Split a String into Exactly Three Palindromes

Problem Statement

Given a string s, determine whether it is possible to split s into exactly three non-empty contiguous substrings, each of which is a palindrome, such that concatenating them in order reconstructs the original string s.

A string is a palindrome if it reads the same forwards and backwards.

Write a function that returns True if such a partition exists, and False otherwise.

Function Signature

def can_split_three_palindromes(s: str) -> bool:
    pass

Input & Output Format

• Input: A single string s containing only lowercase English letters.
• Output: A boolean value (True if a valid 3-palindrome partition exists, False otherwise).

Constraints

• 3 <= len(s) <= 2000
• s consists solely of lowercase English letters ('a' - 'z').

Examples

Example 1

Input: s = "abacaba"
Output: True
Explanation: We can split the string into ["aba", "c", "aba"], all of which are palindromes.

Example 2

Input: s = "abcb"
Output: False
Explanation: The possible 3-part splits are:
- ["a", "b", "cb"] -> "cb" is not a palindrome.
- ["a", "bc", "b"] -> "bc" is not a palindrome.
- ["ab", "c", "b"] -> "ab" is not a palindrome.
None of the splits yield three palindromes.

Example 3

Input: s = "aaaa"
Output: True
Explanation: Splits such as ["a", "a", "aa"] or ["a", "aa", "a"] produce three valid palindromes.

Edge Cases to Consider

• Strings of minimum length (len(s) == 3), where every individual character is naturally a palindrome of length 1.
• Strings where all characters are identical.
• Cases where the first and third parts are valid palindromes, but the middle part is not.