Sponsored
Sponsored
This approach leverages the union-find data structure to connect numbers that share common prime factors. Each number is represented as a node, and we create edges between numbers that have a common prime factor. The largest connected component is determined by finding the maximum size of the connected components formed.
The steps are:
Time Complexity: O(N * sqrt(M)), where N is the number of elements in nums and M is the maximum element value, due to factorization. Space Complexity: O(N + M) for the union-find structure and auxiliary space.
1from collections import defaultdict
2import math
3
4class UnionFind:
5 def __init__(self, n):
6 self.parent = list
The solution uses a union-find data structure to represent connected components. Each number in the array has its factorization computed, and numbers sharing a factor are connected. By the end, the size of the largest component is computed by counting the results of the find operation on the union-find structure.
This graph-based approach builds an adjacency list to represent the graph, then uses BFS or DFS to explore connected components. Each connection is identified by the shared factors between the nodes. The largest connected component's size indicates the solution.
The steps are:
Time Complexity: O(N * sqrt(M)), where N is the number of elements in nums and M is each element's largest value. Space Complexity: O(N + M) for storing adjacency lists and visited sets.
The Python solution constructs an adjacency list using numbers and their factors. A BFS is used to find and measure components in the graph, and the maximum size of these components is returned as the answer.