Connected Groups (Friend Circles)

Problem Given an n × n binary relation matrix supplied as strings (related[i][j] = '1' means person i directly knows person j), and treating friendship as transitive, count the number of connected friend groups (circles).

Input / Output

• Input: a string array related of n rows, each n characters of '0'/'1'.
• Output: the number of friend groups.

Constraints

• n ≤ 300, so an O(n^2) scan of the matrix is fine.
• The relation is symmetric and transitive; related[i][i] = '1'.

Example

• ["110","110","001"] → 2 (persons 0 and 1 form one circle; person 2 is alone).