[('A', 'B'),('C', 'D'),('D', 'C'),('C', 'D')]
のような入力があります。この辺のリストで表される有向グラフにサイクルが存在するかどうかを調べたい。
私はディスカッションを読みます: https://www.geeksforgeeks.org/detect-cycle-in-a-graph/ ですが、次の場合にはいくつかのエラーがあります:
g = Graph(3)
g.addEdge('A', 'B')
g.addEdge('B', 'C')
g.addEdge('C', 'A')
その結果は「グラフに周期がない」です。これは明らかに間違っています。この問題の解決を手伝ってくれませんか?
私自身の実装(再帰的ではないため、サイクル長の制限なし):
from collections import defaultdict
def has_cycle(graph):
try:
next(_iter_cycles(graph))
except StopIteration:
return False
return True
def _iter_cycles(edges):
"""Iterate over simple cycles in the directed graph."""
if isinstance(edges, dict):
graph = edges
else:
graph = defaultdict(set)
for x, y in edges:
graph[x].add(y)
SEP = object()
checked_nodes = set() # already checked nodes
for start_node in graph:
if start_node in checked_nodes:
continue
nodes_left = [start_node]
path = [] # current path from start_node
node_idx = {} # {node: path.index(node)}
while nodes_left:
node = nodes_left.pop()
if node is SEP:
checked_node = path.pop()
del node_idx[checked_node]
checked_nodes.add(checked_node)
continue
if node in checked_nodes:
continue
if node in node_idx:
cycle_path = path[node_idx[node]:]
cycle_path.append(node)
yield cycle_path
continue
next_nodes = graph.get(node)
if not next_nodes:
checked_nodes.add(node)
continue
node_idx[node] = len(path)
path.append(node)
nodes_left.append(SEP)
nodes_left.extend(next_nodes)
assert not has_cycle({0: [1, 2], 1: [3, 4], 5: [6, 7]})
assert has_cycle([(0, 1), (1, 0), (1, 2), (2, 1)])
def assert_cycles(graph, expected):
detected = sorted(_iter_cycles(graph))
if detected != expected:
raise Exception('expected cycles:\n{}\ndetected cycles:\n{}'.format(expected, detected))
assert_cycles([('A', 'B'),('C', 'D'),('D', 'C'),('C', 'D')], [['C', 'D', 'C']])
assert_cycles([('A', 'B'),('B', 'A'),('B', 'C'),('C', 'B')], [['A', 'B', 'A'], ['B', 'C', 'B']])
assert_cycles({1: [2, 3], 2: [3, 4]}, [])
assert_cycles([(1, 2), (1, 3), (2, 3), (2, 4)], [])
assert_cycles({1: [2, 4], 2: [3, 4], 3: [1]}, [[1, 2, 3, 1]])
assert_cycles([(1, 2), (1, 4), (2, 3), (2, 4), (3, 1)], [[1, 2, 3, 1]])
assert_cycles({0: [1, 2], 2: [3], 3: [4], 4: [2]}, [[2, 3, 4, 2]])
assert_cycles([(0, 1), (0, 2), (2, 3), (3, 4), (4, 2)], [[2, 3, 4, 2]])
assert_cycles({1: [2], 3: [4], 4: [5], 5: [3]}, [[3, 4, 5, 3]])
assert_cycles([(1, 2), (3, 4), (4, 5), (5, 3)], [[3, 4, 5, 3]])
assert_cycles({0: [], 1: []}, [])
assert_cycles([], [])
assert_cycles({0: [1, 2], 1: [3, 4], 5: [6, 7]}, [])
assert_cycles([(0, 1), (0, 2), (1, 3), (1, 4), (5, 6), (5, 7)], [])
assert_cycles({0: [1], 1: [0, 2], 2: [1]}, [[0, 1, 0], [1, 2, 1]])
assert_cycles([(0, 1), (1, 0), (1, 2), (2, 1)], [[0, 1, 0], [1, 2, 1]])
編集:
has_cycle
は正しいようですが、_iter_cycles
はnotallサイクル繰り返します!
_iter_cycles
がすべてのサイクルを検出しない例:
assert_cycles([
(0, 1), (1, 2), (2, 0), # Cycle 0-1-2
(0, 2), (2, 0), # Cycle 0-2
(0, 1), (1, 4), (4, 0), # Cycle 0-1-4
],
[
[0, 1, 2, 0], # Not found (in Python 3.7)!
[0, 1, 4, 0],
[0, 2, 0],
]
)