AlgoLounge

Number of Provinces

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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 i^(th) city and the j^(th) city are directly connected, and isConnected[i][j] = 0 otherwise.

Return the total number of provinces.

Examples

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]
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List of test cases (10)
Case 1
isConnected = [[1,1,0],[1,1,0],[0,0,1]]
Case 2
isConnected = [[1,0,0],[0,1,0],[0,0,1]]
Case 3
isConnected = [[1]]
Case 4
isConnected = [[1,1,1,1],[1,1,1,1],[1,1,1,1],[1,1,1,1]]
Case 5
isConnected = [[1,1,0,0],[1,1,1,0],[0,1,1,1],[0,0,1,1]]
Case 6
isConnected = [[1,1,0,0],[1,1,0,0],[0,0,1,1],[0,0,1,1]]
Case 7
isConnected = [[1,0,0,0,0],[0,1,1,0,0],[0,1,1,0,0],[0,0,0,1,0],[0,0,0,0,1]]
Case 8
isConnected = [[1,1,1,1,1],[1,1,0,0,0],[1,0,1,0,0],[1,0,0,1,0],[1,0,0,0,1]]
Case 9
isConnected = [[1,1,1,0,0,0],[1,1,0,0,0,0],[1,0,1,0,0,0],[0,0,0,1,1,1],[0,0,0,1,1,0],[0,0,0,1,0,1]]
Case 10
isConnected = [[1,1,0,0,0,0,0,0],[1,1,1,0,0,0,0,0],[0,1,1,0,0,0,0,0],[0,0,0,1,1,0,0,0],[0,0,0,1,1,1,0,0],[0,0,0,0,1,1,0,0],[0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,1]]