Longest Palindrome After Substring Concatenation II

The most straightforward approach is to exhaustively check every possible palindrome that can be formed. We can iterate through all substrings of s and all substrings of t, concatenate them, and check if the resulting string is a palindrome. We keep track of the maximum length found.

• Initialize maxLength to 0.
• Generate all possible non-empty substrings of s. Let a substring be sub_s.
• Generate all possible non-empty substrings of t. Let a substring be sub_t.
• For each pair of (sub_s, sub_t):
  • Create the concatenated string newStr = sub_s + sub_t.
  • Check if newStr is a palindrome.
  • If it is, update maxLength = max(maxLength, newStr.length()).
• Also consider cases where one of the substrings is empty. This means finding the longest palindromic substring within s and t individually and updating maxLength.
• Return maxLength.

This method involves a nested loop structure to generate all substrings and then test them.

1. Generate Substrings: We use four nested loops to define the start and end indices for substrings from both s and t.
2. Concatenate and Test: For each pair of substrings, sub_s and sub_t, we form a new string. A helper function is used to check if this new string is a palindrome. This check can be done by comparing the string with its reverse.
3. Handle Empty Substrings: The problem allows for empty substrings. This is equivalent to finding the longest palindromic substring within s or t alone. This should be done as a base case.

Here is a conceptual code snippet for the core logic:

public int longestPalindrome(String s, String t) {
    int n = s.length();
    int m = t.length();
    int maxLen = 0;

    // Helper to find longest palindromic substring in a single string
    // maxLen = Math.max(lps(s), lps(t));

    for (int i = 0; i < n; i++) {
        for (int j = i; j < n; j++) {
            String sub_s = s.substring(i, j + 1);
            for (int k = 0; k < m; k++) {
                for (int l = k; l < m; l++) {
                    String sub_t = t.substring(k, l + 1);
                    String combined = sub_s + sub_t;
                    if (isPalindrome(combined)) {
                        maxLen = Math.max(maxLen, combined.length());
                    }
                }
            }
        }
    }
    return maxLen;
}

private boolean isPalindrome(String str) {
    int left = 0, right = str.length() - 1;
    while (left < right) {
        if (str.charAt(left) != str.charAt(right)) {
            return false;
        }
        left++;
        right--;
    }
    return true;
}