Pattern matching

Pattern Matching Dr. Andrew Davison WiG Lab (teachers room) , CoE [email_address] .psu.ac.th 240-301, Computer Engineering Lab III (Software) T: P: Semester 1, 200 6 -200 7

Overview ,[object Object],[object Object],[object Object],[object Object],[object Object]

1. What is Pattern Matching? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

String Concepts ,[object Object],[object Object],[object Object],[object Object],[object Object]

Examples ,[object Object],[object Object],[object Object],[object Object],[object Object],a n d r e w S 0 5

2. The Brute Force Algorithm ,[object Object],a n d r e w T: r e w P: a n d r e w T: r e w P: . . . . P moves 1 char at a time through T

Brute Force in Java ,[object Object],Return index where pattern starts, or -1

Analysis ,[object Object],[object Object],continued

[object Object],[object Object],[object Object],[object Object],continued

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

3. The Boyer-Moore Algorithm ,[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],[object Object],x a T i b a P j

Case 1 ,[object Object],x a T i b a P j x c x a T i new b a P j new x c ? ? and move i and j right, so j at end

Case 2 ,[object Object],a x T i a x P j c w a x T i new a x P j new c w ? and move i and j right, so j at end x x is after j position x

Case 3 ,[object Object],x a T i b a P j d c x a T i new b a P j new d c ? ? and move i and j right, so j at end No x in P ? 0

Last Occurrence Function ,[object Object],[object Object],[object Object],[object Object],[object Object]

L() Example ,[object Object],[object Object],-1 3 5 4 L ( x ) d c b a x a b a c a b 0 1 2 3 4 5 P L() stores indexes into P[]

Note ,[object Object],[object Object],[object Object]

Boyer-Moore Example (2) T: P:  1 3 5 4 L ( x ) d c b a x

Boyer-Moore in Java ,[object Object],Return index where pattern starts, or -1

Analysis ,[object Object],[object Object],[object Object],[object Object]

Worst Case Example ,[object Object],[object Object],T: P:

4. The KMP Algorithm ,[object Object],[object Object],continued

[object Object],[object Object]

Example T: P: j new = 2 j = 5 i

Why ,[object Object],[object Object],[object Object],j == 5

KMP Failure Function ,[object Object],[object Object],[object Object],[object Object]

[object Object],[object Object],[object Object],Failure Function Example F(k) is the size of the largest prefix. (k == j-1) 1 3 2 4 2 1 0 j 1 0 0 F ( j ) k F(k)

Why is F(4) == 2? ,[object Object],[object Object],[object Object],[object Object],[object Object],P: "abaaba"

[object Object],[object Object],Using the Failure Function

KMP in Java ,[object Object],Return index where pattern starts, or -1

[object Object],Similar code to kmpMatch()

Example 0 3 1 4 2 1 0 k 1 0 0 F ( k ) T: P:

Why is F(4) == 1? ,[object Object],[object Object],[object Object],[object Object],[object Object],P: "abacab"

KMP Advantages ,[object Object],[object Object],[object Object],[object Object]

KMP Disadvantages ,[object Object],[object Object],[object Object]

KMP Extensions ,[object Object],a a a b b x T: P: Basic KMP does not do this. a a a b b a a a a b b a

5. More Information ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],This book is in the CoE library.

Pattern matching

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