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Rabin-Karp Algorithm for Pattern Searching

Naive algorithm for Pattern Searching

Last Updated : 20 Apr, 2024

Given text string with length n and a pattern with length m, the task is to prints all occurrences of pattern in text.
Note: You may assume that n > m.

Examples:

Input: text = “THIS IS A TEST TEXT”, pattern = “TEST”
Output: Pattern found at index 10

Input: text = “AABAACAADAABAABA”, pattern = “AABA”
Output: Pattern found at index 0, Pattern found at index 9, Pattern found at index 12

Pattern searching

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

Naive Pattern Searching algorithm:

Slide the pattern over text one by one and check for a match. If a match is found, then slide by 1 again to check for subsequent matches.

C++

#include <iostream> #include <string> using namespace std;  void search(string& pat, string& txt) {     int M = pat.size();     int N = txt.size();      // A loop to slide pat[] one by one     for (int i = 0; i <= N - M; i++) {         int j;          // For current index i, check for pattern match         for (j = 0; j < M; j++) {             if (txt[i + j] != pat[j]) {                 break;             }         }          // If pattern matches at index i         if (j == M) {             cout << "Pattern found at index " << i << endl;         }     } }  // Driver's Code int main() {     // Example 1     string txt1 = "AABAACAADAABAABA";     string pat1 = "AABA";     cout << "Example 1: " << endl;     search(pat1, txt1);          // Example 2     string txt2 = "agd";     string pat2 = "g";     cout << "\nExample 2: " << endl;     search(pat2, txt2);      return 0; }

C

#include <stdio.h> #include <string.h>  void search(char* pat, char* txt) {     int M = strlen(pat);     int N = strlen(txt);      // A loop to slide pat[] one by one     for (int i = 0; i <= N - M; i++) {         int j;          // For current index i, check for pattern match         for (j = 0; j < M; j++) {             if (txt[i + j] != pat[j]) {                 break;             }         }          // If pattern matches at index i         if (j == M) {             printf("Pattern found at index %d\n", i);         }     } }  int main() {     // Example 1     char txt1[] = "AABAACAADAABAABA";     char pat1[] = "AABA";     printf("Example 1:\n");     search(pat1, txt1);          // Example 2     char txt2[] = "agd";     char pat2[] = "g";     printf("\nExample 2:\n");     search(pat2, txt2);      return 0; }

Java

public class PatternSearch {      public static void search(String pat, String txt) {         int M = pat.length();         int N = txt.length();          // A loop to slide pat[] one by one         for (int i = 0; i <= N - M; i++) {             int j;              // For current index i, check for pattern match             for (j = 0; j < M; j++) {                 if (txt.charAt(i + j) != pat.charAt(j)) {                     break;                 }             }              // If pattern matches at index i             if (j == M) {                 System.out.println("Pattern found at index " + i);             }         }     }      public static void main(String[] args) {         // Example 1         String txt1 = "AABAACAADAABAABA";         String pat1 = "AABA";         System.out.println("Example 1:");         search(pat1, txt1);          // Example 2         String txt2 = "agd";         String pat2 = "g";         System.out.println("\nExample 2:");         search(pat2, txt2);     } }

Python3

def search_pattern(pattern, text):     # Get the lengths of the pattern and the text     m = len(pattern)     n = len(text)      # A loop to slide pattern over text one by one     for i in range(n - m + 1):         # For current index i, check for pattern match         j = 0         while j < m and text[i + j] == pattern[j]:             j += 1                  # If the entire pattern matches the text starting at index i         if j == m:             print(f"Pattern found at index {i}")  # Example usage if __name__ == "__main__":     # Example 1     text1 = "AABAACAADAABAABA"     pattern1 = "AABA"     print("Example 1:")     search_pattern(pattern1, text1)          # Example 2     text2 = "agd"     pattern2 = "g"     print("\nExample 2:")     search_pattern(pattern2, text2)

C#

using System;  class PatternSearch {     static void Search(string pat, string txt)     {         int M = pat.Length;         int N = txt.Length;          // A loop to slide pat[] one by one         for (int i = 0; i <= N - M; i++)         {             int j;              // For current index i, check for pattern match             for (j = 0; j < M; j++)             {                 if (txt[i + j] != pat[j])                 {                     break;                 }             }              // If pattern matches at index i             if (j == M)             {                 Console.WriteLine($"Pattern found at index {i}");             }         }     }      static void Main()     {         // Example 1         string txt1 = "AABAACAADAABAABA";         string pat1 = "AABA";         Console.WriteLine("Example 1:");         Search(pat1, txt1);                  // Example 2         string txt2 = "agd";         string pat2 = "g";         Console.WriteLine("\nExample 2:");         Search(pat2, txt2);     } }

JavaScript

   function search(pat, txt) {     const M = pat.length;     const N = txt.length;      // A loop to slide pat[] one by one     for (let i = 0; i <= N - M; i++) {         let j = 0;          // For current index i, check for pattern match         while (j < M && txt[i + j] === pat[j]) {             j++;         }          // If pattern matches at index i         if (j === M) {             console.log(`Pattern found at index ${i}`);         }     } }  // Example 1 const txt1 = "AABAACAADAABAABA"; const pat1 = "AABA"; console.log("Example 1:"); search(pat1, txt1);  // Example 2 const txt2 = "agd"; const pat2 = "g"; console.log("\nExample 2:"); search(pat2, txt2);

PHP

function search($pat, $txt) {     $M = strlen($pat);     $N = strlen($txt);      // A loop to slide pat[] one by one     for ($i = 0; $i <= $N - $M; $i++) {         $j = 0;          // For current index i, check for pattern match         while ($j < $M && $txt[$i + $j] === $pat[$j]) {             $j++;         }          // If pattern matches at index i         if ($j == $M) {             echo "Pattern found at index $i\n";         }     } }  // Example 1 $txt1 = "AABAACAADAABAABA"; $pat1 = "AABA"; echo "Example 1:\n"; search($pat1, $txt1);  // Example 2 $txt2 = "agd"; $pat2 = "g"; echo "\nExample 2:\n"; search($pat2, $txt2);

Output

Pattern found at index 0  Pattern found at index 9  Pattern found at index 13

Time Complexity: O(N²)
Auxiliary Space: O(1)

Complexity Analysis of Naive algorithm for Pattern Searching:

Best Case: O(n)

When the pattern is found at the very beginning of the text (or very early on).
The algorithm will perform a constant number of comparisons, typically on the order of O(n) comparisons, where n is the length of the pattern.

Worst Case: O(n²)

When the pattern doesn’t appear in the text at all or appears only at the very end.
The algorithm will perform O((n-m+1)*m) comparisons, where n is the length of the text and m is the length of the pattern.
In the worst case, for each position in the text, the algorithm may need to compare the entire pattern against the text.

Rabin-Karp Algorithm for Pattern Searching

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