1766 - Tree of Coprimes.

Hard

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.

To represent this tree, you are given an integer array nums and a 2D array edges. Each nums[i] represents the <code>i^th</code> node's value, and each <code>edgesj = u_j, v_j</code> represents an edge between nodes <code>u_j</code> and <code>v_j</code> in the tree.

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.

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.

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.

Example 1:

Input: nums = 2,3,3,2, edges = [0,1,1,2,1,3]

Output: -1,0,0,1

Explanation: In the above figure, each node's value is in parentheses.

• Node 0 has no coprime ancestors.

• Node 1 has only one ancestor, node 0. Their values are coprime (gcd(2,3) == 1). - Node 2 has two ancestors, nodes 1 and 0. Node 1's value is not coprime (gcd(3,3) == 3), but node 0's value is (gcd(2,3) == 1), so node 0 is the closest valid ancestor.

• Node 3 has two ancestors, nodes 1 and 0. It is coprime with node 1 (gcd(3,2) == 1), so node 1 is its closest valid ancestor.

Example 2:

Input: nums = 5,6,10,2,3,6,15, edges = [0,1,0,2,1,3,1,4,2,5,2,6]

Output: -1,0,-1,0,0,0,-1

Constraints:

• nums.length == n

• 1 <= nums[i] <= 50

• <code>1 <= n <= 10⁵</code>

• edges.length == n - 1

• edges[j].length == 2

• <code>0 <= u_j, v_j< n</code>

• <code>u_j != v_j</code>