mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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195 lines
19 KiB
JSON
195 lines
19 KiB
JSON
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"title": "Maximum Elegance of a K-Length Subsequence",
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"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'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' relative order.</p>\n\n<p> </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> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= items.length == n <= 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 <= profit<sub>i</sub> <= 10<sup>9</sup></code></li>\n\t<li><code>1 <= category<sub>i</sub> <= n </code></li>\n\t<li><code>1 <= k <= n</code></li>\n</ul>\n",
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"<div class=\"_1l1MA\">Greedy algorithm.</div>",
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"<div class=\"_1l1MA\">Sort items in non-increasing order of profits.</div>",
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"<div class=\"_1l1MA\">Select the first <code>k</code> items (the top <code>k</code> most profitable items). Keep track of the items as the candidate set.</div>",
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"<div class=\"_1l1MA\">For the remaining <code>n - k</code> items sorted in non-increasing order of profits, try replacing an item in the candidate set using the current item.</div>",
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"<div class=\"_1l1MA\">The replacing item should add a new category to the candidate set and should remove the item with the minimum profit that occurs more than once in the candidate set.</div>"
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