Eg Ccg Upcmg Chg Od h C Pjc Cd d Cc d Ep Ph Pjc Pg 28 dju Pd u 22 200 Tm

More information

,. *â â > V>V. â ND * 828.

,. *â â > V>V. â ND * 828. BL D,. *â â > V>V Z V L. XX. J N R â J N, 828. LL BL D, D NB R H â ND T. D LL, TR ND, L ND N. * 828. n r t d n 20 2 2 0 : 0 T http: hdl.h ndl.n t 202 dp. 0 02802 68 Th N : l nd r.. N > R, L X. Fn r f,

More information

Improving Union. Implementation. Union-by-size Code. Union-by-Size Find Analysis. Path Compression! Improving Find find(e)

Improving Union. Implementation. Union-by-size Code. Union-by-Size Find Analysis. Path Compression! Improving Find find(e) POW CSE 36: Dt Struturs Top #10 T Dynm (Equvln) Duo: Unon-y-Sz & Pt Comprsson Wk!! Luk MDowll Summr Qurtr 003 M! ZING Wt s Goo Mz? Mz Construton lortm Gvn: ollton o rooms V Conntons twn t rooms (ntlly

More information

Executive Committee and Officers ( )

Executive Committee and Officers ( ) Gifted and Talented International V o l u m e 2 4, N u m b e r 2, D e c e m b e r, 2 0 0 9. G i f t e d a n d T a l e n t e d I n t e r n a t i o n a2 l 4 ( 2), D e c e m b e r, 2 0 0 9. 1 T h e W o r

More information

Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v

Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v Th n nt T p n n th V ll f x Th r h l l r r h nd xpl r t n rr d nt ff t b Pr f r ll N v n d r n th r 8 l t p t, n z n l n n th n rth t rn p rt n f th v ll f x, h v nd d pr v n t fr tf l t th f nt r n r

More information

PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D D r r. Pr d nt: n J n r f th r d t r v th tr t d rn z t n pr r f th n t d t t. n

PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D D r r. Pr d nt: n J n r f th r d t r v th tr t d rn z t n pr r f th n t d t t. n R P RT F TH PR D NT N N TR T F R N V R T F NN T V D 0 0 : R PR P R JT..P.. D 2 PR L 8 8 J PR D NT N n TR T F R 6 pr l 8 Th Pr d nt Th h t H h n t n, D.. 20 00 D r r. Pr d nt: n J n r f th r d t r v th

More information

ENGR 7181 LECTURE NOTES WEEK 3 Dr. Amir G. Aghdam Concordia University

ENGR 7181 LECTURE NOTES WEEK 3 Dr. Amir G. Aghdam Concordia University ENGR 78 LECTURE NOTES WEEK Dr. ir G. ga Concoria Univrity DT Equivalnt Tranfr Function for SSO Syt - So far w av tui DT quivalnt tat pac ol uing tp-invariant tranforation. n t ca of SSO yt on can u t following

More information

Last time: introduced our first computational model the DFA.

Last time: introduced our first computational model the DFA. Lctur 7 Homwork #7: 2.2.1, 2.2.2, 2.2.3 (hnd in c nd d), Misc: Givn: M, NFA Prov: (q,xy) * (p,y) iff (q,x) * (p,) (follow proof don in clss tody) Lst tim: introducd our first computtionl modl th DFA. Tody

More information

APPROVAL PROCESS Application Report Part-2

APPROVAL PROCESS Application Report Part-2 A Indi Couni for Tni Edution (An Autonomous Orgniztion, Undr Ministr of HRD, Govt. of Indi) Nson Mnd Mrg,Vsnt Kunj, Nw Di-1100 Wbsit: ttps://www.it-indi.org AROVAL ROCE 2019-20 Appition Rport rt-2 rmnnt

More information

CSE303 - Introduction to the Theory of Computing Sample Solutions for Exercises on Finite Automata

CSE303 - Introduction to the Theory of Computing Sample Solutions for Exercises on Finite Automata CSE303 - Introduction to th Thory of Computing Smpl Solutions for Exrciss on Finit Automt Exrcis 2.1.1 A dtrministic finit utomton M ccpts th mpty string (i.., L(M)) if nd only if its initil stt is finl

More information

16.unified Introduction to Computers and Programming. SOLUTIONS to Examination 4/30/04 9:05am - 10:00am

16.unified Introduction to Computers and Programming. SOLUTIONS to Examination 4/30/04 9:05am - 10:00am 16.unii Introution to Computrs n Prormmin SOLUTIONS to Exmintion /30/0 9:05m - 10:00m Pro. I. Kristin Lunqvist Sprin 00 Grin Stion: Qustion 1 (5) Qustion (15) Qustion 3 (10) Qustion (35) Qustion 5 (10)

More information

Th pr nt n f r n th f ft nth nt r b R b rt Pr t r. Pr t r, R b rt, b. 868. xf rd : Pr nt d f r th B bl r ph l t t th xf rd n v r t Pr, 00. http://hdl.handle.net/2027/nyp.33433006349173 P bl D n n th n

More information

Minimum Spanning Trees

Minimum Spanning Trees Yufi Tao ITEE Univrsity of Qunslan In tis lctur, w will stuy anotr classic prolm: finin a minimum spannin tr of an unirct wit rap. Intrstinly, vn tou t prolm appars ratr iffrnt from SSSP (sinl sourc sortst

More information

COMP108 Algorithmic Foundations

COMP108 Algorithmic Foundations Grdy mthods Prudn Wong http://www.s.liv..uk/~pwong/thing/omp108/01617 Coin Chng Prolm Suppos w hv 3 typs of oins 10p 0p 50p Minimum numr of oins to mk 0.8, 1.0, 1.? Grdy mthod Lrning outoms Undrstnd wht

More information

22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r n. H v v d n f

22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r n. H v v d n f n r t d n 20 2 : 6 T P bl D n, l d t z d http:.h th tr t. r pd l 22 t b r 2, 20 h r, th xp t d bl n nd t fr th b rd r t t. f r r z r t l n l th h r t rl T l t n b rd n n l h d, nd n nh rd f pp t t f r

More information

H NT Z N RT L 0 4 n f lt r h v d lt n r n, h p l," "Fl d nd fl d " ( n l d n l tr l t nt r t t n t nt t nt n fr n nl, th t l n r tr t nt. r d n f d rd n t th nd r nt r d t n th t th n r lth h v b n f

More information

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps

More information

5.5m ETL. Caldicot Level ETL. 5.8m. Sluice. Sluice ETL. 5.8m. Court House 6.7m. Caldicot Level. Pond. Fir Tree Farm. Manor House.

5.5m ETL. Caldicot Level ETL. 5.8m. Sluice. Sluice ETL. 5.8m. Court House 6.7m. Caldicot Level. Pond. Fir Tree Farm. Manor House. t c fr ti wg u fr g purp. igur ii y t b u. A ii ut b c it by t tctr prir t t cct f y fbricti r buig wr. r ppicb, ii ti r t b r cjucti wit pciit cutt' wg; y iprity w wg i t b brugt t t ttti f Svi crptg

More information

46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l pp n nt n th

46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l pp n nt n th n r t d n 20 0 : T P bl D n, l d t z d http:.h th tr t. r pd l 46 D b r 4, 20 : p t n f r n b P l h tr p, pl t z r f r n. nd n th t n t d f t n th tr ht r t b f l n t, nd th ff r n b ttl t th r p rf l

More information

Part 3 System Identification

Part 3 System Identification 2.6 Sy Idnificaion, Eiaion, and Larning Lcur o o. 5 Apri 2, 26 Par 3 Sy Idnificaion Prpci of Sy Idnificaion Tory u Tru Proc S y Exprin Dign Daa S Z { u, y } Conincy Mod S arg inv θ θ ˆ M θ ~ θ? Ky Quion:

More information

5/1/2018. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees

5/1/2018. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees. Huffman Coding Trees /1/018 W usully no strns y ssnn -lnt os to ll rtrs n t lpt (or mpl, 8-t on n ASCII). Howvr, rnt rtrs our wt rnt rquns, w n sv mmory n ru trnsmttl tm y usn vrl-lnt non. T s to ssn sortr os to rtrs tt our

More information

On Hamiltonian Tetrahedralizations Of Convex Polyhedra

On Hamiltonian Tetrahedralizations Of Convex Polyhedra O Ht Ttrrzts O Cvx Pyr Frs C 1 Q-Hu D 2 C A W 3 1 Dprtt Cputr S T Uvrsty H K, H K, C. E: @s.u. 2 R & TV Trsss Ctr, Hu, C. E: q@163.t 3 Dprtt Cputr S, Mr Uvrsty Nwu St. J s, Nwu, C A1B 35. E: w@r.s.u. Astrt

More information

Weighted graphs -- reminder. Data Structures LECTURE 15. Shortest paths algorithms. Example: weighted graph. Two basic properties of shortest paths

Weighted graphs -- reminder. Data Structures LECTURE 15. Shortest paths algorithms. Example: weighted graph. Two basic properties of shortest paths Dt Strutur LECTURE Shortt pth lgorithm Proprti of hortt pth Bllmn-For lgorithm Dijktr lgorithm Chptr in th txtook (pp ). Wight grph -- rminr A wight grph i grph in whih g hv wight (ot) w(v i, v j ) >.

More information

12. Traffic engineering

12. Traffic engineering lt2.ppt S-38. Introution to Tltrffi Thory Spring 200 2 Topology Pths A tlommunition ntwork onsists of nos n links Lt N not th st of nos in with n Lt J not th st of nos in with j N = {,,,,} J = {,2,3,,2}

More information

Theorem 1. An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices.

Theorem 1. An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices. Cptr 11: Trs 11.1 - Introuton to Trs Dnton 1 (Tr). A tr s onnt unrt rp wt no sp ruts. Tor 1. An unrt rp s tr n ony tr s unqu sp pt twn ny two o ts vrts. Dnton 2. A root tr s tr n w on vrtx s n snt s t

More information

Lecture 4: Parsing. Administrivia

Lecture 4: Parsing. Administrivia Adminitrivia Lctur 4: Paring If you do not hav a group, pla pot a rqut on Piazzza ( th Form projct tam... itm. B ur to updat your pot if you find on. W will aign orphan to group randomly in a fw day. Programming

More information

Source code. where each α ij is a terminal or nonterminal symbol. We say that. α 1 α m 1 Bα m+1 α n α 1 α m 1 β 1 β p α m+1 α n

Source code. where each α ij is a terminal or nonterminal symbol. We say that. α 1 α m 1 Bα m+1 α n α 1 α m 1 β 1 β p α m+1 α n Adminitrivia Lctur : Paring If you do not hav a group, pla pot a rqut on Piazzza ( th Form projct tam... itm. B ur to updat your pot if you find on. W will aign orphan to group randomly in a fw day. Programming

More information

0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r

0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n. R v n n th r n r t d n 20 22 0: T P bl D n, l d t z d http:.h th tr t. r pd l 0 t b r 6, 20 t l nf r nt f th l t th t v t f th th lv, ntr t n t th l l l nd d p rt nt th t f ttr t n th p nt t th r f l nd d tr b t n.

More information

Problem solving by search

Problem solving by search Prolm solving y srh Tomáš voo Dprtmnt o Cyrntis, Vision or Roots n Autonomous ystms Mrh 5, 208 / 3 Outlin rh prolm. tt sp grphs. rh trs. trtgis, whih tr rnhs to hoos? trtgy/algorithm proprtis? Progrmming

More information

Aim To manage files and directories using Linux commands. 1. file Examines the type of the given file or directory

Aim To manage files and directories using Linux commands. 1. file Examines the type of the given file or directory m E x. N o. 3 F I L E M A N A G E M E N T Aim To manag ils and dirctoris using Linux commands. I. F i l M a n a g m n t 1. il Examins th typ o th givn il or dirctory i l i l n a m > ( o r ) < d i r c t

More information

Designing A Uniformly Loaded Arch Or Cable

Designing A Uniformly Loaded Arch Or Cable Dsinin A Unirmy Ar Or C T pr wit tis ssn, i n t Nxt uttn r r t t tp ny p. Wn yu r n wit tis ssn, i n t Cntnts uttn r r t t tp ny p t rturn t t ist ssns. Tis is t Mx Eyt Bri in Stuttrt, Grmny, sin y Si

More information

² Ý ² ª ² Þ ² Þ Ң Þ ² Þ. ² à INTROIT. huc. per. xi, sti. su- sur. sum, cum. ia : ia, ia : am, num. VR Mi. est. lis. sci. ia, cta. ia.

² Ý ² ª ² Þ ² Þ Ң Þ ² Þ. ² à INTROIT. huc. per. xi, sti. su- sur. sum, cum. ia : ia, ia : am, num. VR Mi. est. lis. sci. ia, cta. ia. str Dy Ps. 138 R 7 r r x, t huc t m m, l : p - í pr m m num m, l l : VR M rá s f ct st sc n -, l l -. Rpt nphn s fr s VR ftr ch vrs Ps. 1. D n, pr bá m, t c g ví m : c g ví ss s nm m m, t r r r c nm m

More information

L...,,...lllM" l)-""" Si_...,...

L...,,...lllM l)- Si_...,... > 1 122005 14:8 S BF 0tt n FC DRE RE FOR C YER 2004 80?8 P01/ Rc t > uc s cttm tsus H D11) Rqc(tdk ;) wm1111t 4 (d m D m jud: US

More information

APPENDIX F WATER USE SUMMARY

APPENDIX F WATER USE SUMMARY APPENDX F WATER USE SUMMARY From Past Projects Town of Norman Wells Water Storage Facltes Exstng Storage Requrements and Tank Volume Requred Fre Flow 492.5 m 3 See Feb 27/9 letter MACA to Norman Wells

More information

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

Rapid growth in enrolment within the French Immersion program

Rapid growth in enrolment within the French Immersion program Nw Nh Ajx Fch Ii ch- Ovviw R Di PS p i Spb 2009 u ck Egih Fch Ii ch Egih Fch Ii Y E E Pb 2009 333 197 0 2010 405 281 2 2011 431 332 6 2012 466 409 10 2013 486 474 14 Rpi gwh i wihi h Fch Ii pg Pp c Fch

More information

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs.

Paths. Connectivity. Euler and Hamilton Paths. Planar graphs. Pths.. Eulr n Hmilton Pths.. Pth D. A pth rom s to t is squn o gs {x 0, x 1 }, {x 1, x 2 },... {x n 1, x n }, whr x 0 = s, n x n = t. D. Th lngth o pth is th numr o gs in it. {, } {, } {, } {, } {, } {,

More information

Lecture 21 : Graphene Bandstructure

Lecture 21 : Graphene Bandstructure Fundmnls of Nnolcronics Prof. Suprio D C 45 Purdu Univrsi Lcur : Grpn Bndsrucur Rf. Cpr 6. Nwor for Compuionl Nnocnolog Rviw of Rciprocl Lic :5 In ls clss w lrnd ow o consruc rciprocl lic. For D w v: Rl-Spc:

More information

4 8 N v btr 20, 20 th r l f ff nt f l t. r t pl n f r th n tr t n f h h v lr d b n r d t, rd n t h h th t b t f l rd n t f th rld ll b n tr t d n R th

4 8 N v btr 20, 20 th r l f ff nt f l t. r t pl n f r th n tr t n f h h v lr d b n r d t, rd n t h h th t b t f l rd n t f th rld ll b n tr t d n R th n r t d n 20 2 :24 T P bl D n, l d t z d http:.h th tr t. r pd l 4 8 N v btr 20, 20 th r l f ff nt f l t. r t pl n f r th n tr t n f h h v lr d b n r d t, rd n t h h th t b t f l rd n t f th rld ll b n

More information

Spanning Trees. BFS, DFS spanning tree Minimum spanning tree. March 28, 2018 Cinda Heeren / Geoffrey Tien 1

Spanning Trees. BFS, DFS spanning tree Minimum spanning tree. March 28, 2018 Cinda Heeren / Geoffrey Tien 1 Spnnn Trs BFS, DFS spnnn tr Mnmum spnnn tr Mr 28, 2018 Cn Hrn / Gory Tn 1 Dpt-rst sr Vsts vrts lon snl pt s r s t n o, n tn ktrks to t rst junton n rsums own notr pt Mr 28, 2018 Cn Hrn / Gory Tn 2 Dpt-rst

More information

Gilbert the Green Tree Frog

Gilbert the Green Tree Frog Gbrt th Gr Tr Frog A org Kpr Kd book Wrtt by Stph Jk Iutrtd by T Eor ONCE UPON A TIME thr w frog md Gbrt. Gbrt w Gr Tr Frog. H fmy w gr. H hom w gr. Ad omtm v h food w gr. Gbrt w ck d trd of bg o gr th

More information

29'-5" 10'-0" 14B 5 2'-9" W/D 14'-0" NEW STAIRS NEW 1-1/2 HR. F.P.S.C. LIVING ROOM/KITCHEN 26'-8" 8'-6" CLG. 14B (266 SQ.FT.) 30'-0" NEW ELEVATOR 14B

29'-5 10'-0 14B 5 2'-9 W/D 14'-0 NEW STAIRS NEW 1-1/2 HR. F.P.S.C. LIVING ROOM/KITCHEN 26'-8 8'-6 CLG. 14B (266 SQ.FT.) 30'-0 NEW ELEVATOR 14B VILLR CST -7 BT IRON VILLR CST -7 BT IRON -8- SINS TOCCT STINLSS STL -8- SINS TOCCT STINLSS STL SINS TOCCT STINLSS STL -8- '-0" B..I '-0" 9'-" OPN RR YRD VILLR CST -7 BT IRON DISCLIMR NOT '-" 9'-" 8'-"

More information

Beechwood Music Department Staff

Beechwood Music Department Staff Beechwood Music Department Staff MRS SARAH KERSHAW - HEAD OF MUSIC S a ra h K e rs h a w t r a i n e d a t t h e R oy a l We ls h C o l le g e of M u s i c a n d D ra m a w h e re s h e ob t a i n e d

More information

4.8 Huffman Codes. Wordle. Encoding Text. Encoding Text. Prefix Codes. Encoding Text

4.8 Huffman Codes. Wordle. Encoding Text. Encoding Text. Prefix Codes. Encoding Text 2/26/2 Word A word a word coag. A word contrctd ot of on of th ntrctor ar: 4.8 Hffan Cod word contrctd ng th java at at word.nt word a randozd grdy agorth to ov th ackng rob Encodng Txt Q. Gvn a txt that

More information

Computer Graphics. Viewing & Projections

Computer Graphics. Viewing & Projections Vw & Ovrvw rr : rss r t -vw trsrt: st st, rr w.r.t. r rqurs r rr (rt syst) rt: 2 trsrt st, rt trsrt t 2D rqurs t r y rt rts ss Rr P usuy st try trsrt t wr rts t rs t surs trsrt t r rts u rt w.r.t. vw vu

More information

owm and A L T O SOLO 64 Years Nathan W. Blair, a well-known mcnts from the fair association on him. sight. store. We appreciate your business.

owm and A L T O SOLO 64 Years Nathan W. Blair, a well-known mcnts from the fair association on him. sight. store. We appreciate your business. BU RK OC < O OO OU XXX RD D O B O C G U R D Y U G U 929 B O B B D 6 Y C G D / / 7 COO/ U C O Y B - C G - C - R 2 ) -» - - - O 2- - -- 7 - C C? - - D O - G [ B - - - C - - 2 - - 7 R B - - - } 2 - q - D

More information

CLKOUT CLKOUT VCC CLKOUT RESOUT OSCOUT ALE TEST AD0 66 AD2 INT0 INT0 AD INT1 AD INT2/INTA0 AD5 AD7 AD7 INT AD8 AD8 AD10

CLKOUT CLKOUT VCC CLKOUT RESOUT OSCOUT ALE TEST AD0 66 AD2 INT0 INT0 AD INT1 AD INT2/INTA0 AD5 AD7 AD7 INT AD8 AD8 AD10 I U N R 00K RSIN* RST S N.0u Y LK TP RP K L TP USY INT0 INT RISMINT P.0 P. P. P. P. P. P. RY OL RX0 TX0 T P.0 P. P. P. S* S* S* S* RROR* SLK U LKIN LKOUT LKOUT LKIN LKOUT OSOUT 0 OSOUT L L RSIN* L 0 0

More information

Graphs Depth First Search

Graphs Depth First Search Grp Dpt Frt Sr SFO 337 LAX 1843 1743 1233 802 DFW ORD - 1 - Grp Sr Aort - 2 - Outo Ø By unrtnn t tur, you ou to: q L rp orn to t orr n w vrt r ovr, xpor ro n n n pt-rt r. q Cy o t pt-rt r tr,, orwr n ro

More information

learning objectives learn what graphs are in mathematical terms learn how to represent graphs in computers learn about typical graph algorithms

learning objectives learn what graphs are in mathematical terms learn how to represent graphs in computers learn about typical graph algorithms rp loritms lrnin ojtivs loritms your sotwr systm sotwr rwr lrn wt rps r in mtmtil trms lrn ow to rprsnt rps in omputrs lrn out typil rp loritms wy rps? intuitivly, rp is orm y vrtis n s twn vrtis rps r

More information

Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano

Divided. diamonds. Mimic the look of facets in a bracelet that s deceptively deep RIGHT-ANGLE WEAVE. designed by Peggy Brinkman Matteliano RIGHT-ANGLE WEAVE Dv mons Mm t look o ts n rlt tt s ptvly p sn y Py Brnkmn Mttlno Dv your mons nto trnls o two or our olors. FCT-SCON0216_BNB66 2012 Klm Pulsn Co. Ts mtrl my not rprou n ny orm wtout prmsson

More information

Similarity Search. The Binary Branch Distance. Nikolaus Augsten.

Similarity Search. The Binary Branch Distance. Nikolaus Augsten. Similrity Srh Th Binry Brnh Distn Nikolus Augstn nikolus.ugstn@sg..t Dpt. of Computr Sins Univrsity of Slzurg http://rsrh.uni-slzurg.t Vrsion Jnury 11, 2017 Wintrsmstr 2016/2017 Augstn (Univ. Slzurg) Similrity

More information

l f t n nd bj t nd x f r t l n nd rr n n th b nd p phl t f l br r. D, lv l, 8. h r t,., 8 6. http://hdl.handle.net/2027/miun.aey7382.0001.001 P bl D n http://www.hathitrust.org/access_use#pd Th r n th

More information

CSE 373. Graphs 1: Concepts, Depth/Breadth-First Search reading: Weiss Ch. 9. slides created by Marty Stepp

CSE 373. Graphs 1: Concepts, Depth/Breadth-First Search reading: Weiss Ch. 9. slides created by Marty Stepp CSE 373 Grphs 1: Conpts, Dpth/Brth-First Srh ring: Wiss Ch. 9 slis rt y Mrty Stpp http://www.s.wshington.u/373/ Univrsity o Wshington, ll rights rsrv. 1 Wht is grph? 56 Tokyo Sttl Soul 128 16 30 181 140

More information

Table of C on t en t s Global Campus 21 in N umbe r s R e g ional Capac it y D e v e lopme nt in E-L e ar ning Structure a n d C o m p o n en ts R ea

Table of C on t en t s Global Campus 21 in N umbe r s R e g ional Capac it y D e v e lopme nt in E-L e ar ning Structure a n d C o m p o n en ts R ea G Blended L ea r ni ng P r o g r a m R eg i o na l C a p a c i t y D ev elo p m ent i n E -L ea r ni ng H R K C r o s s o r d e r u c a t i o n a n d v e l o p m e n t C o p e r a t i o n 3 0 6 0 7 0 5

More information

N V R T F L F RN P BL T N B ll t n f th D p rt nt f l V l., N., pp NDR. L N, d t r T N P F F L T RTL FR R N. B. P. H. Th t t d n t r n h r d r

N V R T F L F RN P BL T N B ll t n f th D p rt nt f l V l., N., pp NDR. L N, d t r T N P F F L T RTL FR R N. B. P. H. Th t t d n t r n h r d r n r t d n 20 2 04 2 :0 T http: hdl.h ndl.n t 202 dp. 0 02 000 N V R T F L F RN P BL T N B ll t n f th D p rt nt f l V l., N., pp. 2 24. NDR. L N, d t r T N P F F L T RTL FR R N. B. P. H. Th t t d n t r

More information