leetcode-problemset/leetcode-cn/originData/maximum-star-sum-of-a-graph.json

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            "title": "Maximum Star Sum of a Graph",
            "titleSlug": "maximum-star-sum-of-a-graph",
            "content": "<p>There is an undirected graph consisting of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code>. You are given a <strong>0-indexed</strong> integer array <code>vals</code> of length <code>n</code> where <code>vals[i]</code> denotes the value of the <code>i<sup>th</sup></code> node.</p>\n\n<p>You are also given a 2D integer array <code>edges</code> where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> denotes that there exists an <strong>undirected</strong> edge connecting nodes <code>a<sub>i</sub></code> and <code>b<sub>i.</sub></code></p>\n\n<p>A <strong>star graph</strong> is a subgraph of the given graph having a center node containing <code>0</code> or more neighbors. In other words, it is a subset of edges of the given graph such that there exists a common node for all edges.</p>\n\n<p>The image below shows star graphs with <code>3</code> and <code>4</code> neighbors respectively, centered at the blue node.</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/11/07/max-star-sum-descdrawio.png\" style=\"width: 400px; height: 179px;\" />\n<p>The <strong>star sum</strong> is the sum of the values of all the nodes present in the star graph.</p>\n\n<p>Given an integer <code>k</code>, return <em>the <strong>maximum star sum</strong> of a star graph containing <strong>at most</strong> </em><code>k</code><em> edges.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/11/07/max-star-sum-example1drawio.png\" style=\"width: 300px; height: 291px;\" />\n<pre>\n<strong>Input:</strong> vals = [1,2,3,4,10,-10,-20], edges = [[0,1],[1,2],[1,3],[3,4],[3,5],[3,6]], k = 2\n<strong>Output:</strong> 16\n<strong>Explanation:</strong> The above diagram represents the input graph.\nThe star graph with the maximum star sum is denoted by blue. It is centered at 3 and includes its neighbors 1 and 4.\nIt can be shown it is not possible to get a star graph with a sum greater than 16.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> vals = [-5], edges = [], k = 0\n<strong>Output:</strong> -5\n<strong>Explanation:</strong> There is only one possible star graph, which is node 0 itself.\nHence, we return -5.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == vals.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>4</sup> &lt;= vals[i] &lt;= 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= edges.length &lt;= min(n * (n - 1) / 2</code><code>, 10<sup>5</sup>)</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n - 1</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>0 &lt;= k &lt;= n - 1</code></li>\n</ul>\n",
            "translatedTitle": "图中最大星和",
            "translatedContent": "<p>给你一个&nbsp;<code>n</code>&nbsp;个点的无向图，节点从&nbsp;<code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;编号。给你一个长度为 <code>n</code>&nbsp;下标从&nbsp;<strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>vals</code>&nbsp;，其中&nbsp;<code>vals[i]</code>&nbsp;表示第&nbsp;<code>i</code>&nbsp;个节点的值。</p>\n\n<p>同时给你一个二维整数数组&nbsp;<code>edges</code>&nbsp;，其中&nbsp;<code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code>&nbsp;表示节点&nbsp;<code>a<sub>i</sub></code> 和&nbsp;<code>b<sub>i</sub></code>&nbsp;之间有一条双向边。</p>\n\n<p><strong>星图</strong>&nbsp;是给定图中的一个子图，它包含一个中心节点和&nbsp;<code>0</code>&nbsp;个或更多个邻居。换言之，星图是给定图中一个边的子集，且这些边都有一个公共节点。</p>\n\n<p>下图分别展示了有 <code>3</code>&nbsp;个和 <code>4</code>&nbsp;个邻居的星图，蓝色节点为中心节点。</p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/11/07/max-star-sum-descdrawio.png\" style=\"width: 400px; height: 179px;\"></p>\n\n<p><strong>星和</strong> 定义为星图中所有节点值的和。</p>\n\n<p>给你一个整数&nbsp;<code>k</code>&nbsp;，请你返回 <strong>至多</strong>&nbsp;包含 <code>k</code>&nbsp;条边的星图中的 <strong>最大星和</strong>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/11/07/max-star-sum-example1drawio.png\" style=\"width: 300px; height: 291px;\"></p>\n\n<pre><b>输入：</b>vals = [1,2,3,4,10,-10,-20], edges = [[0,1],[1,2],[1,3],[3,4],[3,5],[3,6]], k = 2\n<b>输出：</b>16\n<b>解释：</b>上图展示了输入示例。\n最大星和对应的星图在上图中用蓝色标出。中心节点是 3 ，星图中还包含邻居 1 和 4 。\n无法得到一个和大于 16 且边数不超过 2 的星图。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>vals = [-5], edges = [], k = 0\n<b>输出：</b>-5\n<b>解释：</b>只有一个星图，就是节点 0 自己。\n所以我们返回 -5 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == vals.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>4</sup> &lt;= vals[i] &lt;= 10<sup>4</sup></code></li>\n\t<li><code>0 &lt;= edges.length &lt;= min(n * (n - 1) / 2</code><code>, 10<sup>5</sup>)</code></li>\n\t<li><code>edges[i].length == 2</code></li>\n\t<li><code>0 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n - 1</code></li>\n\t<li><code>a<sub>i</sub> != b<sub>i</sub></code></li>\n\t<li><code>0 &lt;= k &lt;= n - 1</code></li>\n</ul>\n",
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href=\\\"https:\\/\\/github.com\\/emirpasic\\/gods\\/tree\\/v1.18.1\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.10<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap 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