Rabin-karp algorithm and fingerprint thought

The RABIN-KARP algorithm has good practicability for random string matching problems. It is based on the fingerprint mentality.

The main string length is n mode string length is M

Assume

※① we can calculate a P's fingerprint at O (m) time F (P)

※② if F (P) is not equal to F (t[s). S+M-1]) then p must not be equal to t[s. S+M-1]

※③ we can compare fingerprints at O (1) time

※④ we can at O (1) time from F (t[s. S+M-1]) calculation f (t[s+1..s+m])

The fingerprint can be seen as a decimal number, the key to the algorithm is whether it can be in O (1) time from F (t[s. S+M-1]) calculation f (t[s+1..s+m])

If the fingerprint is very large, you can consider a hash of the digital control in a large prime number Q.

i.e. ft = (ft-t[s]*10^ (m-1) mod q) *10+t[s+m]) mod q can be completed within O (1)

where 10^ (m-1) mod q can be calculated once in preprocessing

Pseudo code

Rabin-karp-search (t,p) {    /** q is a larger prime number than M */    /** C is a processed ten (m-1) mod q */    int fp=0,ft=0;    for (int i = 0; i < m; i + +) {        fp = (10*fp+p[i])%q;        FT = (10*ft+t[i])%q;    }    for (int s = 0; s <= n-m; s + +) {        if (fp = = ft) Here The comparison is really the same, if the same direct return;        FT = ((ft-t[s]*c) *10+t[s+m])%q;    }    return-1;/** Search failed */}

Rabin-karp algorithm and fingerprint thought