1766. Tree of Coprimes
https://leetcode.com/problems/tree-of-coprimes
Description
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 ith
node's value, and each edges[j] = [uj, vj]
represents an edge between nodes uj
and vj
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
1 <= n <= 105
edges.length == n - 1
edges[j].length == 2
0 <= uj, vj < n
uj != vj
ac
Last updated
Was this helpful?