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 get_transpose(graph: Graph):
"""Ex 22.1-3."""
tr = Graph()
for v in graph.vertex_keys():
tr.add_vertex(Vertex(v))
for u in graph.vertex_keys():
for v, weight in graph.get_vertex(u).successors():
tr.add_edge(v, u, weight)
return tr
def graph_to_adj_matrix(graph: Graph):
vertex_count = graph.vertex_len
adj_matrix = [([0] * vertex_count) for _ in range(vertex_count)]
for u in graph.vertex_keys():
for v, _ in graph.get_vertex(u).successors():
adj_matrix[u][v] = 1
return adj_matrix
def scc_tarjan(graph: Graph) -> List[List]:
sccs = []
cache = TarjanCache()
time = TimeCounter()
for v_key in graph.vertex_keys():
if v_key not in cache.discover_times:
_tarjan_internal(graph, v_key, sccs, cache, time)
return sccs
def euler_tour_undirected(graph: Graph) -> list:
ret = []
if graph.vertex_len == 0:
return ret
for v_key in graph.vertex_keys():
ret.append(v_key)
break
ret, _ = _euler(graph, ret, 0)
return ret
def bfs(graph: Graph, visit_func: Callable[[Any], bool]=None) -> Tuple[dict, dict]:
open_set = deque()
came_from = {}
depths = {}
visited = set() # Gray or black nodes
if not visit_func:
def visit_func(_): return True
for v in graph.vertex_keys():
if v in visited:
continue
_bfs_internal(graph, v, visit_func, open_set, came_from, depths, visited)
return came_from, depths
def dfs(graph: Graph, pre_visit_func: Callable[[Any], bool]=None, post_visit_func: Callable[[Any], bool]=None)\
-> DFSResult:
"""Ex. 22.3-7"""
if not pre_visit_func:
def pre_visit_func(_):
return True
if not post_visit_func:
def post_visit_func(_):
return True
result = DFSResult()
time = TimeCounter()
for v in graph.vertex_keys():
if v not in result.discover_times and not dfs_internal(
graph, v, pre_visit_func, post_visit_func, result, time):
break
return result