String Matching

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
i1 j1 k1 While j T.length And k
P.length Do If tj pk Then j j
1 k k 1 Else i i 1 j
i k 1 End If End While If k gt
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
fail1 0 For k 2 to P.length Do r
failk-1 While r gt 0 And Pr ¹ Pk-1 Do
r failr End While failk
k1 End For
7
KMP Match Algorithm
j 1 k 1 While jT.Length And kP.Length
Do If k 0 Or Tj Pk Then j j
1 k k 1 Else k failk
End If End While If kgtP.length Then Return
True Else Return False End If