06. string matching
2 likes1,708 views
This document discusses string matching algorithms and their complexity. It introduces the string matching problem of finding all valid shifts where a pattern occurs in a text. It describes the naive algorithm that checks for a match between the pattern and text at each possible shift in O((n-m+1)m) time. It also mentions more advanced algorithms like the Knuth-Morris-Pratt algorithm and using finite automata that have better time complexities.
![String Matching Algorithms & Complexity
Weformalizethestring-matchingproblemasfollows.WeassumethatthetextisanarrayT[1..n]oflengthnandthatthepatternisanarrayP[1..m]oflengthmâ¤n.WefurtherassumethattheelementsofPandTarecharactersdrawnfromafinitealphabetÎŁ. Forexample,wemayhaveÎŁ={0,1}orÎŁ={a,b,...,z}.ThecharacterarraysPandTareoftencalledstringsofcharacters.](https://image.slidesharecdn.com/06-141031094704-conversion-gate02/85/06-string-matching-2-320.jpg)
![String Matching Algorithms
WesaythatpatternPoccurswithshiftsintextT(or,equivalently,thatpatternPoccursbeginningatpositions+1intextT)if0â¤sâ¤nâmandT[s+1..s+m]=P[1..m](thatis,ifT[s+j]=P[j],for1â¤jâ¤m).
IfPoccurswithshiftsinT,thenwecallsavalidshift;otherwise,wecallsaninvalidshift.Thestring-matchingproblemistheproblemoffindingallvalidshiftswithwhichagivenpatternPoccursinagiventextT.Figure32.1illustratesthesedefinitions.](https://image.slidesharecdn.com/06-141031094704-conversion-gate02/85/06-string-matching-3-320.jpg)
![The Naive string-matching algorithm
ThenaivealgorithmfindsallvalidshiftsusingaloopthatcheckstheconditionP[1..m]=T[s+1..s+m]foreachofthenâm+1possiblevaluesofs.
Procedure NAIVE-STRING-MATCHER takes time O((n âm + 1)m), and this bound is tight in the worst case.](https://image.slidesharecdn.com/06-141031094704-conversion-gate02/85/06-string-matching-5-320.jpg)
06. 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]oflengthmâ¤n.WefurtherassumethattheelementsofPandTarecharactersdrawnfromafinitealphabetÎŁ. Forexample,wemayhaveÎŁ={0,1}orÎŁ={a,b,...,z}.ThecharacterarraysPandTareoftencalledstringsofcharacters.
- 3. String Matching Algorithms WesaythatpatternPoccurswithshiftsintextT(or,equivalently,thatpatternPoccursbeginningatpositions+1intextT)if0â¤sâ¤nâmandT[s+1..s+m]=P[1..m](thatis,ifT[s+j]=P[j],for1â¤jâ¤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]foreachofthenâm+1possiblevaluesofs. Procedure NAIVE-STRING-MATCHER takes time O((n âm + 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