Naive algorithm for Pattern Searching

Given a text txt[0..n-1] and a pattern 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

pat[] =  "AABA"
Output: Pattern found at index 0
Pattern found at index 9
Pattern found at index 12

```

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

Naive Pattern Searching:
Slide the pattern over text one by one and check for a match. If a match is found, then slides by 1 again to check for subsequent matches.

Implementation of above approach using CPP

// 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 Code
int main()
{
char pat[] = "AABA";
search(pat, txt);
return 0;
}

Output:
```Pattern found at index 0
Pattern found at index 9
Pattern found at index 13 ```

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

pat[] = "FAA";

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

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

txt[] = "AAAAAAAAAAAAAAAAAA";

pat[] = "AAAAA";

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

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).

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