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

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] = [ai, bi]
• ai != bi
• There are no repeated edges.

Solution

class Solution:
    def countComponents(self, n: int, edges: list[list[int]]) -> int:
        par = [i for i in range(n + 1)]
        rank = [1] * (n + 1)

        def find(n):
            res = n
            while res != par[res]:
                par[res] = par[par[res]]
                res = par[res]
            return res

        def union(n1, n2):
            p1, p2 = find(n1), find(n2)
            if p1 == p2:
                return 0
            if rank[p1] > rank[p2]:
                par[p2] = p1
                rank[p1] += rank[p2]
            else:
                par[p1] = p2
                rank[p2] += rank[p1]
            return 1

        res = n
        for n1, n2 in edges:
            res -= union(n1, n2)
        return res