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 i^th city and the j^th 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
2Cities 0 and 1 are connected to each other, while city 2 forms its own province, so there are 2 provinces.
Example 2
Input
isConnected = [[1,0,0],[0,1,0],[0,0,1]]Output
3No two different cities are connected, so each of the 3 cities forms its own 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]