Twitter Online Assessment (OA) 2021 | Social Network

In a social media website (which is probably Twitter, if you are wondering), there are a total of n users. Each user can follow any number of other users. Let f be a matrix of relationship between these users, where f[i][j] is either 0 or 1. A 1 indicates that person i (starting from 0) is following person j, while 0 means otherwise.

In this question, we assume that each person is following themselves, and following is symmetrical. That is, if i follows j, then j follows i. We can then define a "group" of people. A "group" of people are people that follow each other, either directly or indirectly. For example, if user 0 follows user 1, and user 1 follows user 2, user 0 follows 2 indirectly.

Question: How many groups are among these n people?

Parameter

f: An integer matrix representing the relationship matrix between the users.

Result

An integer representing the number of groups among these people.

Examples

Example 1:

Input:

f = [
    [1, 1, 0],
    [1, 1, 0],
    [0, 0, 1],
]

Output: 2

Explanation: There are 2 groups: User 0, 1 and user 2. User 0 and 1 are in a group because they follow each other.

Constraints

1 <= n <= 300