{ "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 <= 200
1 <= k <= s.length / 2
s
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 <= 200
1 <= k <= s.length / 2
s
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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