leetcode-problemset/leetcode-cn/originData/minimum-changes-to-make-k-semi-palindromes.json

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            "title": "Minimum Changes to Make K Semi-palindromes",
            "titleSlug": "minimum-changes-to-make-k-semi-palindromes",
            "content": "<p>Given a string <code>s</code> and an integer <code>k</code>, partition <code>s</code> into <code>k</code> <strong>substrings</strong> such that the sum of the number of letter changes required to turn each <strong>substring</strong> into a <strong>semi-palindrome</strong> is minimized.</p>\n\n<p>Return <em>an integer denoting the <strong>minimum</strong> number of letter changes required.</em></p>\n\n<p><strong>Notes</strong></p>\n\n<ul>\n\t<li>A string is a <strong>palindrome</strong> if it can be read the same way from left to right and right to left.</li>\n\t<li>A string with a length of <code>len</code> is considered a <strong>semi-palindrome</strong> if there exists a positive integer <code>d</code> such that <code>1 &lt;= d &lt; len</code> and <code>len % d == 0</code>, and if we take indices that have the same modulo by <code>d</code>, they form a <strong>palindrome</strong>. For example, <code>&quot;aa&quot;</code>, <code>&quot;aba&quot;</code>, <code>&quot;adbgad&quot;</code>, and, <code>&quot;abab&quot;</code> are <strong>semi-palindrome</strong> and <code>&quot;a&quot;</code>, <code>&quot;ab&quot;</code>, and, <code>&quot;abca&quot;</code> are not.</li>\n\t<li>A <strong>substring</strong> is a contiguous sequence of characters within a string.</li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;abcac&quot;, k = 2\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> We can divide s into substrings &quot;ab&quot; and &quot;cac&quot;. The string &quot;cac&quot; is already a semi-palindrome. If we change &quot;ab&quot; to &quot;aa&quot;, it becomes a semi-palindrome with d = 1.\nIt can be shown that there is no way to divide the string &quot;abcac&quot; into two semi-palindrome substrings. Therefore, the answer would be at least 1.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;abcdef&quot;, k = 2\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> We can divide it into substrings &quot;abc&quot; and &quot;def&quot;. Each of the substrings &quot;abc&quot; and &quot;def&quot; 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.</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;aabbaa&quot;, k = 3\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> We can divide it into substrings &quot;aa&quot;, &quot;bb&quot; and &quot;aa&quot;.\nThe strings &quot;aa&quot; and &quot;bb&quot; are already semi-palindromes. Thus, the answer is zero.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= s.length &lt;= 200</code></li>\n\t<li><code>1 &lt;= k &lt;= s.length / 2</code></li>\n\t<li><code>s</code> consists only of lowercase English letters.</li>\n</ul>\n",
            "translatedTitle": "得到 K 个半回文串的最少修改次数",
            "translatedContent": "<p>给你一个字符串&nbsp;<code>s</code>&nbsp;和一个整数&nbsp;<code>k</code>&nbsp;，请你将&nbsp;<code>s</code> 分成&nbsp;<code>k</code>&nbsp;个<strong>&nbsp;子字符串</strong>&nbsp;，使得每个 <strong>子字符串</strong>&nbsp;变成&nbsp;<strong>半回文串</strong>&nbsp;需要修改的字符数目最少。</p>\n\n<p>请你返回一个整数，表示需要修改的 <strong>最少</strong>&nbsp;字符数目。</p>\n\n<p><strong>注意：</strong></p>\n\n<ul>\n\t<li>如果一个字符串从左往右和从右往左读是一样的，那么它是一个 <strong>回文串</strong>&nbsp;。</li>\n\t<li>如果长度为 <code>len</code>&nbsp;的字符串存在一个满足&nbsp;<code>1 &lt;= d &lt; len</code>&nbsp;的正整数&nbsp;<code>d</code>&nbsp;，<code>len % d == 0</code>&nbsp;成立且所有对 <code>d</code>&nbsp;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 <strong>回文串</strong>&nbsp;，那么我们说这个字符串是 <strong>半回文串</strong>&nbsp;。比方说&nbsp;<code>\"aa\"</code>&nbsp;，<code>\"aba\"</code> ，<code>\"adbgad\"</code>&nbsp;和&nbsp;<code>\"abab\"</code>&nbsp;都是 <strong>半回文串</strong>&nbsp;，而&nbsp;<code>\"a\"</code>&nbsp;，<code>\"ab\"</code>&nbsp;和&nbsp;<code>\"abca\"</code>&nbsp;不是。</li>\n\t<li><strong>子字符串</strong>&nbsp;指的是一个字符串中一段连续的字符序列。</li>\n</ul>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>s = \"abcac\", k = 2\n<b>输出：</b>1\n<b>解释：</b>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 。</pre>\n\n<p><strong class=\"example\">示例 2:</strong></p>\n\n<pre>\n<b>输入：</b>s = \"abcdef\", k = 2\n<b>输出：</b>2\n<b>解释：</b>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 。</pre>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>s = \"aabbaa\", k = 3\n<b>输出：</b>0\n<b>解释：</b>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</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= s.length &lt;= 200</code></li>\n\t<li><code>1 &lt;= k &lt;= s.length / 2</code></li>\n\t<li><code>s</code>&nbsp;只包含小写英文字母。</li>\n</ul>\n",
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                "Define <code>dp[i][j]</code> as the minimum count of letter changes needed to split the suffix of string <code>s</code> starting from <code>s[i]</code> into <code>j</code> valid parts.",
                "We have <code>dp[i][j] = min(dp[x + 1][j - 1] + v[i][x])</code>. Here <code>v[i][x]</code> is the minimum number of letter changes to change substring <code>s[i..x]</code> into semi-palindrome.",
                "<code>v[i][j]</code> can be calculated separately by <b>brute-force</b>. We can create a table of <code>v[i][j]</code> independently to improve the complexity. Also note that semi-palindrome’s length is at least <code>2</code>."
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