Java Program for Naive algorithm for Pattern Searching

Write a Java 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

Java 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.

// 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

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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