🔍 Rabin-Karp Algorithm

Ever tried finding a word in a huge chunk of text and thought,
There has to be a faster way than checking every single character!😩
Enter the Rabin-Karp Algorithm — a smart and efficient way to search for patterns in strings using a clever trick called rolling hash 🪄
Let’s break it down step by step — no jargon, no confusion, just clarity and fun. 🧠✨
🤔 The Problem
You’re given:
Text → "geeksforgeeks"
Pattern → "geek"
And your task is to find all positions where the pattern appears in the text.
✅ Expected Output:
[1, 9] // Using 1-based indexing (because humans count from 1 😅)

🧠 The Big Idea (Why Rabin-Karp Is Smart?)
Instead of comparing every letter of the pattern with every possible substring of the text, what if we could:
1.Convert the pattern into a number (hash)
2.Convert parts of the text into numbers too
3.Compare those numbers instead of characters
→ Much faster than checking each letter!
If the hashes match, we double-check the actual characters — just to be sure (because different strings can sometimes have the same hash — that's called a collision).

🔢 What's a Hash Anyway?
Think of a hash as a string’s fingerprint:
Same strings → same hash
Different strings → usually different hashes
Rabin-Karp uses a rolling hash, which is just a clever way of updating the hash as we move through the text, without recalculating everything from scratch.

🔄Rolling Hash — The Star of the Show🌟
Let’s say we’ve already calculated the hash for "geek" — now we want the hash for the next window: "eeks".
Instead of this:
Recalculate hash("eeks") from scratch 😩

We do this:
t_new = (d * (t_old - old_char * h) + new_char) % q
Where:
-t_old is the previous window’s hash
-old_char is the character sliding out of the window
-new_char is the character sliding into the window
-d is the number of characters in the alphabet (e.g., 256 for extended -ASCII)
-h = d^(M-1) % q is used to remove the effect of the oldest character
-q is a large prime number used to reduce hash collisions

We move the window and get a new hash in constant time! 🔥

💥Why Rabin-Karp is Awesome
✅ Fast search using hashing
✅ Great for multiple pattern searches
✅ Average time complexity: O(N + M)
✅ Used in:
1.Plagiarism detection 🧑‍🎓
2.Big text search engines
3.DNA sequence matching 🧬
4.Intrusion detection systems 🔐

🧾 Dry Run: Let’s See It in Action
🔸 Input:
Text: "geeksforgeeks"
Pattern: "geek"

Step 1: Initialize Variables
M = 4 // length of pattern
N = 13 // length of text
d = 256 // characters in the alphabet
q = 101 // prime number for hashing

Step 2: Compute Hash Multiplier
h = pow(d, M-1) % q = (256^3) % 101 = 88

Step 3: Calculate Initial Hashes
p = hash("geek") % q = 27
t = hash("geek") % q = 27

Step 4: Slide the Window and Compare
Iteration 1: "geek" → Match found ✅ at index 1
Iteration 2: "eeks" → Hash ≠ 27 → skip ❌
Iteration 3: "eksf" → Hash ≠ 27 → skip ❌
...
Iteration 9: "geek" → Match found ✅ at index 9

🧑‍💻Final Result:
[1, 9]

👨‍💻 C++ Code: Rabin-Karp Algorithm

#include 
#include 
using namespace std;

// Your Rabin-Karp search function
vector search(string pattern, string text) {
    vector result;
    int d = 256;   // Total characters (ASCII)
    int q = 101;   // Prime number to avoid collision
    int M = pattern.length();
    int N = text.length();
    int p = 0;     // hash for pattern
    int t = 0;     // hash for text window
    int h = 1;

    // Step 1: Calculate hash multiplier h = pow(d, M-1) % q
    for (int i = 0; i < M - 1; i++)
        h = (h * d) % q;

    // Step 2: Initial hash values
    for (int i = 0; i < M; i++) {
        p = (d * p + pattern[i]) % q;
        t = (d * t + text[i]) % q;
    }

    // Step 3: Slide pattern over text
    for (int i = 0; i <= N - M; i++) {
        // If hash values match, check characters one by one
        if (p == t) {
            bool match = true;
            for (int j = 0; j < M; j++) {
                if (text[i + j] != pattern[j]) {
                    match = false;
                    break;
                }
            }
            if (match)
                result.push_back(i + 1); // 1-based indexing
        }

        // Step 4: Update hash using rolling hash
        if (i < N - M) {
            t = (d * (t - text[i] * h) + text[i + M]) % q;
            if (t < 0)
                t = t + q; // Make sure hash stays positive
        }
    }

    return result;
}

// Main Function
int main() {
    string text = "ababcabcabababd";
    string pattern = "ababd";

    vector positions = search(pattern, text);

    if (!positions.empty()) {
        cout << "Pattern found at position(s): ";
        for (int pos : positions)
            cout << pos << " ";
        cout << endl;
    } else {
        cout << "Pattern not found in the text." << endl;
    }

    return 0;
}

🧠 Key Takeaways
Rabin-Karp is a hash-based string searching algorithm.
It uses a rolling hash to speed up window comparisons.
Perfect for situations where you need to find multiple patterns efficiently.