mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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180 lines
23 KiB
JSON
180 lines
23 KiB
JSON
{
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"categoryTitle": "Algorithms",
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"boundTopicId": 632718,
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"title": "Count Pairs Of Nodes",
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"content": "<p>You are given an undirected graph defined by an integer <code>n</code>, the number of nodes, and a 2D integer array <code>edges</code>, the edges in the graph, where <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> indicates that there is an <strong>undirected</strong> edge between <code>u<sub>i</sub></code> and <code>v<sub>i</sub></code>. You are also given an integer array <code>queries</code>.</p>\n\n<p>Let <code>incident(a, b)</code> be defined as the <strong>number of edges</strong> that are connected to <strong>either</strong> node <code>a</code> or <code>b</code>.</p>\n\n<p>The answer to the <code>j<sup>th</sup></code> query is the <strong>number of pairs</strong> of nodes <code>(a, b)</code> that satisfy <strong>both</strong> of the following conditions:</p>\n\n<ul>\n\t<li><code>a < b</code></li>\n\t<li><code>incident(a, b) > queries[j]</code></li>\n</ul>\n\n<p>Return <em>an array </em><code>answers</code><em> such that </em><code>answers.length == queries.length</code><em> and </em><code>answers[j]</code><em> is the answer of the </em><code>j<sup>th</sup></code><em> query</em>.</p>\n\n<p>Note that there can be <strong>multiple edges</strong> between the same two nodes.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/08/winword_2021-06-08_00-58-39.png\" style=\"width: 529px; height: 305px;\" />\n<pre>\n<strong>Input:</strong> n = 4, edges = [[1,2],[2,4],[1,3],[2,3],[2,1]], queries = [2,3]\n<strong>Output:</strong> [6,5]\n<strong>Explanation:</strong> The calculations for incident(a, b) are shown in the table above.\nThe answers for each of the queries are as follows:\n- answers[0] = 6. All the pairs have an incident(a, b) value greater than 2.\n- answers[1] = 5. All the pairs except (3, 4) have an incident(a, b) value greater than 3.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5, edges = [[1,5],[1,5],[3,4],[2,5],[1,3],[5,1],[2,3],[2,5]], queries = [1,2,3,4,5]\n<strong>Output:</strong> [10,10,9,8,6]\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= n <= 2 * 10<sup>4</sup></code></li>\n\t<li><code>1 <= edges.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= u<sub>i</sub>, v<sub>i</sub> <= n</code></li>\n\t<li><code>u<sub>i </sub>!= v<sub>i</sub></code></li>\n\t<li><code>1 <= queries.length <= 20</code></li>\n\t<li><code>0 <= queries[j] < edges.length</code></li>\n</ul>\n",
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"translatedTitle": "统计点对的数目",
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"translatedContent": "<p>给你一个无向图，无向图由整数 <code>n</code> ，表示图中节点的数目，和 <code>edges</code> 组成，其中 <code>edges[i] = [u<sub>i</sub>, v<sub>i</sub>]</code> 表示 <code>u<sub>i</sub></code> 和 <code>v<sub>i</sub></code><sub> </sub>之间有一条无向边。同时给你一个代表查询的整数数组 <code>queries</code> 。</p>\n\n<p>第 <code>j</code> 个查询的答案是满足如下条件的点对 <code>(a, b)</code> 的数目：</p>\n\n<ul>\n\t<li><code>a < b</code></li>\n\t<li><code>cnt</code> 是与 <code>a</code> <strong>或者 </strong><code>b</code> 相连的边的数目，且 <code>cnt</code> <strong>严格大于 </strong><code>queries[j]</code> 。</li>\n</ul>\n\n<p>请你返回一个数组 <code>answers</code> ，其中 <code>answers.length == queries.length</code> 且 <code>answers[j]</code> 是第 <code>j</code> 个查询的答案。</p>\n\n<p>请注意，图中可能会有 <strong>重复边</strong> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://pic.leetcode-cn.com/1614828447-GMnLVg-image.png\" style=\"width: 310px; height: 278px;\" />\n<pre>\n<b>输入：</b>n = 4, edges = [[1,2],[2,4],[1,3],[2,3],[2,1]], queries = [2,3]\n<b>输出：</b>[6,5]\n<b>解释：</b>每个点对中，与至少一个点相连的边的数目如上图所示。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>n = 5, edges = [[1,5],[1,5],[3,4],[2,5],[1,3],[5,1],[2,3],[2,5]], queries = [1,2,3,4,5]\n<b>输出：</b>[10,10,9,8,6]\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 <= n <= 2 * 10<sup>4</sup></code></li>\n\t<li><code>1 <= edges.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= u<sub>i</sub>, v<sub>i</sub> <= n</code></li>\n\t<li><code>u<sub>i </sub>!= v<sub>i</sub></code></li>\n\t<li><code>1 <= queries.length <= 20</code></li>\n\t<li><code>0 <= queries[j] < edges.length</code></li>\n</ul>\n",
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"We want to count pairs (x,y) such that degree[x] + degree[y] - occurrences(x,y) > k",
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"Think about iterating on x, and counting the number of valid y to pair with x.",
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"You can consider at first that the (- occurrences(x,y)) isn't there, or it is 0 at first for all y. Count the valid y this way.",
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"Then you can iterate on the neighbors of x, let that neighbor be y, and update occurrences(x,y).",
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"When you update occurrences(x,y), the left-hand side decreases. Once it reaches k, then y is not valid for x anymore, so you should decrease the answer by 1."
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