mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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189 lines
25 KiB
JSON
189 lines
25 KiB
JSON
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"title": "Tree of Coprimes",
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"content": "<p>There is a tree (i.e., a connected, undirected graph that has no cycles) consisting of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code> and exactly <code>n - 1</code> edges. Each node has a value associated with it, and the <strong>root</strong> of the tree is node <code>0</code>.</p>\n\n<p>To represent this tree, you are given an integer array <code>nums</code> and a 2D array <code>edges</code>. Each <code>nums[i]</code> represents the <code>i<sup>th</sup></code> node's value, and each <code>edges[j] = [u<sub>j</sub>, v<sub>j</sub>]</code> represents an edge between nodes <code>u<sub>j</sub></code> and <code>v<sub>j</sub></code> in the tree.</p>\n\n<p>Two values <code>x</code> and <code>y</code> are <strong>coprime</strong> if <code>gcd(x, y) == 1</code> where <code>gcd(x, y)</code> is the <strong>greatest common divisor</strong> of <code>x</code> and <code>y</code>.</p>\n\n<p>An ancestor of a node <code>i</code> is any other node on the shortest path from node <code>i</code> to the <strong>root</strong>. A node is <strong>not </strong>considered an ancestor of itself.</p>\n\n<p>Return <em>an array </em><code>ans</code><em> of size </em><code>n</code>, <em>where </em><code>ans[i]</code><em> is the closest ancestor to node </em><code>i</code><em> such that </em><code>nums[i]</code> <em>and </em><code>nums[ans[i]]</code> are <strong>coprime</strong>, or <code>-1</code><em> if there is no such ancestor</em>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/01/06/untitled-diagram.png\" style=\"width: 191px; height: 281px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [2,3,3,2], edges = [[0,1],[1,2],[1,3]]\n<strong>Output:</strong> [-1,0,0,1]\n<strong>Explanation:</strong> In the above figure, each node's value is in parentheses.\n- Node 0 has no coprime ancestors.\n- Node 1 has only one ancestor, node 0. Their values are coprime (gcd(2,3) == 1).\n- Node 2 has two ancestors, nodes 1 and 0. Node 1's value is not coprime (gcd(3,3) == 3), but node 0's\n value is (gcd(2,3) == 1), so node 0 is the closest valid ancestor.\n- Node 3 has two ancestors, nodes 1 and 0. It is coprime with node 1 (gcd(3,2) == 1), so node 1 is its\n closest valid ancestor.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/01/06/untitled-diagram1.png\" style=\"width: 441px; height: 291px;\" /></p>\n\n<pre>\n<strong>Input:</strong> nums = [5,6,10,2,3,6,15], edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]\n<strong>Output:</strong> [-1,0,-1,0,0,0,-1]\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>nums.length == n</code></li>\n\t<li><code>1 <= nums[i] <= 50</code></li>\n\t<li><code>1 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>edges[j].length == 2</code></li>\n\t<li><code>0 <= u<sub>j</sub>, v<sub>j</sub> < n</code></li>\n\t<li><code>u<sub>j</sub> != v<sub>j</sub></code></li>\n</ul>\n",
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"translatedTitle": "互质树",
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"translatedContent": "<p>给你一个 <code>n</code> 个节点的树（也就是一个无环连通无向图），节点编号从 <code>0</code> 到 <code>n - 1</code> ，且恰好有 <code>n - 1</code> 条边，每个节点有一个值。树的 <strong>根节点</strong> 为 0 号点。</p>\n\n<p>给你一个整数数组 <code>nums</code> 和一个二维数组 <code>edges</code> 来表示这棵树。<code>nums[i]</code> 表示第 <code>i</code> 个点的值，<code>edges[j] = [u<sub>j</sub>, v<sub>j</sub>]</code> 表示节点 <code>u<sub>j</sub></code> 和节点 <code>v<sub>j</sub></code> 在树中有一条边。</p>\n\n<p>当 <code>gcd(x, y) == 1</code> ，我们称两个数 <code>x</code> 和 <code>y</code> 是 <strong>互质的</strong> ，其中 <code>gcd(x, y)</code> 是 <code>x</code> 和 <code>y</code> 的 <strong>最大公约数</strong> 。</p>\n\n<p>从节点 <code>i</code> 到 <strong>根</strong> 最短路径上的点都是节点 <code>i</code> 的祖先节点。一个节点 <strong>不是</strong> 它自己的祖先节点。</p>\n\n<p>请你返回一个大小为 <code>n</code> 的数组 <code>ans</code> ，其中<em> </em><code>ans[i]</code>是离节点 <code>i</code> 最近的祖先节点且满足<em> </em><code>nums[i]</code> 和<em> </em><code>nums[ans[i]]</code> 是 <strong>互质的</strong> ，如果不存在这样的祖先节点，<code>ans[i]</code> 为 <code>-1</code> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2021/02/20/untitled-diagram.png\" style=\"width: 191px; height: 281px;\" /></strong></p>\n\n<pre>\n<b>输入：</b>nums = [2,3,3,2], edges = [[0,1],[1,2],[1,3]]\n<b>输出：</b>[-1,0,0,1]\n<b>解释：</b>上图中，每个节点的值在括号中表示。\n- 节点 0 没有互质祖先。\n- 节点 1 只有一个祖先节点 0 。它们的值是互质的（gcd(2,3) == 1）。\n- 节点 2 有两个祖先节点，分别是节点 1 和节点 0 。节点 1 的值与它的值不是互质的（gcd(3,3) == 3）但节点 0 的值是互质的(gcd(2,3) == 1)，所以节点 0 是最近的符合要求的祖先节点。\n- 节点 3 有两个祖先节点，分别是节点 1 和节点 0 。它与节点 1 互质（gcd(3,2) == 1），所以节点 1 是离它最近的符合要求的祖先节点。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2021/02/20/untitled-diagram1.png\" style=\"width: 441px; height: 291px;\" /></p>\n\n<pre>\n<strong>输入：</strong>nums = [5,6,10,2,3,6,15], edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]\n<b>输出：</b>[-1,0,-1,0,0,0,-1]\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>nums.length == n</code></li>\n\t<li><code>1 <= nums[i] <= 50</code></li>\n\t<li><code>1 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>edges.length == n - 1</code></li>\n\t<li><code>edges[j].length == 2</code></li>\n\t<li><code>0 <= u<sub>j</sub>, v<sub>j</sub> < n</code></li>\n\t<li><code>u<sub>j</sub> != v<sub>j</sub></code></li>\n</ul>\n",
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