Minimum Changes to Make K Semi-palindromes

Description

Given a string s and an integer k, partition s into k substrings such that the letter changes needed to make each substring a semi-palindrome are minimized.

Return the minimum number of letter changes required.

A semi-palindrome is a special type of string that can be divided into palindromes based on a repeating pattern. To check if a string is a semi-palindrome:​

- Choose a positive divisor d of the string's length. d can range from 1 up to, but not including, the string's length. For a string of length 1, it does not have a valid divisor as per this definition, since the only divisor is its length, which is not allowed.

- For a given divisor d, divide the string into groups where each group contains characters from the string that follow a repeating pattern of length d. Specifically, the first group consists of characters at positions 1, 1 + d, 1 + 2d, and so on; the second group includes characters at positions 2, 2 + d, 2 + 2d, etc.

- The string is considered a semi-palindrome if each of these groups forms a palindrome.

Consider the string "abcabc":

- The length of "abcabc" is 6. Valid divisors are 1, 2, and 3.

- For d = 1: The entire string "abcabc" forms one group. Not a palindrome.

- For d = 2:


- Group 1 (positions 1, 3, 5): "acb"

- Group 2 (positions 2, 4, 6): "bac"

- Neither group forms a palindrome.





- For d = 3:


- Group 1 (positions 1, 4): "aa"

- Group 2 (positions 2, 5): "bb"

- Group 3 (positions 3, 6): "cc"

- All groups form palindromes. Therefore, "abcabc" is a semi-palindrome.