{ "data": { "question": { "questionId": "2879", "questionFrontendId": "2911", "categoryTitle": "Algorithms", "boundTopicId": 2490371, "title": "Minimum Changes to Make K Semi-palindromes", "titleSlug": "minimum-changes-to-make-k-semi-palindromes", "content": "
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.
\n\nA 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:
\n\nd 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.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.Consider the string "abcabc":
"abcabc" is 6. Valid divisors are 1, 2, and 3.d = 1: The entire string "abcabc" forms one group. Not a palindrome.d = 2:\n\t1, 3, 5): "acb"2, 4, 6): "bac"d = 3:\n\t1, 4): "aa"2, 5): "bb"3, 6): "cc""abcabc" is a semi-palindrome.\n
Example 1:
\n\nInput: s = "abcac", k = 2
\n\nOutput: 1
\n\nExplanation: Divide s into "ab" and "cac". "cac" is already semi-palindrome. Change "ab" to "aa", it becomes semi-palindrome with d = 1.
Example 2:
\n\nInput: s = "abcdef", k = 2
\n\nOutput: 2
\n\nExplanation: Divide s into substrings "abc" and "def". Each needs one change to become semi-palindrome.
Example 3:
\n\nInput: s = "aabbaa", k = 3
\n\nOutput: 0
\n\nExplanation: Divide s into substrings "aa", "bb" and "aa". All are already semi-palindromes.
\n
Constraints:
\n\n2 <= s.length <= 2001 <= k <= s.length / 2s contains only lowercase English letters.给你一个字符串 s 和一个整数 k ,请你将 s 分成 k 个 子字符串 ,使得每个 子字符串 变成 半回文串 需要修改的字符数目最少。
请你返回一个整数,表示需要修改的 最少 字符数目。
\n\n注意:
\n\nlen 的字符串存在一个满足 1 <= d < len 的正整数 d ,len % d == 0 成立且所有对 d 做除法余数相同的下标对应的字符连起来得到的字符串都是 回文串 ,那么我们说这个字符串是 半回文串 。比方说 \"aa\" ,\"aba\" ,\"adbgad\" 和 \"abab\" 都是 半回文串 ,而 \"a\" ,\"ab\" 和 \"abca\" 不是。\n\n
示例 1:
\n\n\n输入:s = \"abcac\", k = 2\n输出:1\n解释:我们可以将 s 分成子字符串 \"ab\" 和 \"cac\" 。子字符串 \"cac\" 已经是半回文串。如果我们将 \"ab\" 变成 \"aa\" ,它也会变成一个 d = 1 的半回文串。\n该方案是将 s 分成 2 个子字符串的前提下,得到 2 个半回文子字符串需要的最少修改次数。所以答案为 1 。\n\n
示例 2:
\n\n\n输入:s = \"abcdef\", k = 2\n输出:2\n解释:我们可以将 s 分成子字符串 \"abc\" 和 \"def\" 。子字符串 \"abc\" 和 \"def\" 都需要修改一个字符得到半回文串,所以我们总共需要 2 次字符修改使所有子字符串变成半回文串。\n该方案是将 s 分成 2 个子字符串的前提下,得到 2 个半回文子字符串需要的最少修改次数。所以答案为 2 。\n\n
示例 3:
\n\n\n输入:s = \"aabbaa\", k = 3\n输出:0\n解释:我们可以将 s 分成子字符串 \"aa\" ,\"bb\" 和 \"aa\" 。\n字符串 \"aa\" 和 \"bb\" 都已经是半回文串了。所以答案为 0 。\n\n\n
\n\n
提示:
\n\n2 <= s.length <= 2001 <= k <= s.length / 2s 只包含小写英文字母。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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