Rabin-Karp Algorithm for Pattern Searching

Last Updated : 06 Sep, 2023

Given a text T[0. . .n-1] and a pattern P[0. . .m-1], write a function search(char P[], char T[]) that prints all occurrences of P[] present in T[] using Rabin Karp algorithm. You may assume that n > m.

Examples:

Input: T[] = “THIS IS A TEST TEXT”, P[] = “TEST”
Output: Pattern found at index 10

Input: T[] = “AABAACAADAABAABA”, P[] = “AABA”
Output: Pattern found at index 0
Pattern found at index 9
Pattern found at index 12

Rabin-Karp Algorithm:

In the Naive String Matching algorithm, we check whether every substring of the text of the pattern’s size is equal to the pattern or not one by one.

Like the Naive Algorithm, the Rabin-Karp algorithm also check every substring. But unlike the Naive algorithm, the Rabin Karp algorithm matches the hash value of the pattern with the hash value of the current substring of text, and if the hash values match then only it starts matching individual characters. So Rabin Karp algorithm needs to calculate hash values for the following strings.

Pattern itself

All the substrings of the text of length m which is the size of pattern.

How is Hash Value calculated in Rabin-Karp?

Hash value is used to efficiently check for potential matches between a pattern and substrings of a larger text. The hash value is calculated using a rolling hash function, which allows you to update the hash value for a new substring by efficiently removing the contribution of the old character and adding the contribution of the new character. This makes it possible to slide the pattern over the text and calculate the hash value for each substring without recalculating the entire hash from scratch.

Here’s how the hash value is typically calculated in Rabin-Karp:

Step 1: Choose a suitable base and a modulus:

Select a prime number ‘p‘ as the modulus. This choice helps avoid overflow issues and ensures a good distribution of hash values.
Choose a base ‘b‘ (usually a prime number as well), which is often the size of the character set (e.g., 256 for ASCII characters).

Step 2: Initialize the hash value:

Set an initial hash value ‘hash‘ to 0.

Step 3: Calculate the initial hash value for the pattern:

Iterate over each character in the pattern from left to right.
For each character ‘c’ at position ‘i’, calculate its contribution to the hash value as ‘c * (b^{pattern_length – i – 1}) % p’ and add it to ‘hash‘.
This gives you the hash value for the entire pattern.

Step 4: Slide the pattern over the text:

Start by calculating the hash value for the first substring of the text that is the same length as the pattern.

Step 5: Update the hash value for each subsequent substring:

To slide the pattern one position to the right, you remove the contribution of the leftmost character and add the contribution of the new character on the right.
The formula for updating the hash value when moving from position ‘i’ to ‘i+1’ is:

hash = (hash - (text[i - pattern_length] * (b^{pattern_length - 1})) % p) * b + text[i]

Step 6: Compare hash values:

When the hash value of a substring in the text matches the hash value of the pattern, it’s a potential match.
If the hash values match, we should perform a character-by-character comparison to confirm the match, as hash collisions can occur.

Below is the Illustration of above algorithm:

rabin-karp-final

Step-by-step approach:

Initially calculate the hash value of the pattern.
Start iterating from the starting of the string:
- Calculate the hash value of the current substring having length m.
- If the hash value of the current substring and the pattern are same check if the substring is same as the pattern.
- If they are same, store the starting index as a valid answer. Otherwise, continue for the next substrings.
Return the starting indices as the required answer.

Below is the implementation of the above approach:

C++

/* Following program is a C++ implementation of Rabin Karp
Algorithm given in the CLRS book */
#include <bits/stdc++.h>
using namespace std;
 
// d is the number of characters in the input alphabet
#define d 256
 
/* pat -> pattern
    txt -> text
    q -> A prime number
*/
void search(char pat[], char txt[], int q)
{
    int M = strlen(pat);
    int N = strlen(txt);
    int i, j;
    int p = 0; // hash value for pattern
    int t = 0; // hash value for txt
    int h = 1;
 
    // The value of h would be "pow(d, M-1)%q"
    for (i = 0; i < M - 1; i++)
        h = (h * d) % q;
 
    // Calculate the hash value of pattern and first
    // window of text
    for (i = 0; i < M; i++) {
        p = (d * p + pat[i]) % q;
        t = (d * t + txt[i]) % q;
    }
 
    // Slide the pattern over text one by one
    for (i = 0; i <= N - M; i++) {
 
        // Check the hash values of current window of text
        // and pattern. If the hash values match then only
        // check for characters one by one
        if (p == t) {
            /* Check for characters one by one */
            for (j = 0; j < M; j++) {
                if (txt[i + j] != pat[j]) {
                    break;
                }
            }
 
            // if p == t and pat[0...M-1] = txt[i, i+1,
            // ...i+M-1]
 
            if (j == M)
                cout << "Pattern found at index " << i
                     << endl;
        }
 
        // Calculate hash value for next window of text:
        // Remove leading digit, add trailing digit
        if (i < N - M) {
            t = (d * (t - txt[i] * h) + txt[i + M]) % q;
 
            // We might get negative value of t, converting
            // it to positive
            if (t < 0)
                t = (t + q);
        }
    }
}
 
/* Driver code */
int main()
{
    char txt[] = "GEEKS FOR GEEKS";
    char pat[] = "GEEK";
 
    // we mod to avoid overflowing of value but we should
    // take as big q as possible to avoid the collison
    int q = INT_MAX;
 
    // Function Call
    search(pat, txt, q);
    return 0;
}
 
// This is code is contributed by rathbhupendra

C

/* Following program is a C implementation of Rabin Karp
Algorithm given in the CLRS book */
#include <stdio.h>
#include <string.h>
 
// d is the number of characters in the input alphabet
#define d 256
 
/* pat -> pattern
    txt -> text
    q -> A prime number
*/
void search(char pat[], char txt[], int q)
{
    int M = strlen(pat);
    int N = strlen(txt);
    int i, j;
    int p = 0; // hash value for pattern
    int t = 0; // hash value for txt
    int h = 1;
 
    // The value of h would be "pow(d, M-1)%q"
    for (i = 0; i < M - 1; i++)
        h = (h * d) % q;
 
    // Calculate the hash value of pattern and first
    // window of text
    for (i = 0; i < M; i++) {
        p = (d * p + pat[i]) % q;
        t = (d * t + txt[i]) % q;
    }
 
    // Slide the pattern over text one by one
    for (i = 0; i <= N - M; i++) {
 
        // Check the hash values of current window of text
        // and pattern. If the hash values match then only
        // check for characters one by one
        if (p == t) {
            /* Check for characters one by one */
            for (j = 0; j < M; j++) {
                if (txt[i + j] != pat[j])
                    break;
            }
 
            // if p == t and pat[0...M-1] = txt[i, i+1,
            // ...i+M-1]
            if (j == M)
                printf("Pattern found at index %d \n", i);
        }
 
        // Calculate hash value for next window of text:
        // Remove leading digit, add trailing digit
        if (i < N - M) {
            t = (d * (t - txt[i] * h) + txt[i + M]) % q;
 
            // We might get negative value of t, converting
            // it to positive
            if (t < 0)
                t = (t + q);
        }
    }
}
 
/* Driver Code */
int main()
{
    char txt[] = "GEEKS FOR GEEKS";
    char pat[] = "GEEK";
 
    // A prime number
    int q = 101;
 
    // function call
    search(pat, txt, q);
    return 0;
}

Java

// Following program is a Java implementation
// of Rabin Karp Algorithm given in the CLRS book
 
public class Main {
    // d is the number of characters in the input alphabet
    public final static int d = 256;
 
    /* pat -> pattern
        txt -> text
        q -> A prime number
    */
    static void search(String pat, String txt, int q)
    {
        int M = pat.length();
        int N = txt.length();
        int i, j;
        int p = 0; // hash value for pattern
        int t = 0; // hash value for txt
        int h = 1;
 
        // The value of h would be "pow(d, M-1)%q"
        for (i = 0; i < M - 1; i++)
            h = (h * d) % q;
 
        // Calculate the hash value of pattern and first
        // window of text
        for (i = 0; i < M; i++) {
            p = (d * p + pat.charAt(i)) % q;
            t = (d * t + txt.charAt(i)) % q;
        }
 
        // Slide the pattern over text one by one
        for (i = 0; i <= N - M; i++) {
 
            // Check the hash values of current window of
            // text and pattern. If the hash values match
            // then only check for characters one by one
            if (p == t) {
                /* Check for characters one by one */
                for (j = 0; j < M; j++) {
                    if (txt.charAt(i + j) != pat.charAt(j))
                        break;
                }
 
                // if p == t and pat[0...M-1] = txt[i, i+1,
                // ...i+M-1]
                if (j == M)
                    System.out.println(
                        "Pattern found at index " + i);
            }
 
            // Calculate hash value for next window of text:
            // Remove leading digit, add trailing digit
            if (i < N - M) {
                t = (d * (t - txt.charAt(i) * h)
                     + txt.charAt(i + M))
                    % q;
 
                // We might get negative value of t,
                // converting it to positive
                if (t < 0)
                    t = (t + q);
            }
        }
    }
 
    /* Driver Code */
    public static void main(String[] args)
    {
        String txt = "GEEKS FOR GEEKS";
        String pat = "GEEK";
 
        // A prime number
        int q = 101;
 
        // Function Call
        search(pat, txt, q);
    }
}
 
// This code is contributed by nuclode

Python3

# Following program is the python implementation of
# Rabin Karp Algorithm given in CLRS book
 
# d is the number of characters in the input alphabet
d = 256
 
# pat  -> pattern
# txt  -> text
# q    -> A prime number
 
 
def search(pat, txt, q):
    M = len(pat)
    N = len(txt)
    i = 0
    j = 0
    p = 0    # hash value for pattern
    t = 0    # hash value for txt
    h = 1
 
    # The value of h would be "pow(d, M-1)%q"
    for i in range(M-1):
        h = (h*d) % q
 
    # Calculate the hash value of pattern and first window
    # of text
    for i in range(M):
        p = (d*p + ord(pat[i])) % q
        t = (d*t + ord(txt[i])) % q
 
    # Slide the pattern over text one by one
    for i in range(N-M+1):
        # Check the hash values of current window of text and
        # pattern if the hash values match then only check
        # for characters one by one
        if p == t:
            # Check for characters one by one
            for j in range(M):
                if txt[i+j] != pat[j]:
                    break
                else:
                    j += 1
 
            # if p == t and pat[0...M-1] = txt[i, i+1, ...i+M-1]
            if j == M:
                print("Pattern found at index " + str(i))
 
        # Calculate hash value for next window of text: Remove
        # leading digit, add trailing digit
        if i < N-M:
            t = (d*(t-ord(txt[i])*h) + ord(txt[i+M])) % q
 
            # We might get negative values of t, converting it to
            # positive
            if t < 0:
                t = t+q
 
 
# Driver Code
if __name__ == '__main__':
    txt = "GEEKS FOR GEEKS"
    pat = "GEEK"
 
    # A prime number
    q = 101
 
    # Function Call
    search(pat, txt, q)
 
# This code is contributed by Bhavya Jain

C#

// Following program is a C# implementation
// of Rabin Karp Algorithm given in the CLRS book
using System;
public class GFG {
    // d is the number of characters in the input alphabet
    public readonly static int d = 256;
 
    /* pat -> pattern
        txt -> text
        q -> A prime number
    */
    static void search(String pat, String txt, int q)
    {
        int M = pat.Length;
        int N = txt.Length;
        int i, j;
        int p = 0; // hash value for pattern
        int t = 0; // hash value for txt
        int h = 1;
 
        // The value of h would be "pow(d, M-1)%q"
        for (i = 0; i < M - 1; i++)
            h = (h * d) % q;
 
        // Calculate the hash value of pattern and first
        // window of text
        for (i = 0; i < M; i++) {
            p = (d * p + pat[i]) % q;
            t = (d * t + txt[i]) % q;
        }
 
        // Slide the pattern over text one by one
        for (i = 0; i <= N - M; i++) {
 
            // Check the hash values of current window of
            // text and pattern. If the hash values match
            // then only check for characters one by one
            if (p == t) {
                /* Check for characters one by one */
                for (j = 0; j < M; j++) {
                    if (txt[i + j] != pat[j])
                        break;
                }
 
                // if p == t and pat[0...M-1] = txt[i, i+1,
                // ...i+M-1]
                if (j == M)
                    Console.WriteLine(
                        "Pattern found at index " + i);
            }
 
            // Calculate hash value for next window of text:
            // Remove leading digit, add trailing digit
            if (i < N - M) {
                t = (d * (t - txt[i] * h) + txt[i + M]) % q;
 
                // We might get negative value of t,
                // converting it to positive
                if (t < 0)
                    t = (t + q);
            }
        }
    }
 
    /* Driver Code */
    public static void Main()
    {
        String txt = "GEEKS FOR GEEKS";
        String pat = "GEEK";
 
        // A prime number
        int q = 101;
 
        // Function Call
        search(pat, txt, q);
    }
}
 
// This code is contributed by PrinciRaj19992

Javascript

<script>
 
// Following program is a Javascript implementation 
// of Rabin Karp Algorithm given in the CLRS book 
 
// d is the number of characters in
// the input alphabet 
let d = 256; 
 
/* pat -> pattern 
    txt -> text 
    q -> A prime number 
*/
function search(pat, txt, q) 
{ 
    let M = pat.length; 
    let N = txt.length; 
    let i, j; 
     
    // Hash value for pattern 
    let p = 0; 
     
    // Hash value for txt 
    let t = 0; 
    let h = 1; 
 
    // The value of h would be "pow(d, M-1)%q" 
    for(i = 0; i < M - 1; i++) 
        h = (h * d) % q; 
 
    // Calculate the hash value of pattern and 
    // first window of text 
    for(i = 0; i < M; i++) 
    { 
        p = (d * p + pat[i].charCodeAt()) % q; 
        t = (d * t + txt[i].charCodeAt()) % q; 
    } 
 
    // Slide the pattern over text one by one 
    for(i = 0; i <= N - M; i++) 
    { 
 
        // Check the hash values of current
        // window of text and pattern. If the
        // hash values match then only 
        // check for characters one by one 
        if (p == t) 
        { 
             
            /* Check for characters one by one */
            for(j = 0; j < M; j++) 
            { 
                if (txt[i+j] != pat[j]) 
                    break; 
            } 
 
            // if p == t and pat[0...M-1] = 
            // txt[i, i+1, ...i+M-1] 
            if (j == M) 
                 document.write("Pattern found at index " + 
                                i + "<br/>"); 
        } 
 
        // Calculate hash value for next window 
        // of text: Remove leading digit, add 
        // trailing digit 
        if (i < N - M) 
        { 
            t = (d * (t - txt[i].charCodeAt() * h) + 
                      txt[i + M].charCodeAt()) % q; 
 
            // We might get negative value of t, 
            // converting it to positive 
            if (t < 0) 
                t = (t + q); 
        } 
    } 
} 
 
// Driver code
let txt = "GEEKS FOR GEEKS";
let pat = "GEEK";
 
// A prime number
let q = 101; 
 
// Function Call
search(pat, txt, q);
 
// This code is contributed by target_2
 
</script>

Output

Pattern found at index 0
Pattern found at index 10

Time Complexity:

The average and best-case running time of the Rabin-Karp algorithm is O(n+m), but its worst-case time is O(nm).
The worst case of the Rabin-Karp algorithm occurs when all characters of pattern and text are the same as the hash values of all the substrings of T[] match with the hash value of P[].

Auxiliary Space: O(1)

Limitations of Rabin-Karp Algorithm

Spurious Hit: When the hash value of the pattern matches with the hash value of a window of the text but the window is not the actual pattern then it is called a spurious hit. Spurious hit increases the time complexity of the algorithm. In order to minimize spurious hit, we use good hash function. It greatly reduces the spurious hit.

Suggest improvement

Naive algorithm for Pattern Searching

KMP Algorithm for Pattern Searching

Share your thoughts in the comments

Suffix Tree construction

Suffix Tree Application

More practice problems on pattern searching algorithms