Naive algorithm for Pattern Searching

Given a text of length N txt[0..N-1] and a pattern of length M pat[0..M-1], write a function search(char pat[], char txt[]) that prints all occurrences of pat[] in txt[]. You may assume that N > M.
Examples:

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

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

Pattern searching

Pattern searching is an important problem in computer science. When we do search for a string in a notepad/word file or browser or database, pattern searching algorithms are used to show the search results. 

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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

// C program for Naive Pattern Searching algorithm
#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 (j
            == M) // if pat[0...M-1] = txt[i, i+1, ...i+M-1]
            printf("Pattern found at index %d \n", i);
    }
}

// Driver's code
int main()
{
    char txt[] = "AABAACAADAABAAABAA";
    char pat[] = "AABA";

      // Function call
    search(pat, txt);
    return 0;
}

C++

// C++ program for Naive Pattern
// Searching algorithm
#include <bits/stdc++.h>
using namespace std;

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 (j
            == M) // if pat[0...M-1] = txt[i, i+1, ...i+M-1]
            cout << "Pattern found at index " << i << endl;
    }
}

// Driver's Code
int main()
{
    char txt[] = "AABAACAADAABAAABAA";
    char pat[] = "AABA";

      // Function call
    search(pat, txt);
    return 0;
}

// This code is contributed
// by Akanksha Rai

Java

// Java program for Naive Pattern Searching

public class NaiveSearch {

    static void search(String pat, String txt)
    {
        int l1 = pat.length();
        int l2 = txt.length();
        int i = 0, j = l2 - 1;

        for (i = 0, j = l2 - 1; j < l1;) {

            if (txt.equals(pat.substring(i, j + 1))) {
                System.out.println("Pattern found at index "
                                   + i);
            }
            i++;
            j++;
        }
    }

      // Driver's code
    public static void main(String args[])
    {
        String pat = "AABAACAADAABAAABAA";
        String txt = "AABA";

          // Function call
        search(pat, txt);
    }
}
// This code is contributed by D. Vishnu Rahul Varma

Python3

# Python3 program for Naive Pattern
# Searching algorithm


def search(pat, txt):
    M = len(pat)
    N = len(txt)

    # A loop to slide pat[] one by one */
    for i in range(N - M + 1):
        j = 0

        # For current index i, check
        # for pattern match */
        while(j < M):
            if (txt[i + j] != pat[j]):
                break
            j += 1

        if (j == M):
            print("Pattern found at index ", i)


# Driver's Code
if __name__ == '__main__':
    txt = "AABAACAADAABAAABAA"
    pat = "AABA"

    # Function call
    search(pat, txt)

# This code is contributed
# by PrinciRaj1992

C#

// C# program for Naive Pattern Searching
using System;

class GFG {

    public static void search(String txt, String pat)
    {
        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 pat[0...M-1] = txt[i, i+1, ...i+M-1]
            if (j == M)
                Console.WriteLine("Pattern found at index "
                                  + i);
        }
    }

    // Driver's code
    public static void Main()
    {
        String txt = "AABAACAADAABAAABAA";
        String pat = "AABA";

          // Function call
        search(txt, pat);
    }
}
// This code is Contributed by Sam007

PHP

<?php
// PHP program for Naive Pattern
// Searching algorithm

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++)
    {

        // 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";
    }
}

    // Driver Code
    $txt = "AABAACAADAABAAABAA";
    $pat = "AABA";
    search($pat, $txt);

// This code is contributed by Sam007
?>

Javascript

// Javascript program for Naive Pattern Searching

function search(txt, pat)
{
    let M = pat.length;
    let N = txt.length;

    /* A loop to slide pat one by one */
    for (let i = 0; i <= N - M; i++) {
        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>");
    }
}

let txt = "AABAACAADAABAAABAA";
let pat = "AABA";
search(txt, pat);

Output

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

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

What is the best case of Naive algorithm for Pattern Searching?

The best case occurs when the first character of the pattern is not present in the text at all.

C

txt[] = "AABCCAADDEE";
pat[] = "FAA";

The number of comparisons in the best case is O(N). 

What is the worst caseof Naive algorithm for Pattern Searching?

The worst case of Naive Pattern Searching occurs in the following scenarios. 
1) When all characters of the text and pattern are the same. 

C

txt[] = "AAAAAAAAAAAAAAAAAA";
pat[] = "AAAAA";

2) Worst case also occurs when only the last character is different. 

C

txt[] = "AAAAAAAAAAAAAAAAAB";
pat[] = "AAAAB";

The number of comparisons in the worst case is O(M * (N – M + 1)). Although strings which have repeated characters are not likely to appear in English text, they may well occur in other applications (for example, in binary texts). The KMP matching algorithm improves the worst case to O(N). We will be covering KMP in the next post. Also, we will be writing more posts to cover all pattern searching algorithms and data structures. 

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