mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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190 lines
25 KiB
JSON
190 lines
25 KiB
JSON
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"title": "Maximum Element-Sum of a Complete Subset of Indices",
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"content": "<p>You are given a <strong>1</strong><strong>-indexed</strong> array <code>nums</code>. Your task is to select a <strong>complete subset</strong> from <code>nums</code> where every pair of selected indices multiplied is a <span data-keyword=\"perfect-square\">perfect square,</span>. i. e. if you select <code>a<sub>i</sub></code> and <code>a<sub>j</sub></code>, <code>i * j</code> must be a perfect square.</p>\n\n<p>Return the <em>sum</em> of the complete subset with the <em>maximum sum</em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [8,7,3,5,7,2,4,9]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">16</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>We select elements at indices 2 and 8 and <code>2 * 8</code> is a perfect square.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">nums = [8,10,3,8,1,13,7,9,4]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">20</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>We select elements at indices 1, 4, and 9. <code>1 * 4</code>, <code>1 * 9</code>, <code>4 * 9</code> are perfect squares.</p>\n</div>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n == nums.length <= 10<sup>4</sup></code></li>\n\t<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"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。你需要从 <code>nums</code> 选择一个 <strong>完全集</strong>，其中每对元素下标的乘积都是一个 <span data-keyword=\"perfect-square\">完全平方数</span>，例如选择 <code>a<sub>i</sub></code> 和 <code>a<sub>j</sub></code> ，<code>i * j</code> 一定是完全平方数。</p>\n\n<p>返回 <strong>完全子集</strong> 所能取到的 <strong>最大元素和</strong> 。</p>\n\n<p> </p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong><span class=\"example-io\">nums = [8,7,3,5,7,2,4,9]</span></p>\n\n<p><strong>输出：</strong><span class=\"example-io\">16</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>我们选择下标为 2 和 8 的元素，并且 <code>2 * 8</code> 是一个完全平方数。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>nums = [8,10,3,8,1,13,7,9,4]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>20</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>我们选择下标为 1, 4, 9 的元素。<code>1 * 4</code>, <code>1 * 9</code>, <code>4 * 9</code> 是完全平方数。</p>\n</div>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 <= n == nums.length <= 10<sup>4</sup></code></li>\n\t<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"Define <strong>P(x)</strong> as the product of primes <strong>p</strong> with odd exponents in <strong>x</strong>'s factorization. Examples: For <code>x = 18</code>, factorization <code>2<sup>1</sup> × 3<sup>2</sup></code>, <strong>P(18) = 2</strong>; for <code>x = 45</code>, factorization <code>3<sup>2</sup> × 5<sup>1</sup></code>, <strong>P(45) = 5</strong>; for <code>x = 50</code>, factorization <code>2<sup>1</sup> × 5<sup>2</sup></code>, <strong>P(50) = 2</strong>; for <code>x = 210</code>, factorization <code>2<sup>1</sup> × 3<sup>1</sup> × 5<sup>1</sup> × 7<sup>1</sup></code>, <strong>P(210) = 210</strong>.",
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