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57 lines
3.2 KiB
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<p>You are given a <strong>0-indexed</strong> 2D integer array <code>items</code> of length <code>n</code> and an integer <code>k</code>.</p>
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<p><code>items[i] = [profit<sub>i</sub>, category<sub>i</sub>]</code>, where <code>profit<sub>i</sub></code> and <code>category<sub>i</sub></code> denote the profit and category of the <code>i<sup>th</sup></code> item respectively.</p>
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<p>Let's define the <strong>elegance</strong> of a <strong>subsequence</strong> of <code>items</code> as <code>total_profit + distinct_categories<sup>2</sup></code>, where <code>total_profit</code> is the sum of all profits in the subsequence, and <code>distinct_categories</code> is the number of <strong>distinct</strong> categories from all the categories in the selected subsequence.</p>
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<p>Your task is to find the <strong>maximum elegance</strong> from all subsequences of size <code>k</code> in <code>items</code>.</p>
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<p>Return <em>an integer denoting the maximum elegance of a subsequence of </em><code>items</code><em> with size exactly </em><code>k</code>.</p>
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<p><strong>Note:</strong> A subsequence of an array is a new array generated from the original array by deleting some elements (possibly none) without changing the remaining elements' relative order.</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> items = [[3,2],[5,1],[10,1]], k = 2
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<strong>Output:</strong> 17
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<strong>Explanation: </strong>In this example, we have to select a subsequence of size 2.
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We can select items[0] = [3,2] and items[2] = [10,1].
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The total profit in this subsequence is 3 + 10 = 13, and the subsequence contains 2 distinct categories [2,1].
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Hence, the elegance is 13 + 2<sup>2</sup> = 17, and we can show that it is the maximum achievable elegance.
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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> items = [[3,1],[3,1],[2,2],[5,3]], k = 3
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<strong>Output:</strong> 19
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<strong>Explanation:</strong> In this example, we have to select a subsequence of size 3.
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We can select items[0] = [3,1], items[2] = [2,2], and items[3] = [5,3].
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The total profit in this subsequence is 3 + 2 + 5 = 10, and the subsequence contains 3 distinct categories [1,2,3].
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Hence, the elegance is 10 + 3<sup>2</sup> = 19, and we can show that it is the maximum achievable elegance.</pre>
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<p><strong class="example">Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> items = [[1,1],[2,1],[3,1]], k = 3
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<strong>Output:</strong> 7
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<strong>Explanation:</strong> In this example, we have to select a subsequence of size 3.
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We should select all the items.
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The total profit will be 1 + 2 + 3 = 6, and the subsequence contains 1 distinct category [1].
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Hence, the maximum elegance is 6 + 1<sup>2</sup> = 7. </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 <= items.length == n <= 10<sup>5</sup></code></li>
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<li><code>items[i].length == 2</code></li>
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<li><code>items[i][0] == profit<sub>i</sub></code></li>
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<li><code>items[i][1] == category<sub>i</sub></code></li>
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<li><code>1 <= profit<sub>i</sub> <= 10<sup>9</sup></code></li>
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<li><code>1 <= category<sub>i</sub> <= n </code></li>
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<li><code>1 <= k <= n</code></li>
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</ul>
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