Number of Connected Components in an Undirected Graph — LC Medium

323. Number of Connected Components in an Undirected Graph

You have a graph of n nodes. You are given an integer n and an array edges where edges[i] = [ai, bi] indicates that there is an edge between ai and bi in the graph.

Return the number of connected components in the graph.

Example 1:

Input: n = 5, edges = [[0,1],[1,2],[3,4]]
Output: 2

Example 2:

Input: n = 5, edges = [[0,1],[1,2],[2,3],[3,4]]
Output: 1

Constraints:

• 1 <= n <= 2000
• 1 <= edges.length <= 5000
• edges[i].length == 2
• 0 <= ai <= bi < n
• ai != bi
• There are no repeated edges.

class Solution:
    def countComponents(self, n: int, edges: List[List[int]]) -> int:
        self.root = [i for i in range(n)]
        for vertex1, vertex2 in edges:
            self.union(vertex1, vertex2)
        unique = set()
        for i in self.root:
            element = self.findRoot(i)
            unique.add(element)
        return len(unique)
        
    def findRoot(self, target: int) -> int:
        while target != self.root[target]:
            target = self.root[target]
        return target
    
    def union(self, vertex1: int, vertex2: int) -> None:
        root1 = self.findRoot(vertex1)
        root2 = self.findRoot(vertex2)
        
        if root1 != root2:
            self.root[root2] = root1