leetcode-problemset/leetcode-cn/originData/maximum-element-sum-of-a-complete-subset-of-indices.json

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            "questionId": "3047",
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            "categoryTitle": "Algorithms",
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            "title": "Maximum Element-Sum of a Complete Subset of Indices",
            "titleSlug": "maximum-element-sum-of-a-complete-subset-of-indices",
            "content": "<p>You are given a <strong>1</strong><strong>-indexed</strong> array <code>nums</code> of <code>n</code> integers.</p>\n\n<p>A set of numbers is <strong>complete</strong> if the product of every pair of its elements is a perfect square.</p>\n\n<p>For a subset of the indices set <code>{1, 2, ..., n}</code> represented as <code>{i<sub>1</sub>, i<sub>2</sub>, ..., i<sub>k</sub>}</code>, we define its <strong>element-sum</strong> as: <code>nums[i<sub>1</sub>] + nums[i<sub>2</sub>] + ... + nums[i<sub>k</sub>]</code>.</p>\n\n<p>Return <em>the <strong>maximum element-sum</strong> of a <strong>complete</strong> subset of the indices set</em> <code>{1, 2, ..., n}</code>.</p>\n\n<p>A perfect square is a number that can be expressed as the product of an integer by itself.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [8,7,3,5,7,2,4,9]\n<strong>Output:</strong> 16\n<strong>Explanation:</strong> Apart from the subsets consisting of a single index, there are two other complete subsets of indices: {1,4} and {2,8}.\nThe sum of the elements corresponding to indices 1 and 4 is equal to nums[1] + nums[4] = 8 + 5 = 13.\nThe sum of the elements corresponding to indices 2 and 8 is equal to nums[2] + nums[8] = 7 + 9 = 16.\nHence, the maximum element-sum of a complete subset of indices is 16.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,10,3,10,1,13,7,9,4]\n<strong>Output:</strong> 19\n<strong>Explanation:</strong> Apart from the subsets consisting of a single index, there are four other complete subsets of indices: {1,4}, {1,9}, {2,8}, {4,9}, and {1,4,9}.\nThe sum of the elements corresponding to indices 1 and 4 is equal to nums[1] + nums[4] = 5 + 10 = 15.\nThe sum of the elements corresponding to indices 1 and 9 is equal to nums[1] + nums[9] = 5 + 4 = 9.\nThe sum of the elements corresponding to indices 2 and 8 is equal to nums[2] + nums[8] = 10 + 9 = 19.\nThe sum of the elements corresponding to indices 4 and 9 is equal to nums[4] + nums[9] = 10 + 4 = 14.\nThe sum of the elements corresponding to indices 1, 4, and 9 is equal to nums[1] + nums[4] + nums[9] = 5 + 10 + 4 = 19.\nHence, the maximum element-sum of a complete subset of indices is 19.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n == nums.length &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "完全子集的最大元素和",
            "translatedContent": "<p>给你一个下标从 <strong>1</strong> 开始、由 <code>n</code> 个整数组成的数组。</p>\n\n<p>如果一组数字中每对元素的乘积都是一个完全平方数，则称这组数字是一个 <strong>完全集</strong> 。</p>\n\n<p>下标集 <code>{1, 2, ..., n}</code> 的子集可以表示为 <code>{i<sub>1</sub>, i<sub>2</sub>, ..., i<sub>k</sub>}</code>，我们定义对应该子集的 <strong>元素和</strong> 为 <code>nums[i<sub>1</sub>] + nums[i<sub>2</sub>] + ... + nums[i<sub>k</sub>]</code> 。</p>\n\n<p>返回下标集&nbsp;<code>{1, 2, ..., n}</code> 的 <strong>完全子集</strong> 所能取到的 <strong>最大元素和</strong> 。</p>\n\n<p>完全平方数是指可以表示为一个整数和其自身相乘的数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [8,7,3,5,7,2,4,9]\n<strong>输出：</strong>16\n<strong>解释：</strong>除了由单个下标组成的子集之外，还有两个下标集的完全子集：{1,4} 和 {2,8} 。\n与下标 1 和 4 对应的元素和等于 nums[1] + nums[4] = 8 + 5 = 13 。\n与下标 2 和 8 对应的元素和等于 nums[2] + nums[8] = 7 + 9 = 16 。\n因此，下标集的完全子集可以取到的最大元素和为 16 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [5,10,3,10,1,13,7,9,4]\n<strong>输出：</strong>19\n<strong>解释：</strong>除了由单个下标组成的子集之外，还有四个下标集的完全子集：{1,4}、{1,9}、{2,8}、{4,9} 和 {1,4,9} 。 \n与下标 1 和 4 对应的元素和等于 nums[1] + nums[4] = 5 + 10 = 15 。 \n与下标 1 和 9 对应的元素和等于 nums[1] + nums[9] = 5 + 4 = 9 。 \n与下标 2 和 8 对应的元素和等于 nums[2] + nums[8] = 10 + 9 = 19 。\n与下标 4 和 9 对应的元素和等于 nums[4] + nums[9] = 10 + 4 = 14 。 \n与下标 1、4 和 9 对应的元素和等于 nums[1] + nums[4] + nums[9] = 5 + 10 + 4 = 19 。 \n因此，下标集的完全子集可以取到的最大元素和为 19 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n == nums.length &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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                "Let <code>P(x)</code> be the product of all prime numbers <code>p</code> such that <code>p</code> divides <code>x</code>, and there exists an <strong>odd</strong> <code>k</code> such that <code>p^k</code> divides <code>x</code> but <code>p^(k+1)</code> does not.",
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