def topological_sort_kahn(graph: Graph) -> list:
"""
Ex 22.4-5. If return list is shorter than graph vertex length, it means the topological sort cannot be performed.
O(V + E) time.
"""
in_degrees = {}
ret = []
for v_key in graph.vertex_keys():
in_degrees[v_key] = 0
for u_key in graph.vertex_keys():
for v_key, _ in graph.get_vertex(u_key).successors():
in_degrees[v_key] += 1
zero_in_degree_set = deque()
for v_key in graph.vertex_keys():
if in_degrees[v_key] == 0:
zero_in_degree_set.append(v_key)
while zero_in_degree_set:
u_key = zero_in_degree_set.popleft()
ret.append(u_key)
for v_key, _ in list(graph.get_vertex(u_key).successors()):
graph.remove_edge(u_key, v_key)
in_degrees[v_key] -= 1
if in_degrees[v_key] == 0:
zero_in_degree_set.append(v_key)
return ret
def _euler(graph: Graph, path: list, src_index: int) -> Tuple[list, int]:
src_key = path[src_index]
src = graph.get_vertex(src_key)
u = src
sub_path = [src_key]
while u.successor_len > 0:
v = None
for v_key, _ in u.successors():
v = graph.get_vertex(v_key)
break
graph.remove_edge(u.key, v.key)
graph.remove_edge(v.key, u.key)
sub_path.append(v.key)
u = v
i = 1
while i < len(sub_path):
sub_path, delta_len = _euler(graph, sub_path, i)
i += delta_len
path = path[0:src_index] + sub_path + path[src_index + 1:]
return path, len(sub_path)