Rabin Karp - String Matching Algorithm
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This document describes the Rabin-Karp string matching algorithm. It proposes using hashing to improve on the naive string matching algorithm. The Rabin-Karp algorithm calculates a hash of the pattern string and compares it to the hash of successive substring slices of the text. If the hashes match, it does a character-by-character comparison. This allows it to avoid unnecessary comparisons and achieves an average runtime of O(m+n), improving on the naive algorithm. It also discusses how to mitigate hash collisions.
Rabin Karp - String Matching Algorithm
- 1. Yet another string matching algorithm PRESENTED BY P14-6011 P14-6016 Rabin Karp
- 2. Proposed in 1987 Michael O. Rabin Richard M. Karp Improved Naive String Matching By HASHING Average Running Time O(m+n) Introduction
- 3. Let text string be T of length N Pattern string be P of length M Example T=“hello world”; N=11; P=“llo”; M=3 Application Keyword matching in large files Good for Plagiarism detection Statement
- 4. Calculate Hash of Pattern As well of M characters of text If hash is not equal Calculate hash of next M characters If hash is equal then Compare both character by character Note: Only one comparison for sub sequence Working
- 5. H10 E20 L30 L30 O40 50 W60 O40 R70 L30 D80 Example tHash = Hash(“HEL”) = 10+20+30 = 60 pHash = Hash(“LLO”) = 30+30+40 = 100 tHash == pHash FALSE H10 E20 L30 L30 O40 50 W60 O40 R70 L30 D80 tHash = Hash(“ELL”) = 20+30+30 = 80 tHash == pHash FALSE H10 E20 L30 L30 O40 50 W60 O40 R70 L30 D80 tHash = Hash(“LLO”) = 30+30+40 = 100 tHash == pHash TRUE
- 6. int RabinKarp(string t, string p) { int pHash = Hash(p); int limit = t.size() - p.size() + 1; // n – m + 1 for (int i = 0; i < limit; i++) { string substr = t.substr(i, p.size()); int tHash = Hash(substr); if (pHash == tHash && p == substr) return i; } return -1; } Implementation
- 7. Hash to two string match then it is called Hit There is possibility Hash of “LLO” is 100 Hash of “OLL” is 100 This is called Hash Collision Minimize Collision by Scaling with index position 30(3)+30(2)+40(1) = 190 | 40(3)+30(2)+30(1) = 210 Taking mod with prime number Hash Collision
- 8. Hash of Pattern O(m) Hash Comparison O(n-m+1) = O(n) ; m < n Average Running Time O(m+n) Worst Case Running Time m comparison in each iteration O(mn) Analysis
- 9. 1. CLRS – 2nd Edition, Page 911-916 2. slideshare.net/GajanandSharma1/rabin-karp-string-matching-algorithm 3. stoimen.com/blog/2012/04/02/computer-algorithms-rabin-karp-string- searching/ 4. en.wikipedia.org/wiki/Rabin%E2%80%93Karp_algorithm 5. cs.princeton.edu/courses/archive/fall04/cos226/lectures/string.4up.pdf References