leetcode-problemset/leetcode-cn/originData/count-sorted-vowel-strings.json

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            "questionId": "1761",
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            "categoryTitle": "Algorithms",
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            "title": "Count Sorted Vowel Strings",
            "titleSlug": "count-sorted-vowel-strings",
            "content": "<p>Given an integer <code>n</code>, return <em>the number of strings of length </em><code>n</code><em> that consist only of vowels (</em><code>a</code><em>, </em><code>e</code><em>, </em><code>i</code><em>, </em><code>o</code><em>, </em><code>u</code><em>) and are <strong>lexicographically sorted</strong>.</em></p>\n\n<p>A string <code>s</code> is <strong>lexicographically sorted</strong> if for all valid <code>i</code>, <code>s[i]</code> is the same as or comes before <code>s[i+1]</code> in the alphabet.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The 5 sorted strings that consist of vowels only are <code>[&quot;a&quot;,&quot;e&quot;,&quot;i&quot;,&quot;o&quot;,&quot;u&quot;].</code>\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2\n<strong>Output:</strong> 15\n<strong>Explanation:</strong> The 15 sorted strings that consist of vowels only are\n[&quot;aa&quot;,&quot;ae&quot;,&quot;ai&quot;,&quot;ao&quot;,&quot;au&quot;,&quot;ee&quot;,&quot;ei&quot;,&quot;eo&quot;,&quot;eu&quot;,&quot;ii&quot;,&quot;io&quot;,&quot;iu&quot;,&quot;oo&quot;,&quot;ou&quot;,&quot;uu&quot;].\nNote that &quot;ea&quot; is not a valid string since &#39;e&#39; comes after &#39;a&#39; in the alphabet.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 33\n<strong>Output:</strong> 66045\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 50</code>&nbsp;</li>\n</ul>\n",
            "translatedTitle": "统计字典序元音字符串的数目",
            "translatedContent": "<p>给你一个整数 <code>n</code>，请返回长度为 <code>n</code> 、仅由元音 (<code>a</code>, <code>e</code>, <code>i</code>, <code>o</code>, <code>u</code>) 组成且按 <strong>字典序排列</strong> 的字符串数量。</p>\n\n<p>字符串 <code>s</code> 按 <strong>字典序排列</strong> 需要满足：对于所有有效的 <code>i</code>，<code>s[i]</code> 在字母表中的位置总是与 <code>s[i+1]</code> 相同或在 <code>s[i+1]</code> 之前。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 1\n<strong>输出：</strong>5\n<strong>解释：</strong>仅由元音组成的 5 个字典序字符串为 <code>[\"a\",\"e\",\"i\",\"o\",\"u\"]</code>\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 2\n<strong>输出：</strong>15\n<strong>解释：</strong>仅由元音组成的 15 个字典序字符串为\n[\"aa\",\"ae\",\"ai\",\"ao\",\"au\",\"ee\",\"ei\",\"eo\",\"eu\",\"ii\",\"io\",\"iu\",\"oo\",\"ou\",\"uu\"]\n注意，\"ea\" 不是符合题意的字符串，因为 'e' 在字母表中的位置比 'a' 靠后\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 33\n<strong>输出：</strong>66045\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 50</code> </li>\n</ul>\n",
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            "hints": [
                "For each character, its possible values will depend on the value of its previous character, because it needs to be not smaller than it.",
                "Think backtracking. Build a recursive function count(n, last_character) that counts the number of valid strings of length n and whose first characters are not less than last_character.",
                "In this recursive function, iterate on the possible characters for the first character, which will be all the vowels not less than last_character, and for each possible value c, increase the answer by count(n-1, c)."
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