leetcode-problemset/leetcode-cn/originData/maximum-elegance-of-a-k-length-subsequence.json

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            "title": "Maximum Elegance of a K-Length Subsequence",
            "titleSlug": "maximum-elegance-of-a-k-length-subsequence",
            "content": "<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>\n\n<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>\n\n<p>Let&#39;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>\n\n<p>Your task is to find the <strong>maximum elegance</strong> from all subsequences of size <code>k</code> in <code>items</code>.</p>\n\n<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>\n\n<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&#39; relative order.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> items = [[3,2],[5,1],[10,1]], k = 2\n<strong>Output:</strong> 17\n<strong>Explanation: </strong>In this example, we have to select a subsequence of size 2.\nWe can select items[0] = [3,2] and items[2] = [10,1].\nThe total profit in this subsequence is 3 + 10 = 13, and the subsequence contains 2 distinct categories [2,1].\nHence, the elegance is 13 + 2<sup>2</sup> = 17, and we can show that it is the maximum achievable elegance. \n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> items = [[3,1],[3,1],[2,2],[5,3]], k = 3\n<strong>Output:</strong> 19\n<strong>Explanation:</strong> In this example, we have to select a subsequence of size 3. \nWe can select items[0] = [3,1], items[2] = [2,2], and items[3] = [5,3]. \nThe total profit in this subsequence is 3 + 2 + 5 = 10, and the subsequence contains 3 distinct categories [1,2,3]. \nHence, the elegance is 10 + 3<sup>2</sup> = 19, and we can show that it is the maximum achievable elegance.</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> items = [[1,1],[2,1],[3,1]], k = 3\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> In this example, we have to select a subsequence of size 3. \nWe should select all the items. \nThe total profit will be 1 + 2 + 3 = 6, and the subsequence contains 1 distinct category [1]. \nHence, the maximum elegance is 6 + 1<sup>2</sup> = 7.  </pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= items.length == n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>items[i].length == 2</code></li>\n\t<li><code>items[i][0] == profit<sub>i</sub></code></li>\n\t<li><code>items[i][1] == category<sub>i</sub></code></li>\n\t<li><code>1 &lt;= profit<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= category<sub>i</sub> &lt;= n </code></li>\n\t<li><code>1 &lt;= k &lt;= n</code></li>\n</ul>\n",
            "translatedTitle": "子序列最大优雅度",
            "translatedContent": "<p>给你一个长度为 <code>n</code> 的二维整数数组 <code>items</code> 和一个整数 <code>k</code> 。</p>\n\n<p><code>items[i] = [profit<sub>i</sub>, category<sub>i</sub>]</code>，其中 <code>profit<sub>i</sub></code> 和 <code>category<sub>i</sub></code> 分别表示第 <code>i</code> 个项目的利润和类别。</p>\n\n<p>现定义&nbsp;<code>items</code> 的 <strong>子序列</strong> 的 <strong>优雅度</strong> 可以用 <code>total_profit + distinct_categories<sup>2</sup></code> 计算，其中 <code>total_profit</code> 是子序列中所有项目的利润总和，<code>distinct_categories</code> 是所选子序列所含的所有类别中不同类别的数量。</p>\n\n<p>你的任务是从 <code>items</code> 所有长度为 <code>k</code> 的子序列中，找出 <strong>最大优雅度</strong> 。</p>\n\n<p>用整数形式表示并返回 <code>items</code> 中所有长度恰好为 <code>k</code> 的子序列的最大优雅度。</p>\n\n<p><strong>注意：</strong>数组的子序列是经由原数组删除一些元素（可能不删除）而产生的新数组，且删除不改变其余元素相对顺序。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>items = [[3,2],[5,1],[10,1]], k = 2\n<strong>输出：</strong>17\n<strong>解释：\n</strong>在这个例子中，我们需要选出长度为 2 的子序列。\n其中一种方案是 items[0] = [3,2] 和 items[2] = [10,1] 。\n子序列的总利润为 3 + 10 = 13 ，子序列包含 2 种不同类别 [2,1] 。\n因此，优雅度为 13 + 2<sup>2</sup> = 17 ，可以证明 17 是可以获得的最大优雅度。 \n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>items = [[3,1],[3,1],[2,2],[5,3]], k = 3\n<strong>输出：</strong>19\n<strong>解释：</strong>\n在这个例子中，我们需要选出长度为 3 的子序列。 \n其中一种方案是 items[0] = [3,1] ，items[2] = [2,2] 和 items[3] = [5,3] 。\n子序列的总利润为 3 + 2 + 5 = 10 ，子序列包含 3 种不同类别 [1, 2, 3] 。 \n因此，优雅度为 10 + 3<sup>2</sup> = 19 ，可以证明 19 是可以获得的最大优雅度。</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>items = [[1,1],[2,1],[3,1]], k = 3\n<strong>输出：</strong>7\n<strong>解释：\n</strong>在这个例子中，我们需要选出长度为 3 的子序列。\n我们需要选中所有项目。\n子序列的总利润为 1 + 2 + 3 = 6，子序列包含 1 种不同类别 [1] 。\n因此，最大优雅度为 6 + 1<sup>2</sup> = 7 。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= items.length == n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>items[i].length == 2</code></li>\n\t<li><code>items[i][0] == profit<sub>i</sub></code></li>\n\t<li><code>items[i][1] == category<sub>i</sub></code></li>\n\t<li><code>1 &lt;= profit<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= category<sub>i</sub> &lt;= n </code></li>\n\t<li><code>1 &lt;= k &lt;= n</code></li>\n</ul>\n",
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