Count Connected Friend Groups

Problem Statement

You are given an n x n binary matrix is_connected, where n represents the total number of people in a social network. The people are indexed from 0 to n - 1.

is_connected[i][j] = 1 if person i and person j are direct friends, and 0 otherwise. Friendship is mutually symmetric, meaning if person i is friends with person j, then person j is also friends with person i. Friendship is also transitive: if person A is friends with person B, and person B is friends with person C, then A, B, and C all belong to the same friend group.

Return the total number of distinct friend groups in the network.

Your function must treat the input matrix as read-only and avoid mutating it.

Function Signature

def count_friend_groups(is_connected: list[list[int]]) -> int:
    pass

Input & Output Format

• Input: is_connected: A list of lists of integers representing an n x n symmetric adjacency matrix.
• Output: An integer representing the count of connected components.

Constraints

• 1 <= n <= 200, where n == len(is_connected) == len(is_connected[i])
• is_connected[i][j] is either 0 or 1
• is_connected[i][i] == 1 for all 0 <= i < n
• is_connected[i][j] == is_connected[j][i] for all 0 <= i, j < n

Examples

Example 1

Input:
is_connected = [
  [1, 1, 0],
  [1, 1, 0],
  [0, 0, 1]
]
Output: 2
Explanation: 
Person 0 and Person 1 are friends, forming group 1.
Person 2 has no other friends and forms group 2 on their own.
Total groups = 2.

Example 2

Input:
is_connected = [
  [1, 0, 0, 1],
  [0, 1, 1, 0],
  [0, 1, 1, 0],
  [1, 0, 0, 1]
]
Output: 2
Explanation:
Person 0 and Person 3 are friends (group 1).
Person 1 and Person 2 are friends (group 2).
Total groups = 2.

Edge Cases to Consider

• n = 1: A single isolated person should return 1.
• Completely disconnected network (is_connected[i][j] == 0 for all i != j): Should return n.
• Fully connected network (all entries are 1): Should return 1.