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String Matching

String Matching. Statement of the Problem. Given a Target string T, such as ABABABCCA And a Pattern string P, such as ABABC Find the First Occurence of P in T. The Simple Algorithm. i:=1; j:=1; k:=1; While j £ T.length And k £ P.length Do If t[j] = p[k] Then

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String Matching

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  1. String Matching

  2. Statement of the Problem • Given a Target string T, such as ABABABCCA • And a Pattern string P, such as ABABC • Find the First Occurence of P in T

  3. The Simple Algorithm i:=1; j:=1; k:=1; While j £ T.length And k £ P.length Do If t[j] = p[k] Then j := j + 1; k := k + 1; Else i := i + 1; j := i; k := 1; End If End While; If k > P.length Then Return True; Else Return False; Endif

  4. Better Algorithms? • The Simple Algorithm is Q(nm) where n and m are the lengths of the two strings • The Simple Algorithm Searches places that are “Proven to be bad” • Complete fore-knowledge of the pattern string is assumed

  5. The KMP Diagram Pattern String: “ABABCB” f f f f Get Next Character s s s s s s s A B A B C B * f 1 2 3 4 5 6 7 f 0 Following “s” link gets next character Refers to Target String

  6. Setting The Fail Links fail[1] := 0; For k := 2 to P.length Do r := fail[k-1]; While r > 0 And P[r] ¹ P[k-1] Do r := fail[r]; End While; fail[k] := k+1; End For

  7. KMP Match Algorithm j := 1; k := 1; While j£T.Length And k£P.Length Do If k = 0 Or T[j] = P[k] Then j := j + 1; k := k + 1; Else k := fail[k]; End If End While; If k>P.length Then Return True; Else Return False; End If

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