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

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            "title": "Count the Number of Ideal Arrays",
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            "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",
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                    "lang": "C++",
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                    "code": "class Solution(object):\n    def idealArrays(self, n, maxValue):\n        \"\"\"\n        :type n: int\n        :type maxValue: int\n        :rtype: int\n        \"\"\"\n        ",
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                    "code": "/**\n * @param {number} n\n * @param {number} maxValue\n * @return {number}\n */\nvar idealArrays = function(n, maxValue) {\n    \n};",
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                    "code": "# @param {Integer} n\n# @param {Integer} max_value\n# @return {Integer}\ndef ideal_arrays(n, max_value)\n    \nend",
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                    "code": "impl Solution {\n    pub fn ideal_arrays(n: i32, max_value: i32) -> i32 {\n        \n    }\n}",
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            "hints": [
                "Notice that an ideal array is non-decreasing.",
                "Consider an alternative problem: where an ideal array must also be strictly increasing. Can you use DP to solve it?",
                "Will combinatorics help to get an answer from the alternative problem to the actual problem?"
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