"""

Checks the given DAG for cycles and returns nodes that are part of a cycle.

:param node_successors: A dictionary where keys are node names and values are lists of successor node names.

:return: A tuple (has_cycle, faulty_nodes) where has_cycle is a boolean indicating whether a cycle was found and

faulty_nodes is a list of nodes that are part of the cycle.

"""

# Step 1: Calculate in-degree (number of incoming edges) for each node

in_degree = dict.fromkeys(node_successors.keys(), 0)

for successors in node_successors.values():

for successor in successors:

in_degree[successor] += 1

# Step 2: Initialize a queue with all nodes that have in-degree 0

queue = collections.deque([node for node in node_successors.keys() if in_degree[node] == 0])

# Number of processed nodes

processed_count = 0

# Step 3: Process nodes with in-degree 0

while queue:

current_node = queue.popleft()

processed_count += 1

# Decrease the in-degree of each successor by 1

for successor in node_successors[current_node]:

in_degree[successor] -= 1

# If in-degree becomes 0, add it to the queue

if in_degree[successor] == 0:

queue.append(successor)

# Step 4: Identify the faulty nodes (those still with in-degree > 0)

faulty_nodes = [node for node in node_successors.keys() if in_degree[node] > 0]

# If there are faulty nodes, there's a cycle

if faulty_nodes:

return True, faulty_nodes

else: