C Program for Naive algorithm for Pattern Searching

Write a C program for a given text string with length n and a pattern with length m, the task is to print all occurrences of the 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

C Program for 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 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;
}

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.
• Naive algorithm for Pattern Searching

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