String Matching

1. String Matching Algorithms
Kamalesh Karmakar
Assistant Professor,
Dept. of CSE & IT,
Meghnad Saha Institute of Technology.

2. String Matching Algorithms & Complexity
Weformalizethestring-matchingproblemasfollows.WeassumethatthetextisanarrayT[1..n]oflengthnandthatthepatternisanarrayP[1..m]oflengthm≤n.WefurtherassumethattheelementsofPandTarecharactersdrawnfromafinitealphabetΣ. Forexample,wemayhaveΣ={0,1}orΣ={a,b,...,z}.ThecharacterarraysPandTareoftencalledstringsofcharacters.

3. String Matching Algorithms
WesaythatpatternPoccurswithshiftsintextT(or,equivalently,thatpatternPoccursbeginningatpositions+1intextT)if0≤s≤n−mandT[s+1..s+m]=P[1..m](thatis,ifT[s+j]=P[j],for1≤j≤m).
IfPoccurswithshiftsinT,thenwecallsavalidshift;otherwise,wecallsaninvalidshift.Thestring-matchingproblemistheproblemoffindingallvalidshiftswithwhichagivenpatternPoccursinagiventextT.Figure32.1illustratesthesedefinitions.

4. Complexity comparison of Different Algorithms

5. The Naive string-matching algorithm
ThenaivealgorithmfindsallvalidshiftsusingaloopthatcheckstheconditionP[1..m]=T[s+1..s+m]foreachofthen−m+1possiblevaluesofs.
Procedure NAIVE-STRING-MATCHER takes time O((n −m + 1)m), and this bound is tight in the worst case.

6. String matching with finite automata

7. String matching with finite automata

8. String matching with finite automata

9. String matching with finite automata

10. The Knuth-Morris-Pratt matching algorithm

11. The Knuth-Morris-Pratt matching algorithm

13. Example

14. Q & A