Trading Desk Cluster Connectivity and Communication Groups

An electronic trading floor at Two Sigma consists of $N$ automated quantitative trading desks numbered $0$ to $N - 1$. Some desks share direct private high-frequency communication links, while others communicate indirectly through intermediate desks.

Desk connectivity is represented as an $N \times N$ binary adjacency matrix is_connected where is_connected[i][j] == 1 indicates a direct bidirectional communication link between desk $i$ and desk $j$, and is_connected[i][j] == 0 indicates no direct link. Direct links are symmetric (is_connected[i][j] == is_connected[j][i]) and reflective (is_connected[i][i] == 1).

A trading cluster is a maximal connected component of trading desks where any desk in the cluster can communicate with any other desk in the cluster directly or indirectly.

Your Task

Implement the function count_trading_clusters(is_connected: list[list[int]]) -> int that returns the total number of disjoint, independent trading clusters operating on the floor.

Constraints

• $1 \le N \le 300$
• is_connected[i][j] is either $0$ or $1$.
• is_connected[i][i] == 1 for all $0 \le i < N$.
• is_connected[i][j] == is_connected[j][i] for all $i, j$.

Examples

is_connected = [
    [1, 1, 0],
    [1, 1, 0],
    [0, 0, 1]
]
# Desk 0 and 1 are connected. Desk 2 is isolated.
# Output: 2