RABIN KARP ALGORITHM STRING MATCHING

PRESENTED BY
ABHISHEK KUMAR SINGH
RABIN KARP
String Matching
Algorithm

 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
Problem Statement
H E L L O W O R L D
L L O

 The Rabin-Karp string matching algorithm calculates a hash value
for the pattern, as well as for each M-character subsequence of
given text to be compared.
 If the hash values for a particular subsequence are unequal, the
algorithm will calculate the hash value for next M-character
sequence.
 If the hash values are equal, the algorithm will do a Brute Force
comparison between the pattern and the M-character sequence.
 Therefore there is only one comparison per text subsequence, and
Brute Force is only needed when hash values match.
Note: Only one comparison for sub sequence
Rabin-Karp Algorithm

 Consider an M-character sequence as an M-
digit number in the alphabet. The text
subsequence t[I ... i+M-1] is mapped to the
number
x(i) = t[i]*3^0+ t[i+1]*b^1+...+ t[i+M-1]*3^(M-
1)
 Furthermore, given x(i) we can compute x(i+1)
for the next subsequence t[i+1 .. i+M] in
constant time,as follows:
x(i+1) = (x(i)-(t[i]))/3+(3^(M-1))*t[i+M-1]
Rolling Hash Function

A B D A B C
Example
tHash = Hash(“ABD”) = 1*3^0+2*3^1+4*3^2= 43
pHash = Hash(“ABC”) = 1*3^0+2*3^1+3*3^2 = 34
tHash == pHash  FALSE
tHash = Hash(“BDA”) = 2*3^0+4*3^1+1*3^2 = 23
tHash = Hash(“DAB”) = 4*3^0+1*3^1+2*3^2 = 25
A B D A B C
A B D A B C
A B D A B C
tHash = Hash(“ABC”) = 30+30+40 = 34
tHash == pHash  TRUE

 TEXT :
 PATTERN :
HERE PATTERN MATCHES THE
SUBSTRING SO INDEX NO. 3 IS RETURNED
Incase of HIT
A B D A B C
A B C

int main()
{
string s1,s2;
cin>>s1>>s2;
int
l1=s1.size(),l2=s2.size(),
i,j,k;
int hs1=0,p=0,ar[l1];
for(i=0;i<l2;i++)
hs1+=(int)s2[i]*pow(3,i);
int hs2=0;
for(i=0;i<l1;i++)
{
if(i==0)
int c=0;
if(hs2==hs1)
{
for(j=i;j<i+l2;j++)
if(s1[j]==s2[j-
i])
c++;
else
break;
}
if(c==l2)
ar[p++]=i;
}
cout<<l1<<endl;
cout<<"Stored index

 Hash to two string match then it is called Hit
 There is possibility
 Hash of “abc” is 34
 Hash of “dga” is 34
 This is called Hash Collision
 Minimize Collision by
 Taking mod with prime number
HASH COLLISION

 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

 Keyword matching in large files
 Good for Plagiarism detection
 Searching engines
 Database searching
 Bioinformatics

APPLICATION

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_algori
thm
5. cs.princeton.edu/courses/archive/fall04/cos226/lectur
es/string.4up.pdf
References

RABIN KARP ALGORITHM STRING MATCHING

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