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public class OverlappingSubstringCountOptimized {
    public static void main(String[] args) {
        String input = "ababababa";
        String substringToCount = "aba";

        int count = countSubstringOccurrences(input, substringToCount);

        System.out.println("The overlapping substring appears " + count + " times.");
    }

    static int countSubstringOccurrences(String text, String pattern) {
        int n = text.length();
        int m = pattern.length();

        int[] lps = computeLPSArray(pattern);

        int count = 0;
        int i = 0;
        int j = 0;

        while (i < n) {
            if (pattern.charAt(j) == text.charAt(i)) {
                i++;
                j++;
            }
            if (j == m) {
                count++;
                j = lps[j - 1];
            }
            else if (i < n && pattern.charAt(j) != text.charAt(i)) {
                if (j != 0) {
                    j = lps[j - 1];
                } else {
                    i++;
                }
            }
        }
        return count;
    }

    static int[] computeLPSArray(String pattern) {
        int length = 0;
        int i = 1;
        int m = pattern.length();
        int[] lps = new int[m];

        while (i < m) {
            if (pattern.charAt(i) == pattern.charAt(length)) {
                length++;
                lps[i] = length;
                i++;
            } else {
                if (length != 0) {
                    length = lps[length - 1];
                } else {
                    lps[i] = 0;
                    i++;
                }
            }
        }
        return lps;
    }
}