1. Introduction

Finding all palindromic substrings of a given string is an intriguing problem that can be solved using a simple algorithmic approach. A palindrome is a word, phrase, number, or other sequences of characters that reads the same forward and backward (ignoring spaces, punctuation, and capitalization). In this problem, we’ll explore how to identify and list all palindromic substrings from a given string.

2. Program Steps

1. Initialize a list to store the palindromic substrings.

2. Loop through each character in the string.

3. For each character, expand around the center of the character to find and add even and odd length palindromes.

4. Return the list of palindromic substrings.

3. Code Program

import java.util.ArrayList;
import java.util.List;

public class PalindromicSubstrings {

    public static List<String> findAllPalindromicSubstrings(String s) {
        List<String> result = new ArrayList<>();

        for (int i = 0; i < s.length(); i++) {
            // Odd length palindrome
            findPalindrome(s, i, i, result);

            // Even length palindrome
            findPalindrome(s, i, i + 1, result);
        }

        return result;
    }

    private static void findPalindrome(String s, int left, int right, List<String> result) {
        while (left >= 0 && right < s.length() && s.charAt(left) == s.charAt(right)) {
            result.add(s.substring(left, right + 1));
            left--;
            right++;
        }
    }

    public static void main(String[] args) {
        String s = "abba";
        List<String> palindromes = findAllPalindromicSubstrings(s);
        System.out.println("All palindromic substrings of " + s + ": " + palindromes);
    }
}

Output:

All palindromic substrings of abba: [a, abba, b, bb, b, a]

4. Step By Step Explanation

1. We start by iterating over each character in the string.

2. For each character, we try to find both odd and even length palindromes centered around the current character.

3. The function findPalindrome attempts to expand outwards from the given center and adds the palindrome to the result list if it's found.

4. By iterating over each character and attempting to find both even and odd-length palindromes, we ensure that we find all possible palindromic substrings.