Palindromic Substrings

Given a string, your task is to count how many palindromic substrings in this string.

The substrings with different start indexes or end indexes are counted as different substrings even they consist of same characters.

Example 1:

Input: "abc"
Output: 3
Explanation: Three palindromic strings: "a", "b", "c".

Example 2:

Input: "aaa"
Output: 6
Explanation: Six palindromic strings: "a", "a", "a", "aa", "aa", "aaa".

public class Solution {

    public static int numberOfPalindromicSubstrings(String S) {
        // Conversion of string into required form
        char[] str = new char[2 * S.length() + 3];
        str[0] = '@';
        str[1] = '#';
        str[str.length - 1] = '$';
        int index = 2;
        for (char c : S.toCharArray()) {
            str[index++] = c;
            str[index++] = '#';
        }

        int[] palindromicLength = new int[str.length];
        int center = 0, right = 0;
        for (int i = 1; i < palindromicLength.length - 1; ++i) {
            // Finding mirror element
            int mirror = i - 2 * (i - c);
            // If i is within range
            if (i < right)
                palindromicLength[i] = Math.min(right - i, palindromicLength[mirror]);
            // Expanding about center, using any min length we have
            while (str[i + palindromicLength[i] + 1] == str[i - palindromicLength[i] - 1])
                palindromicLength[i]++;
            // If range of palindrome of i, is greater than range of "main" palindrome
            if (i + palindromicLength[i] > right) {
                center = i;
                right = i + palindromicLength[i];
            }
        }
        int ans = 0;
        for (int length : palindromicLength)
            ans += (length + 1) / 2;
        return ans;
    }
}