LeetCode 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.

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


  • 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]


Conduct depth-first search to find number of provinces.

Python Solution

class Solution:
    def findCircleNum(self, isConnected: List[List[int]]) -> int:
        count = 0
        visited = set()
        for i in range(len(isConnected)):
            if i not in visited:
                self.dfs_helper(isConnected, i, visited)                
                count += 1
        return count    
    def dfs_helper(self, isConnected, vertice, visited):
        for j in range(len(isConnected[vertice])):
            if isConnected[vertice][j] == 0:
            if j not in visited:
                self.dfs_helper(isConnected, j, visited)

  • Time Complexity: O(N).
  • Space Complexity: O(N).

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