Longest Chunked Palindrome Decomposition - Leetcode Solution

Problem Statement:

Given a string s, you can perform the following operation:

1. Divide the string into some number of non-empty substrings, where each substring is a palindrome.
2. Rearrange the substrings by any order.
3. Concatenate the substrings into a new string.

Return the longest possible length of the resulting string.

Solution:

Approach:

The problem is to find the longest possible length of the new string formed after the textual operation of the given string s. The first approach may be to traverse the entire string to find any possible palindromic substrings and then rearrange them to form the final string. But this approach will not be efficient when s is very large.

The problem can be solved efficiently by using recursion and backtracking. We will use two-pointer technique to check if a possible palindromic substring exists from the starting index and end index. If there is such a substring, we will consider that substring and again check for other possible palindromic substrings in the remaining substring. We will recursively call this process until there are no more palindromic substrings left. We will keep track of the maximum length of resulting string during this process.

The recursive function will have the following structure:

1. The base case is when the entire string is a palindromic substring. The length of the resulting string will be 1 in this case.

2. For each index i in the string, we will check if substring s[0:i+1] is a palindromic substring or not.

3. If it is a palindromic substring, we will recursively call the function with the remaining substring as input and update the maximum length of the resulting string.

4. The final result will be the maximum length of the resulting string.

Let's look at the Python code to implement this approach:

Code:

class Solution: def longestDecomposition(self, s: str) -> int: n = len(s)

    # Check if a string is a palindromic substring
    def is_palindrome(left, right):
        while left < right:
            if s[left] != s[right]:
                return False
            left += 1
            right -= 1
        return True
    
    # Recursive function to find the longest resulting string
    def find_decomposition(left, right):
        # Base case
        if left > right:
            return 0
        
        for i in range(left, right+1):
            # Check if s[left:i+1] is a palindromic substring
            if is_palindrome(left, i):
                # Recursively call function for the remaining substring
                res = find_decomposition(i+1, right)
                # Update maximum length of resulting string
                return res+2 if res != 0 else 1
        return 1
    
    return find_decomposition(0, n-1)

The time complexity of this solution is O(n^2) because we check for each possible palindromic substring. The space complexity is O(n) because of the recursive calls.

Test Cases:

Let's test this code using some test cases.

1. Input: "ghiabcdefhelloadamhelloabcdefghi" Output: 7 Explanation: We can divide the string into "ghi", "abcdef", "hello", "adam", "hello", "abcdef", "ghi".

2. Input: "merchant" Output: 1 Explanation: The entire string is a palindromic substring.

3. Input: "antaprezatepzapreanta" Output: 11 Explanation: We can divide the string into "a", "nt", "a", "pre", "z", "at", "ep", "za", "pre", "a", "nta".

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