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 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; Return False; Endif

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

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

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

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; Return False;