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Optimized Algorithm for Pattern Searching

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  • Difficulty Level : Easy
  • Last Updated : 14 Dec, 2022
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Question: We have discussed the Naive String matching algorithm here. Consider a situation where all characters of a pattern are different. Can we modify the original Naive String Matching algorithm so that it works better for these types of patterns? If we can, then what are the changes to the original algorithm?

Solution: In the original Naive String matching algorithm, we always slide the pattern by 1. When all characters of the pattern are different, we can slide the pattern by more than 1. Let us see how can we do this. When a mismatch occurs after j matches, we know that the first character of the pattern will not match the j-matched characters because all characters of the pattern are different. So we can always slide the pattern by j without missing any valid shifts. Following is the modified code that is optimized for the special patterns. 

N.B:  This algorithm only works when the search pattern pat has all different characters.

C++




/* C++ program for A modified Naive Pattern Searching
algorithm that is optimized for the cases when all
characters of pattern are different */
#include <bits/stdc++.h>
using namespace std;
 
/* A modified Naive Pattern Searching
algorithm that is optimized for the
cases when all characters of pattern are different */
void search(string pat, string txt)
{
    int M = pat.size();
    int N = txt.size();
    int i = 0;
 
    while (i <= N - M) {
        int j;
 
        /* For current index i, check for pattern match */
        for (j = 0; j < M; j++)
            if (txt[i + j] != pat[j])
                break;
 
        if (j == M) // if pat[0...M-1] = txt[i, i+1, ...i+M-1]
        {
            cout << "Pattern found at index " << i << endl;
            i = i + M;
        }
        else if (j == 0)
            i = i + 1;
        else
            i = i + j; // slide the pattern by j
    }
}
 
/* Driver code*/
int main()
{
    string txt = "ABCEABCDABCEABCD";
    string pat = "ABCD";
    search(pat, txt);
    return 0;
}
 
// This code is contributed by rathbhupendra


C




/* C program for A modified Naive Pattern Searching
  algorithm that is optimized for the cases when all
  characters of pattern are different */
#include <stdio.h>
#include <string.h>
 
/* A modified Naive Pattern Searching algorithm that is optimized
   for the cases when all characters of pattern are different */
void search(char pat[], char txt[])
{
    int M = strlen(pat);
    int N = strlen(txt);
    int i = 0;
 
    while (i <= N - M) {
        int j;
 
        /* For current index i, check for pattern match */
        for (j = 0; j < M; j++)
            if (txt[i + j] != pat[j])
                break;
 
        if (j == M) // if pat[0...M-1] = txt[i, i+1, ...i+M-1]
        {
            printf("Pattern found at index %d \n", i);
            i = i + M;
        }
        else if (j == 0)
            i = i + 1;
        else
            i = i + j; // slide the pattern by j
    }
}
 
/* Driver program to test above function */
int main()
{
    char txt[] = "ABCEABCDABCEABCD";
    char pat[] = "ABCD";
    search(pat, txt);
    return 0;
}


Java




/* Java program for A modified Naive Pattern Searching
algorithm that is optimized for the cases when all
characters of pattern are different */
 
class GFG {
 
    /* A modified Naive Pattern Searching
algorithm that is optimized for the
cases when all characters of pattern are different */
    static void search(String pat, String txt)
    {
        int M = pat.length();
        int N = txt.length();
        int i = 0;
 
        while (i <= N - M) {
            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 (j == M) // if pat[0...M-1] = txt[i, i+1, ...i+M-1]
            {
                System.out.println("Pattern found at index " + i);
                i = i + M;
            }
            else if (j == 0)
                i = i + 1;
            else
                i = i + j; // slide the pattern by j
        }
    }
 
    /* Driver code*/
    public static void main(String[] args)
    {
        String txt = "ABCEABCDABCEABCD";
        String pat = "ABCD";
        search(pat, txt);
    }
}
 
// This code is contributed by chandan_jnu


Python3




# Python program for A modified Naive Pattern Searching
# algorithm that is optimized for the cases when all
# characters of pattern are different
def search(pat, txt):
    M = len(pat)
    N = len(txt)
    i = 0
 
    while i <= N-M:
        # For current index i, check for pattern match
        for j in range(M):
            if txt[i + j] != pat[j]:
                break
            j += 1
 
        if j == M:    # if pat[0...M-1] = txt[i, i + 1, ...i + M-1]
            print ("Pattern found at index " + str(i))
            i = i + M
        elif j == 0:
            i = i + 1
        else:
            i = i + j    # slide the pattern by j
 
# Driver program to test the above function
txt = "ABCEABCDABCEABCD"
pat = "ABCD"
search(pat, txt)
 
# This code is contributed by Bhavya Jain


C#




/* C# program for A modified Naive Pattern Searching
algorithm that is optimized for the cases when all
characters of pattern are different */
 
using System;
 
class GFG {
 
    /* A modified Naive Pattern Searching
algorithm that is optimized for the
cases when all characters of pattern are different */
    static void search(string pat, string txt)
    {
        int M = pat.Length;
        int N = txt.Length;
        int i = 0;
 
        while (i <= N - M) {
            int j;
 
            /* For current index i, check for pattern match */
            for (j = 0; j < M; j++)
                if (txt[i + j] != pat[j])
                    break;
 
            if (j == M) // if pat[0...M-1] = txt[i, i+1, ...i+M-1]
            {
                Console.WriteLine("Pattern found at index " + i);
                i = i + M;
            }
            else if (j == 0)
                i = i + 1;
            else
                i = i + j; // slide the pattern by j
        }
    }
 
    /* Driver code*/
    static void Main()
    {
        string txt = "ABCEABCDABCEABCD";
        string pat = "ABCD";
        search(pat, txt);
    }
}
 
// This code is contributed by chandan_jnu


PHP




<?php
// PHP program for A modified Naive
// Pattern Searching algorithm that
// is optimized for the cases when all
// characters of pattern are different
 
/* A modified Naive Pattern Searching
   algorithm that is optimized for the
   cases when all characters of
   pattern are different */
function search($pat, $txt)
{
    $M = strlen($pat);
    $N = strlen($txt);
    $i = 0;
 
    while ($i <= $N - $M)
    {
        $j;
 
        /* For current index i,
           check for pattern match */
        for ($j = 0; $j < $M; $j++)
            if ($txt[$i + $j] != $pat[$j])
                break;
 
        // if pat[0...M-1] =
        // txt[i, i+1, ...i+M-1]
        if ($j == $M)
        {
            echo("Pattern found at index $i"."\n" );
            $i = $i + $M;
        }
        else if ($j == 0)
            $i = $i + 1;
        else
         
            // slide the pattern by j
            $i = $i + $j;
    }
}
 
// Driver Code
$txt = "ABCEABCDABCEABCD";
$pat = "ABCD";
search($pat, $txt);
 
// This code is contributed by nitin mittal.
?>


Javascript




<script>
 
// Javascript program for A modified
// Naive Pattern Searching algorithm
// that is optimized for the cases
// when all characters of pattern
// are different
 
// A modified Naive Pattern Searching
// algorithm that is optimized for the
// cases when all characters of pattern
// are different
function search(pat, txt)
{
    let M = pat.length;
    let N = txt.length;
    let i = 0;
 
    while (i <= N - M)
    {
        let j;
 
        // For current index i, check
        // for pattern match
        for(j = 0; j < M; j++)
            if (txt[i + j] != pat[j])
                break;
                 
        // If pat[0...M-1] = txt[i, i+1, ...i+M-1]
        if (j == M) 
        {
            document.write("Pattern found at index " +
                           i + "<br/>");
            i = i + M;
        }
        else if (j == 0)
            i = i + 1;
        else
         
            // Slide the pattern by j
            i = i + j;
    }
}
     
// Driver code
let txt = "ABCEABCDABCEABCD";
let pat = "ABCD";
 
search(pat, txt);
 
// This code is contributed by target_2
 
</script>


Output

Pattern found at index 4
Pattern found at index 12

Time Complexity: O(N*M), where N is the length of txt and M is the pat length.
Auxiliary Space: O(1), We are not using any extra space.

Please write comments if you find anything incorrect, or if you want to share more information about the topic discussed above.
 


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