leetcode-problemset/leetcode-cn/originData/number-of-beautiful-partitions.json

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            "title": "Number of Beautiful Partitions",
            "titleSlug": "number-of-beautiful-partitions",
            "content": "<p>You are given a string <code>s</code> that consists of the digits <code>&#39;1&#39;</code> to <code>&#39;9&#39;</code> and two integers <code>k</code> and <code>minLength</code>.</p>\n\n<p>A partition of <code>s</code> is called <strong>beautiful</strong> if:</p>\n\n<ul>\n\t<li><code>s</code> is partitioned into <code>k</code> non-intersecting substrings.</li>\n\t<li>Each substring has a length of <strong>at least</strong> <code>minLength</code>.</li>\n\t<li>Each substring starts with a <strong>prime</strong> digit and ends with a <strong>non-prime</strong> digit. Prime digits are <code>&#39;2&#39;</code>, <code>&#39;3&#39;</code>, <code>&#39;5&#39;</code>, and <code>&#39;7&#39;</code>, and the rest of the digits are non-prime.</li>\n</ul>\n\n<p>Return<em> the number of <strong>beautiful</strong> partitions of </em><code>s</code>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;23542185131&quot;, k = 3, minLength = 2\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> There exists three ways to create a beautiful partition:\n&quot;2354 | 218 | 5131&quot;\n&quot;2354 | 21851 | 31&quot;\n&quot;2354218 | 51 | 31&quot;\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;23542185131&quot;, k = 3, minLength = 3\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> There exists one way to create a beautiful partition: &quot;2354 | 218 | 5131&quot;.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;3312958&quot;, k = 3, minLength = 1\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> There exists one way to create a beautiful partition: &quot;331 | 29 | 58&quot;.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k, minLength &lt;= s.length &lt;= 1000</code></li>\n\t<li><code>s</code> consists of the digits <code>&#39;1&#39;</code> to <code>&#39;9&#39;</code>.</li>\n</ul>\n",
            "translatedTitle": "完美分割的方案数",
            "translatedContent": "<p>给你一个字符串&nbsp;<code>s</code>&nbsp;，每个字符是数字&nbsp;<code>'1'</code>&nbsp;到&nbsp;<code>'9'</code>&nbsp;，再给你两个整数&nbsp;<code>k</code> 和&nbsp;<code>minLength</code>&nbsp;。</p>\n\n<p>如果对 <code>s</code>&nbsp;的分割满足以下条件，那么我们认为它是一个 <strong>完美</strong>&nbsp;分割：</p>\n\n<ul>\n\t<li><code>s</code>&nbsp;被分成 <code>k</code>&nbsp;段互不相交的子字符串。</li>\n\t<li>每个子字符串长度都 <strong>至少</strong>&nbsp;为&nbsp;<code>minLength</code>&nbsp;。</li>\n\t<li>每个子字符串的第一个字符都是一个 <b>质数</b> 数字，最后一个字符都是一个 <strong>非质数</strong>&nbsp;数字。质数数字为&nbsp;<code>'2'</code>&nbsp;，<code>'3'</code>&nbsp;，<code>'5'</code>&nbsp;和&nbsp;<code>'7'</code>&nbsp;，剩下的都是非质数数字。</li>\n</ul>\n\n<p>请你返回 <code>s</code>&nbsp;的 <strong>完美</strong>&nbsp;分割数目。由于答案可能很大，请返回答案对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;<strong>取余</strong>&nbsp;后的结果。</p>\n\n<p>一个 <strong>子字符串</strong>&nbsp;是字符串中一段连续字符串序列。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>s = \"23542185131\", k = 3, minLength = 2\n<b>输出：</b>3\n<b>解释：</b>存在 3 种完美分割方案：\n\"2354 | 218 | 5131\"\n\"2354 | 21851 | 31\"\n\"2354218 | 51 | 31\"\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>s = \"23542185131\", k = 3, minLength = 3\n<b>输出：</b>1\n<b>解释：</b>存在一种完美分割方案：\"2354 | 218 | 5131\" 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>s = \"3312958\", k = 3, minLength = 1\n<b>输出：</b>1\n<b>解释：</b>存在一种完美分割方案：\"331 | 29 | 58\" 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= k, minLength &lt;= s.length &lt;= 1000</code></li>\n\t<li><code>s</code>&nbsp;每个字符都为数字&nbsp;<code>'1'</code>&nbsp;到&nbsp;<code>'9'</code> 之一。</li>\n</ul>\n",
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            "hints": [
                "Try using a greedy approach where you take as many digits as possible from the left of the string for each partition.",
                "You can also use a dynamic programming approach, let an array dp where dp[i] is the solution of the problem for the prefix of the string ending at index i, the answer of the problem will be dp[n-1]. What are the transitions of this dp?"
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