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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

Solutions

Solution 1

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