leetcode-problemset/leetcode-cn/originData/count-the-number-of-ideal-arrays.json

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            "questionId": "2415",
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            "title": "Count the Number of Ideal Arrays",
            "titleSlug": "count-the-number-of-ideal-arrays",
            "content": "<p>You are given two integers <code>n</code> and <code>maxValue</code>, which are used to describe an <strong>ideal</strong> array.</p>\n\n<p>A <strong>0-indexed</strong> integer array <code>arr</code> of length <code>n</code> is considered <strong>ideal</strong> if the following conditions hold:</p>\n\n<ul>\n\t<li>Every <code>arr[i]</code> is a value from <code>1</code> to <code>maxValue</code>, for <code>0 &lt;= i &lt; n</code>.</li>\n\t<li>Every <code>arr[i]</code> is divisible by <code>arr[i - 1]</code>, for <code>0 &lt; i &lt; n</code>.</li>\n</ul>\n\n<p>Return <em>the number of <strong>distinct</strong> ideal arrays of length </em><code>n</code>. Since the answer may be very large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2, maxValue = 5\n<strong>Output:</strong> 10\n<strong>Explanation:</strong> The following are the possible ideal arrays:\n- Arrays starting with the value 1 (5 arrays): [1,1], [1,2], [1,3], [1,4], [1,5]\n- Arrays starting with the value 2 (2 arrays): [2,2], [2,4]\n- Arrays starting with the value 3 (1 array): [3,3]\n- Arrays starting with the value 4 (1 array): [4,4]\n- Arrays starting with the value 5 (1 array): [5,5]\nThere are a total of 5 + 2 + 1 + 1 + 1 = 10 distinct ideal arrays.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, maxValue = 3\n<strong>Output:</strong> 11\n<strong>Explanation:</strong> The following are the possible ideal arrays:\n- Arrays starting with the value 1 (9 arrays): \n   - With no other distinct values (1 array): [1,1,1,1,1] \n   - With 2<sup>nd</sup> distinct value 2 (4 arrays): [1,1,1,1,2], [1,1,1,2,2], [1,1,2,2,2], [1,2,2,2,2]\n   - With 2<sup>nd</sup> distinct value 3 (4 arrays): [1,1,1,1,3], [1,1,1,3,3], [1,1,3,3,3], [1,3,3,3,3]\n- Arrays starting with the value 2 (1 array): [2,2,2,2,2]\n- Arrays starting with the value 3 (1 array): [3,3,3,3,3]\nThere are a total of 9 + 1 + 1 = 11 distinct ideal arrays.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= maxValue &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
            "translatedTitle": "统计理想数组的数目",
            "translatedContent": "<p>给你两个整数 <code>n</code> 和 <code>maxValue</code> ，用于描述一个 <strong>理想数组</strong> 。</p>\n\n<p>对于下标从 <strong>0</strong> 开始、长度为 <code>n</code> 的整数数组 <code>arr</code> ，如果满足以下条件，则认为该数组是一个 <strong>理想数组</strong> ：</p>\n\n<ul>\n\t<li>每个 <code>arr[i]</code> 都是从 <code>1</code> 到 <code>maxValue</code> 范围内的一个值，其中 <code>0 &lt;= i &lt; n</code> 。</li>\n\t<li>每个 <code>arr[i]</code> 都可以被 <code>arr[i - 1]</code> 整除，其中 <code>0 &lt; i &lt; n</code> 。</li>\n</ul>\n\n<p>返回长度为 <code>n</code> 的 <strong>不同</strong> 理想数组的数目。由于答案可能很大，返回对 <code>10<sup>9</sup> + 7</code> 取余的结果。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre><strong>输入：</strong>n = 2, maxValue = 5\n<strong>输出：</strong>10\n<strong>解释：</strong>存在以下理想数组：\n- 以 1 开头的数组（5 个）：[1,1]、[1,2]、[1,3]、[1,4]、[1,5]\n- 以 2 开头的数组（2 个）：[2,2]、[2,4]\n- 以 3 开头的数组（1 个）：[3,3]\n- 以 4 开头的数组（1 个）：[4,4]\n- 以 5 开头的数组（1 个）：[5,5]\n共计 5 + 2 + 1 + 1 + 1 = 10 个不同理想数组。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><strong>输入：</strong>n = 5, maxValue = 3\n<strong>输出：</strong>11\n<strong>解释：</strong>存在以下理想数组：\n- 以 1 开头的数组（9 个）：\n   - 不含其他不同值（1 个）：[1,1,1,1,1] \n   - 含一个不同值 2（4 个）：[1,1,1,1,2], [1,1,1,2,2], [1,1,2,2,2], [1,2,2,2,2]\n   - 含一个不同值 3（4 个）：[1,1,1,1,3], [1,1,1,3,3], [1,1,3,3,3], [1,3,3,3,3]\n- 以 2 开头的数组（1 个）：[2,2,2,2,2]\n- 以 3 开头的数组（1 个）：[3,3,3,3,3]\n共计 9 + 1 + 1 = 11 个不同理想数组。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= n &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= maxValue &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
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                "Notice that an ideal array is non-decreasing.",
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