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3378. Count Connected Components in LCM Graph
Description
You are given an array of integers nums
of size n
and a positive integer threshold
.
There is a graph consisting of n
nodes with the ith
node having a value of nums[i]
. Two nodes i
and j
in the graph are connected via an undirected edge if lcm(nums[i], nums[j]) <= threshold
.
Return the number of connected components in this graph.
A connected component is a subgraph of a graph in which there exists a path between any two vertices, and no vertex of the subgraph shares an edge with a vertex outside of the subgraph.
The term lcm(a, b)
denotes the least common multiple of a
and b
.
Example 1:
Input: nums = [2,4,8,3,9], threshold = 5
Output: 4
Explanation:
The four connected components are (2, 4)
, (3)
, (8)
, (9)
.
Example 2:
Input: nums = [2,4,8,3,9,12], threshold = 10
Output: 2
Explanation:
The two connected components are (2, 3, 4, 8, 9)
, and (12)
.
Constraints:
1 <= nums.length <= 105
1 <= nums[i] <= 109
- All elements of
nums
are unique. 1 <= threshold <= 2 * 105