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Maximum Number of Non-overlapping Palindrome Substrings

You are given a string s and a positive integer k.

You are given a string s and a positive integer k.

Select a set of non-overlapping substrings from the string s that satisfy the following conditions:

Return the maximum number of substrings in an optimal selection.

A substring is a contiguous sequence of characters within a string.

Maximum Number of Non-overlapping Palindrome Substrings diagram

Example 1

Input: s = "abaccdbbd", k = 3

Output: 2

Explanation: We can select the substrings underlined in s = "abaccdbbd". Both "aba" and "dbbd" are palindromes and have a length of at least k = 3. It can be shown that we cannot find a selection with more than two valid substrings.

Example 2

Input: s = "adbcda", k = 2

Output: 0

Explanation: There is no palindrome substring of length at least 2 in the string.

Constraints

  • 1 <= k <= s.length <= 2000
  • s consists of lowercase English letters.

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