1. Knuth-Morris-Pratt algorithm
Presented by
Sathyasathish

2. Agenda Problem/issue Conventional Solution(Compare/one shift) & Ѳ
KMP solution & Ѳ

3. Pattern Matching Problem/issue
Finding occurrence of a pattern(string) ‘P’ in String ‘S’ and also finding the position in ‘S’ where the pattern match occurs
Source:

4. Conventional Solution
Compare each character of P with S if match continue else shift one position String S a b c a b
Pattern p
Source:

5. Comparison S S a b c a b p Step 2: compare p[2] with S[2] a b c p a b
Source:

6. Comparison a b c p a b Step 3: compare p[3] with S[3] S
Mismatch occurs here.. p a b
“Since mismatch is detected, shift ‘P’ one position to the Right and
perform steps analogous to those from step 1 to step 3. At position
where mismatch is detected, shift ‘P’ one position to the right and
repeat matching procedure. “
Source:

7. Conventional match program
for ( i=0;i+P.length<T.length; i++) { x++; for ( j=0; i+j <T.length && j< P.length && T[i+j]==P[j]; ++z,j++) { //System.out.println(""+T[i+j]+P[j]); flag=false } j++; m=m+j; if (j ==P.length+1 ) System.out.println("found a match at "+(i+1)); System.out.println("Program Charecter comparision : "+(m)+"\nNumber of attepmts : "+x)
Soucrce: migrated from C to java by Sathya

8. of Conventional Outer loop n times (n length of String ‘S’)
Inner loop m times (m length of Pattern ‘P’)
Code:
for (m){
for(n); }
Ѳ (mn)

9. KMP
Potential area where conventional algorithm can be improved are a follows
It never keep track previously known character in the then string when there is a partial match , on mis- match it again does comparison for all character in the string
KMP uses learning(from partial match) in the String and Pattern (overlap in the pattern)while comparison and we will see how much efficiency it has delivered

10. Example
T: b a n a n a n o b a n o i=0: X i=1: X i=2: n a n X i=3: X i=4: n a n o i=5: X i=6: n X i=7: X i=8: X i=9: n X i=10: X After investing a lot of work making comparisons in the inner loop of the code, a lot about what's in the text in known (partial match of j characters starting at position i, you know what's in positions S[i]...S[i+j-1]. ), KMP uses this learning

11. KMP Solution
Issue with Conventional Algorithm i=2: n a n i=3: n a n o(Invalid Shift or wasted shift) KMP First Optimization step -skipping Outer loop i=2: n a n x i=4: n a n o(valid shift or learnt shift) KMP Second Optimization step -skipping Inner loop i=2: n a n x

12. Comparison
KMP

13. KMP Algorithm
It differ from conventional algorithm when there is partial mismatch
How it differ we will see in a while!
First we have to under stand proper prefix and a proper suffix
Example
S=“nano “
Prefix-n,na , nan but not (nano itself)
Suffix- 0, no, ano but not (nano itself)
why we need to know this ?

14. Suffix Prefix
Take : String :- abcdabfxxxxx Pattern :- abcdabe Start next comparison from String :- abcdabfXXXXXX Pattern :- abcdabe

15. How KMP achieve this
First it preprocess the pattern irrespective of String to compared. And identify the occurrence of same proper prefix or suffix this is called border or window
When there is a mismatch it goes and tries with next largest window
Example :ABAMABA

16. Preprocessing

17. Preprocessing & window width table

18. String and Pattern matching

19. Ѳ KMP Table can be computed in Ѳ (m)
The searching phase can be performed in O(m+n) time
Knuth-Morris-Pratt algorithm performs at most 2n-1 text character comparisons during the searching phase
Since m<n overall Ѳ (n)

20. Thank you
Questions??????????????????