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Longest Chunked Palindrome Decomposition

Difficulty: Hard

Problem Description

You are given a string text. You should split it to k substrings (subtext1, subtext2, ..., subtextk) such that:

  • subtexti is a non-empty string.
  • The concatenation of all the substrings is equal to text (i.e., subtext1 + subtext2 + ... + subtextk == text).
  • subtexti == subtextk - i + 1 for all valid values of i (i.e., 1 <= i <= k).

Return the largest possible value of k.

Key Insights

  • The problem involves finding palindromic substrings that can be chunked together to maximize the number of segments.
  • Utilizing two pointers can help in identifying valid chunks from both ends of the string and working towards the center.
  • A greedy approach can be effective: continually match segments from the beginning and end of the string until no longer possible.
  • Dynamic programming can be employed to store intermediate results and avoid redundant calculations, particularly for substring comparisons.

Space and Time Complexity

Time Complexity: O(n^2)
Space Complexity: O(n)

Solution

The solution uses a two-pointer approach to identify the longest palindromic chunks. The main idea is to check for matching substrings starting from both ends of the string and move inward. Each time a matching pair is found, we can increase the count of chunks.

Code Solutions

def longestChunkedPalindromeDecomposition(text: str) -> int:
    n = len(text)
    i, j = 0, n - 1
    count = 0
    
    while i <= j:
        left = i
        right = j
        # Check for matching substrings
        while left <= right and text[left] == text[right]:
            left += 1
            right -= 1
        # If we have found a complete matching pair
        if left > right:
            count += 1
            # Move to the next chunk
            i += 1
            j -= 1
        else:
            # No more matches, break
            break
    
    return count
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