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44 lines
2.4 KiB
HTML
44 lines
2.4 KiB
HTML
<p>You are given a <strong>1</strong><strong>-indexed</strong> array <code>nums</code> of <code>n</code> integers.</p>
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<p>A set of numbers is <strong>complete</strong> if the product of every pair of its elements is a perfect square.</p>
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<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>
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<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>
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<p>A perfect square is a number that can be expressed as the product of an integer by itself.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [8,7,3,5,7,2,4,9]
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<strong>Output:</strong> 16
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<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}.
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The sum of the elements corresponding to indices 1 and 4 is equal to nums[1] + nums[4] = 8 + 5 = 13.
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The sum of the elements corresponding to indices 2 and 8 is equal to nums[2] + nums[8] = 7 + 9 = 16.
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Hence, the maximum element-sum of a complete subset of indices is 16.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [5,10,3,10,1,13,7,9,4]
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<strong>Output:</strong> 19
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<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}.
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The sum of the elements corresponding to indices 1 and 4 is equal to nums[1] + nums[4] = 5 + 10 = 15.
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The sum of the elements corresponding to indices 1 and 9 is equal to nums[1] + nums[9] = 5 + 4 = 9.
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The sum of the elements corresponding to indices 2 and 8 is equal to nums[2] + nums[8] = 10 + 9 = 19.
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The sum of the elements corresponding to indices 4 and 9 is equal to nums[4] + nums[9] = 10 + 4 = 14.
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The sum of the elements corresponding to indices 1, 4, and 9 is equal to nums[1] + nums[4] + nums[9] = 5 + 10 + 4 = 19.
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Hence, the maximum element-sum of a complete subset of indices is 19.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= n == nums.length <= 10<sup>4</sup></code></li>
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<li><code>1 <= nums[i] <= 10<sup>9</sup></code></li>
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</ul>
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