{ "data": { "question": { "questionId": "1875", "questionFrontendId": "1766", "categoryTitle": "Algorithms", "boundTopicId": 607740, "title": "Tree of Coprimes", "titleSlug": "tree-of-coprimes", "content": "

There is a tree (i.e., a connected, undirected graph that has no cycles) consisting of n nodes numbered from 0 to n - 1 and exactly n - 1 edges. Each node has a value associated with it, and the root of the tree is node 0.

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To represent this tree, you are given an integer array nums and a 2D array edges. Each nums[i] represents the ith node's value, and each edges[j] = [uj, vj] represents an edge between nodes uj and vj in the tree.

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Two values x and y are coprime if gcd(x, y) == 1 where gcd(x, y) is the greatest common divisor of x and y.

\n\n

An ancestor of a node i is any other node on the shortest path from node i to the root. A node is not considered an ancestor of itself.

\n\n

Return an array ans of size n, where ans[i] is the closest ancestor to node i such that nums[i] and nums[ans[i]] are coprime, or -1 if there is no such ancestor.

\n\n

 

\n

Example 1:

\n\n

\"\"

\n\n
\nInput: nums = [2,3,3,2], edges = [[0,1],[1,2],[1,3]]\nOutput: [-1,0,0,1]\nExplanation: 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
\n\n

Example 2:

\n\n

\"\"

\n\n
\nInput: nums = [5,6,10,2,3,6,15], edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]\nOutput: [-1,0,-1,0,0,0,-1]\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "互质树", "translatedContent": "

给你一个 n 个节点的树（也就是一个无环连通无向图），节点编号从 0 到 n - 1 ，且恰好有 n - 1 条边，每个节点有一个值。树的 根节点 为 0 号点。

\n\n

给你一个整数数组 nums 和一个二维数组 edges 来表示这棵树。nums[i] 表示第 i 个点的值，edges[j] = [uj, vj] 表示节点 uj 和节点 vj 在树中有一条边。

\n\n

当 gcd(x, y) == 1 ，我们称两个数 x 和 y 是 互质的 ，其中 gcd(x, y) 是 x 和 y 的 最大公约数 。

\n\n

从节点 i 到 根 最短路径上的点都是节点 i 的祖先节点。一个节点 不是 它自己的祖先节点。

\n\n

请你返回一个大小为 n 的数组 ans ，其中 ans[i]是离节点 i 最近的祖先节点且满足 nums[i] 和 nums[ans[i]] 是 互质的 ，如果不存在这样的祖先节点，ans[i] 为 -1 。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：nums = [2,3,3,2], edges = [[0,1],[1,2],[1,3]]\n输出：[-1,0,0,1]\n解释：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
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：nums = [5,6,10,2,3,6,15], edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]\n输出：[-1,0,-1,0,0,0,-1]\n
\n\n

 

\n\n

提示：

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