Number of Provinces

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.

Examples

Example 1:

Input: isConnected = [[1,1,0],[1,1,0],[0,0,1]]
Output: 2
Explanation: Cities 0 and 1 are connected (province 1).
City 2 is alone (province 2).

Example 2:

Input: isConnected = [[1,0,0],[0,1,0],[0,0,1]]
Output: 3
Explanation: Each city is its own province.

Example 3:

Input: isConnected = [[1,1,1],[1,1,1],[1,1,1]]
Output: 1
Explanation: All cities are connected, one province.

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]

Expected Complexity

• Time: O(n^2)
• Space: O(n)