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;
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* 1 2 3 f 4 5 6 7 f
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;
Return False;