Tries and Suffix Trees. Inge Li Gørtz
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1 Tri nd Suffix Tr Ing Li Gørtz
2 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) tim nd pc String indxing prom. Givn tring S of crctr from n pt Σ. Prproc S into dt tructur to upport Src(P): Rturn trting poition of occurrnc of P in S. Tod: Dt tructur uing O(n) pc nd upporting Src(P) in O(m) tim. Appiction: Src ngin,.g. prfix rc. Finding common utring of mn ioogic tring Finding rpting utructur in ioogic tring Dtcting DNA contmintion
3 Outin Tri Comprd tri Suffix tr Appiction of uffix tr
4 Tri
5 Tri Txt rtriv t S 2 S 4 S 6 S 3 S 1 S 5 Tri ovr t tring:,, t,,, t.
6 Tri Txt rtriv Prfix-fr? t S 2 S 4 S 6 S 3 S 1 S 5 Tri ovr t tring:,, t,,, t,.
7 Tri Txt rtriv Prfix-fr? t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
8 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
9 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
10 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
11 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
12 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
13 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
14 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
15 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
16 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
17 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
18 Tri Txt rtriv Src for t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
19 Tri Txt rtriv Src for t S 2 S 4 S 7 S 6 S 3 S 1 S5 Tri ovr t tring:,, t,,, t,.
20 Tri Txt rtriv Src for ort t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
21 Tri Txt rtriv Src for ort t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
22 Tri Txt rtriv Src for ort t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
23 Tri Txt rtriv Src for ort t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
24 Tri Txt rtriv Src for ort t S 2 S 4 S 6 S 3 S 7 S 1 S5 Tri ovr t tring:,, t,,, t,.
25 Tri Buid tri ovr t tring:,,. S 2 S 4 S 1
26 Tri Proprti of t tri. A tri T toring coction S of tring of tot ngt n from n pt of iz d t foowing proprti: How mn cidrn cn nod v? How mn v do T v? Wt i t igt of T? Wt i t numr of nod in T?
27 Tri Src tim: O(d) in c nod => O(dm). O(m) if d contnt. d not contnt: u dictionr Hing O(1) Bncd BST: O(og d) Tim nd pc for tri (for m/contnt d): O(m) for rcing for tring of ngt m. O(n) pc. Prprocing: O(n)
28 Tri Prfix rc: rturn word in t tri trting wit t S 2 S 4 S 6 S 3 S 7 S 1 S5
29 Tri Prfix rc: rturn word in t tri trting wit t S 2 S 4 S 6 S 3 S 7 S 1 S5
30 Tri Prfix rc: rturn word in t tri trting wit t S 2 S 4 S 6 S 3 S 7 S 1 S5
31 Tri Tim for prfix rc: O(m) + tim to rport occurrnc. Coud rg!! Soution: compct tri.
32 Compct tri
33 Tri Compct tri: Cin of nod wit ing cid i mrgd into ing nod. t S 2 S 4 S 6 S 3 S 7 S 1 S5
34 Tri Compct tri: Cin of nod wit ing cid i mrgd into ing nod. t t S 2 S6 S3 S4 S1 S5 S7
35 Tri Proprti of t compct tri. A compct tri T toring coction S of tring of tot ngt n from n pt of iz d t foowing proprti: Evr intrn nod of T t t 2 nd t mot d cidrn. T v T numr of nod in T i < 2. Tim nd pc for compct tri (contnt d): O(m) for rcing for tring of ngt m. O(m + occ) for prfix rc, wr occ = #occurrnc O() pc. Prprocing: O(n)
36 Suffix tr
37 Suffix tr String indxing prom. Givn tring S of crctr from n pt Σ. Prproc S into dt tructur to upport Src(P): Rturn trting poition of occurrnc of P in S. Buid comprd tri ovr uffix of S (uffix tr). L v wit indx of uffix. Orvtion: An occurrnc of P i prfix of uffix of S. occurrnc of P Suffix of S
38 Suffix tr String indxing prom. Givn tring S of crctr from n pt Σ. Prproc S into dt tructur to upport Src(P): Rturn trting poition of occurrnc of P in S. Buid comprd tri ovr uffix of S (uffix tr). L v wit indx of uffix. Orvtion: An occurrnc of P i prfix of uffix of S. occurrnc of P Suffix of S Exmp: P = n. n n t r i n g d Suffix of S Suffix of S
39 Suffix Tr Suffix tr: ovr t tring nn n n 6 n n 1 n n
40 Suffix Tr Suffix tr: ovr t tring nn n n 6 n n 1 n n Src for P. Rport of v ow fin nod
41 Suffix Tr Suffix tr: ovr t tring nn Find occurrnc of P= n n n 6 n n 1 n n Src for P. Rport of v ow fin nod
42 Suffix Tr Suffix tr: ovr t tring nn n n 6 n n 1 n n Stor S nd tor nod rfrnc to S n n
43 Suffix Tr Suffix tr: ovr t tring nn [2,2] [3,4] [7,7] [1,7] [3,4] [7,7] 7 6 [5,7] [7,7] [5,7] [7,7] Stor S nd tor nod rfrnc to S n n
44 Suffix tr nd common utring
45 Suffix tr Suffix tr of tring S: Compct tri ovr uffix of S. Spc nd tim: Spc: O(n) Src tim: O(m) + tim to rport occurrnc = O(m+occ) Prprocing: Cn don in O(ort(n, Σ )) tim, wr ort(n, Σ ) i t tim it tk to ort n crctr from n pt Σ. Suffix tr cn ud to ov t String indxing prom in: Spc: O(n) Src tim: O(m+occ) Prprocing: O(ort(n, Σ )) tim
46 Appiction of uffix tr
47 Longt common utring Find ongt common utring of tring S1 nd S2. Contruct t uffix tr ovr S11S22. Exmp: Find ongt common utring of pipi nd pipi: Contruct uffix tr of pipi1pipi2.
48 Gnrizd uffix tr Suffix tr of pipi1pipi i p i p i 2 2 p i 2 2 p i p i p i p i p i
49 Gnrizd uffix tr Suffix tr of pipi1pipi2. Mrk f wit if 1 uffix trt in S
50 Gnrizd uffix tr Suffix tr of pipi1pipi2. Mrk f wit if 1 uffix trt in S
51 Gnrizd uffix tr Suffix tr of pipi1pipi2. Mrk f wit if 1 uffix trt in S1. Add tring-dpt. [18,18] [9,18] [15,15] [14,15] [13,15] [17,17] [16,18] [17,17] [13,18] [16,18] [8,8] [13,18] [16,18] [8,8] [13,18] [18,18] [5,18] [9,18] [18,18] [9,18] [5,18] [9,18] [5,18] [9,18] [5,18]
52 Gnrizd uffix tr Suffix tr of pipi1pipi2. Mrk f wit if 1 uffix trt in S1. Add tring-dpt. [18,18] [9,18] [15,15] [14,15] [13,15] [17,17] [16,18] [17,17] [13,18] [16,18] [8,8] [13,18] [16,18] [8,8] [13,18] [18,18] [5,18] [9,18] [18,18] [9,18] [5,18] [9,18] [5,18] [9,18] [5,18] S[13,15] = pi i t ongt common utring.
53 Longt common utring Uing uffix tr w cn ov t ongt common utring prom in inr tim (for contnt iz pt).
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