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1960. Maximum Product of the Length of Two Palindromic Substrings (Hard)

You are given a 0-indexed string s and are tasked with finding two non-intersecting palindromic substrings of odd length such that the product of their lengths is maximized.

More formally, you want to choose four integers i, j, k, l such that 0 <= i <= j < k <= l < s.length and both the substrings s[i...j] and s[k...l] are palindromes and have odd lengths. s[i...j] denotes a substring from index i to index j inclusive.

Return the maximum possible product of the lengths of the two non-intersecting palindromic substrings.

A palindrome is a string that is the same forward and backward. A substring is a contiguous sequence of characters in a string.

 

Example 1:

Input: s = "ababbb"
Output: 9
Explanation: Substrings "aba" and "bbb" are palindromes with odd length. product = 3 * 3 = 9.

Example 2:

Input: s = "zaaaxbbby"
Output: 9
Explanation: Substrings "aaa" and "bbb" are palindromes with odd length. product = 3 * 3 = 9.

 

Constraints:

• 2 <= s.length <= 105
• s consists of lowercase English letters.

Related Topics

[String] [Hash Function] [Rolling Hash]

Hints

Hint 1

You can use Manacher's algorithm to get the maximum palindromic substring centered at each index

Hint 2

After using Manacher's for each center use a line sweep from the center to the left and from the center to the right to find for each index the farthest center to it with distance ≤ palin[center]

Hint 3

After that, find the maximum palindrome size for each prefix in the string and for each suffix and the answer would be max(prefix[i] * suffix[i + 1])