# see the overview from 2026.07.31

sample_graph = {
    'Alice': set(['Bob', 'Carol']),
    'Bob': set(['Alice', 'Dave']),
    'Carol': set(['Alice', 'Eve', 'Mallory']),
    'Dave': set(['Frank', 'Eve', 'Bob']),
    'Eve': set(['Carol', 'Grace', 'Dave']),
    'Frank': set(['Dave', 'Heidi']),
    'Grace': set(['Eve', 'Ivan', 'Mallory']),
    'Heidi': set(['Frank', 'Ivan']),
    'Ivan': set(['Heidi', 'Grace']),
    'Mallory': set(['Carol', 'Grace'])
}

def nth_degree_connections(
    graph: dict[str, set[str]],
    starting_vertex: str,
    max_n: int
):
    # TODO
    pass

print(nth_degree_connections(sample_graph, 'Mallory', 2))
print(nth_degree_connections(sample_graph, 'Alice', 4))
print(nth_degree_connections(sample_graph, 'Ivan', 1))
print(nth_degree_connections(sample_graph, 'Grace', 0))
print(nth_degree_connections(sample_graph, 'Carol', 100))