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Rabin-Karp algorithm

Definition 📖​

Rabin-Karp algorithm is a string-searching algorithm that utilizes hashing to find a pattern within a text. This algorithm is particularly efficient for finding multiple patterns within the same text by comparing hash values, reducing the need for repeated character comparisons.

Characteristics ✨​

  • Hash-Based Search:

    • Rabin-Karp uses a hash function to convert a pattern and substrings of the text into hash values. It compares these hash values to identify matching patterns.

  • Efficient for Multiple Patterns:

    • Ideal for cases with multiple patterns, as it can reuse the hash calculations, making it efficient in such scenarios.

  • Rolling Hash:

    • Uses a rolling hash technique to quickly update the hash value for the next substring, enhancing efficiency for large texts.

Time Complexity ⏱️​

  • Best Case: O(n + m) 🌟

    When there are no hash collisions, the algorithm efficiently processes both text and pattern in linear time.

  • Average Case: O(n + m) 🔄

    Typically performs well with a low number of hash collisions, maintaining linear time complexity.

  • Worst Case: O(n * m) 💥

    In cases with many hash collisions, the algorithm may degrade to checking each substring individually.

Space Complexity 💾​

  • Space Complexity: O(1)
    Requires constant space for the hash values and other variables, making it memory-efficient.

C++ Implementation 💻​

Here’s a simple implementation of the Rabin-Karp algorithm in C++:

#include <iostream>
#include <string>
using namespace std;

const int d = 256; // Number of characters in the input alphabet
const int q = 101; // A prime number for modulo operation

void rabinKarpSearch(string pattern, string text) {
    int m = pattern.length();
    int n = text.length();
    int i, j;
    int p = 0; // Hash value for pattern
    int t = 0; // Hash value for text
    int h = 1;

    // Calculate the hash value of the pattern and first window of text
    for (i = 0; i < m - 1; i++)
        h = (h * d) % q;

    for (i = 0; i < m; i++) {
        p = (d * p + pattern[i]) % q;
        t = (d * t + text[i]) % q;
    }

    // Slide the pattern over text
    for (i = 0; i <= n - m; i++) {
        if (p == t) { // Check for hash match
            for (j = 0; j < m; j++) {
                if (text[i + j] != pattern[j])
                    break;
            }
            if (j == m)
                cout << "Pattern found at index " << i << endl;
        }
        
        if (i < n - m) {
            t = (d * (t - text[i] * h) + text[i + m]) % q;
            if (t < 0)
                t += q;
        }
    }
}

int main() {
    string text = "ABCCDABCDABCD";
    string pattern = "ABCD";
    rabinKarpSearch(pattern, text);
    return 0;
}

Applications of Rabin-Karp Algorithm 🌐​

Text Search Engines:

  • Widely used in text search applications where multiple patterns need to be matched, as it can efficiently handle repeated hash calculations.

Plagiarism Detection:

  • Helps in detecting plagiarism by checking for large sections of identical or similar text within documents.

DNA Sequence Analysis:

  • Useful for matching specific gene sequences by searching for patterns in large DNA strands.

Advantages and Disadvantages​

Advantages: ✅

  • Efficient for Multiple Patterns:

    Offers efficient handling of multiple patterns in a single pass.

  • Low Memory Requirement:

    Uses constant memory, as it doesn’t require additional space for each character.

Disadvantages: ⚠️

  • Hash Collisions:

    Performance can degrade in the presence of hash collisions, especially in repetitive or similar text.

  • Not Ideal for Small Texts:

    Other algorithms may be more efficient for shorter texts where the hash calculation overhead is less advantageous.

Summary 📚​

The Rabin-Karp algorithm is an efficient, hash-based approach for pattern searching, especially suitable for finding multiple patterns in a large body of text. It balances memory efficiency and speed in scenarios with minimal hash collisions, making it a preferred choice in applications like text searching and DNA analysis.