Number of Provinces — LC Medium

547. Number of Provinces

There are n cities. Some of them are connected, while some are not. If city a is connected directly with city b, and city b is connected directly with city c, then city a is connected indirectly with city c.

A province is a group of directly or indirectly connected cities and no other cities outside of the group.

You are given an n x n matrix isConnected where isConnected[i][j] = 1 if the ith city and the jth city are directly connected, and isConnected[i][j] = 0 otherwise.

Return the total number of provinces.

Example 1:

Input: isConnected = [[1,1,0],[1,1,0],[0,0,1]]
Output: 2

Example 2:

Input: isConnected = [[1,0,0],[0,1,0],[0,0,1]]
Output: 3

Constraints:

• 1 <= n <= 200
• n == isConnected.length
• n == isConnected[i].length
• isConnected[i][j] is 1 or 0.
• isConnected[i][i] == 1
• isConnected[i][j] == isConnected[j][i]

class Solution:
    def findCircleNum(self, isConnected: List[List[int]]) -> int:
        # [0,1,2]
        self.root = [i for i in range(len(isConnected))]
        
        for rootIdx, guide in enumerate(isConnected):
            for idx, val in enumerate(guide):
                if val == 1:
                    self.union(rootIdx, idx)
        print(self.root)
        return len(set(self.root))
        
        
    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:
            for i in range(len(self.root)):
                if self.root[i] == root2:
                    self.root[i] = root1