Given a string s and an integer k, partition s into k substrings such that the sum of the number of letter changes required to turn each substring into a semi-palindrome is minimized.
Return an integer denoting the minimum number of letter changes required.
\n\nNotes
\n\nlen is considered a semi-palindrome if there exists a positive integer d such that 1 <= d < len and len % d == 0, and if we take indices that have the same modulo by d, they form a palindrome. For example, "aa", "aba", "adbgad", and, "abab" are semi-palindrome and "a", "ab", and, "abca" are not.\n
Example 1:
\n\n\nInput: s = "abcac", k = 2\nOutput: 1\nExplanation: We can divide s into substrings "ab" and "cac". The string "cac" is already a semi-palindrome. If we change "ab" to "aa", it becomes a semi-palindrome with d = 1.\nIt can be shown that there is no way to divide the string "abcac" into two semi-palindrome substrings. Therefore, the answer would be at least 1.\n\n
Example 2:
\n\n\nInput: s = "abcdef", k = 2\nOutput: 2\nExplanation: We can divide it into substrings "abc" and "def". Each of the substrings "abc" and "def" requires one change to become a semi-palindrome, so we need 2 changes in total to make all substrings semi-palindrome.\nIt can be shown that we cannot divide the given string into two substrings in a way that it would require less than 2 changes.\n\n
Example 3:
\n\n\nInput: s = "aabbaa", k = 3\nOutput: 0\nExplanation: We can divide it into substrings "aa", "bb" and "aa".\nThe strings "aa" and "bb" are already semi-palindromes. Thus, the answer is zero.\n\n\n
\n
Constraints:
\n\n2 <= s.length <= 2001 <= k <= s.length / 2s consists only of lowercase English letters.dp[i][j] as the minimum count of letter changes needed to split the suffix of string s starting from s[i] into j valid parts.",
"We have dp[i][j] = min(dp[x + 1][j - 1] + v[i][x]). Here v[i][x] is the minimum number of letter changes to change substring s[i..x] into semi-palindrome.",
"v[i][j] can be calculated separately by brute-force. We can create a table of v[i][j] independently to improve the complexity. Also note that semi-palindrome’s length is at least 2."
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