A Fast String Matching Algorithm

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A Fast String Matching Algorithm

• The Boyer Moore Algorithm

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The obvious search algorithm

• Considers each character position of str and
  determines whether the successive patlen
  characters of str matches pat.
• In worst case, the number of comparisons is in
  the order of ipatlen.
• Ex. pat aab str ..aaaaac .

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Knuth-Pratt-Morris Algoritm

• Linear search algorithm.
• Preprocesses pat in time linear in patlen and
  searches str in time linear in ipatlen.
• EXAMPLE
• HERE IS A SIMPLE EXAMPLE

EXAMPLE
EXAMPLE
EXAMPLE
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Characteristics of Boyer Moore Algorithm

• Basic idea string matches the pattern from the
  right rather than from the left.
• Expected value c( i patlen ), clt1
• Preprocessing pat and compute two tables delta1
  delta2 for shifting pat the pointer of str.
• Ex. pat AT-THAT str WHICH-FINALLY-HALTS
  .AT-THAT-POINT

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Informal Description

• Compare the last char of the pat with the
  patlenth char of str
• AT-THAT
• WHICH-FINALLY-HALTS.AT-THAT-POINT
• Observation 1 char is not to occur in pat, skip
  patlen( delta1(F) ) chars of str.

AT-THAT
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Informal Description

• Observation 2 char is in pat, slide pat down
  delta1(-) positions so that char is aligned to
  the corresponding character in pat.
• delta1(char) if char not occur in pat,then
  patlen else patlen j , where j is the maximum
  integer such that pat(j)char.

AT-THAT WHICH-FINALLY-HALTS.--AT-THAT-P
OINT
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Informal Description

• Observation 3a str matches the last m chars of
  pat, and came to a mismatch at some new char.
  Move strptr by delta1(L).(pat shifted by
  delta1(L)-m)
• AT-THAT
• FINALLY-HALTS.--AT-THAT-POINT

AT-THAT
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Informal Description

• Observation 3b the final m chars of pat (a
  subpat) is matched, find the right most plausible
  reoccurrence of the subpat, align it with the
  matched m chars of str (slide pat delta2(-)
  positions).
• AT-THAT
• FINALLY-HALTS.AT-THAT-POINT

AT-THAT
AT-THAT
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The delta1 delta2 tables

• The delta1 table has as many entries as there are
  chars in the alphabet.
• Ex. pat a b c d e a t t h a t
• delta1 4 3 2 1 0 else,5 1 0 4 0 2 1 0
  else,7
• The delta2 table has as many entries as there are
  chars in pat.
• delta2( j ) ( j 1- rpr(j) ) (patlen j)
  patlen 1 - rpr(j)
• Ex. pat a b c d e a t - t h a t
• delta2 9 8 7 6 1 11 10 9 8 7 8 1

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The algorithm

• stringlen length of string.
• i patlen.
• top if i gt stringlen then return false.
• j patlen.
• loop if j0 then return i1.
• if string(i)pat(j)
• then
• j j-1
• i i-1
• goto loop.
• close
• i i max( delta1(sting(i)) , delta2(j))
• goto top.

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(No Transcript)
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Performance (empirical evidence)
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The Implementation in mstring.c

• Function make_skip(char, int)
• Purpose create the skip(delta 1) table
• Function inputs char ptrn, int plen
• Local variables int skip, sptr
• Return int skip
• Function make_shift(char, int)
• Purpose create the shift(delta2) table
• Function inputs charptrn, int plen
• Local variables int shift, sptr char pptr, c
• Return int shift

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Flowchart of make_skip()
Return skip
true

• Allocate
• memory
• to skip

skipplen1
plen0?
false
skipptrnplen--
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make_skip()

• int make_skip(char ptrn, int plen)
• int skip (int ) malloc(256
  sizeof(int))
• int sptr skip256
• if (skip NULL)
• FatalPrintError("malloc")
• while(sptr-- ! skip)
• sptr plen 1
• while(plen ! 0)
• skip(unsigned char) ptrn plen--
• return skip

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• Allocate memory to shift

Procedures of make_shift()
cptrnplen-1
Look for rpr of c
Look for two identical subpat
Assign values to shift
Return shift
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make_shift()

• int shift (int ) malloc(plen
  sizeof(int))
• int sptr shift plen - 1
• char pptr ptrn plen - 1
• char c
• if (shift NULL)
• FatalPrintError("malloc")
• c ptrnplen - 1
• sptr 1

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make_shift()

• while(sptr-- ! shift)
• char p1 ptrn plen - 2, p2, p3
• do
• while(p1 gt ptrn p1-- ! c)
• p2 ptrn plen - 2
• p3 p1
• while(p3 gt ptrn p3-- p2--
  p2 gt pptr)
• while(p3 gt ptrn p2 gt pptr) //
  p2gtj,p3gt1
• sptr shift plen - sptr p2 - p3
• pptr--
• return shift

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• Exj5
• j 1 2 3 4 5 6 7
• Pat e d b c a b c
• step1 p1
• step2 p3 p2
• syep3 p3 p2
• ? delta2( j ) (p2-p3) (plen j) 5