Count Connected Components in LCM Graph
You are given an array of integers nums of size n and a positive integer threshold.
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 <= 10^5
- 1 <= nums[i] <= 10^9
- All elements of nums are unique.
- 1 <= threshold <= 2 * 10^5
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