DIY: Number of Provinces

Problem statement

Suppose there are n cities, where some are connected, while others are not. If a city c1 is connected to city c2, and city c2 is connected to city c3, then c1 is indirectly connected to c3.

A group of directly or indirectly connected cities, where no other city is part of this group, is called a province.

You are given a matrix, is_connected with a size of n x n. An entry is_connected[i][j] = 1 if the $i^{th}$ and $j^{th}$ cities are directly connected, and is_connected[i][j] = 0 otherwise. Note that is_connected[i][j] is either 1 or 0.

Your task is to return the total number of provinces.

Constrainsts

• 1 <= n <= 200
• n == is_connected.length
• n == is_connected[i].length
• is_connected[i][i] == 1
• is_connected[i][j] == is_connected[j][i]

Input

The input will be a list of lists representing a matrix. The following are examples of input to the function:

# Sample Input 1:
is_connected = [[1,1,0],[1,1,0],[0,0,1]]

# Sample Input 2:
is_connected = [[1,0,0],[0,1,0],[0,0,1]]

Output

The output will be an integer. The following are examples of the outputs:

# Sample Output 1:
2

# Sample Output 2:
3