Number of Provinces

Medium~20 min

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 to each other, forming one province. City 2 is on its own, forming another province. Total: 2 provinces.

Example 2

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

Output: 3

Explanation: No cities are connected to each other. Each city is its own province. Total: 3 provinces.

Example 3

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

Output: 1

Explanation: City 0 is connected to city 1, and city 1 is connected to city 2. All cities are in 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]

Code

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Output

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