"""
323. Number of Connected Components in an Undirected Graph
Difficulty: Medium
https://leetcode.com/problems/number-of-connected-components-in-an-undirected-graph/

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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] = [ai, bi]

        • ai != bi

        • There are no repeated edges.
"""


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