Rabin–Karp algorithm or Karp–Rabin algorithm is a string-searching algorithm that uses hashing to find an exact match of a pattern string in a text. It uses a rolling hash to quickly filter out positions of the text that cannot match the pattern, and then checks for a match at the remaining positions. Generalizations of the same idea can be used to find more than one match of a single pattern, or to find matches for more than one pattern.

To find a single match of a single pattern, the expected time of the algorithm is linear in the combined length of the pattern and text, although its worst-case time complexity is the product of the two lengths. To find multiple matches, the expected time is linear in the input lengths, plus the combined length of all the matches, which could be greater than linear.

Pseudocode

function RabinKarp(string s[1..n], string pattern[1..m])
    hpattern := hash(pattern[1..m]);
    for i from 1 to n-m+1
        hs := hash(s[i..i+m-1])
        if hs = hpattern
            if s[i..i+m-1] = pattern[1..m]
                return i
    return not found

# rolling hash
s[i+1..i+m] = s[i..i+m-1] - s[i] + s[i+m]

# Multiple pattern search
function RabinKarpSet(string s[1..n], set of string subs, m):
    set hsubs := emptySet
    foreach sub in subs
        insert hash(sub[1..m]) into hsubs
    hs := hash(s[1..m])
    for i from 1 to n-m+1
        if hs ∈ hsubs and s[i..i+m-1] ∈ subs
            return i
        hs := hash(s[i+1..i+m])
    return not found

References

• https://en.wikipedia.org/wiki/Rabin%E2%80%93Karp_algorithm