[英]How to detect a cycle in a directed graph with Python?
我有一些輸入,如: [('A', 'B'),('C', 'D'),('D', 'C'),('C', 'D')]
。 我想在這個 edgeList 表示的有向圖中尋找循環是否存在。
我讀了一個討論: https : //www.geeksforgeeks.org/detect-cycle-in-a-graph/ ,但是當情況是這樣時它有一些錯誤:
g = Graph(3)
g.addEdge('A', 'B')
g.addEdge('B', 'C')
g.addEdge('C', 'A')
它的結果是“圖沒有循環”。 這顯然是錯誤的。 你能幫我解決這個問題嗎?
使用networkx庫,我們可以使用simple_cycles
函數查找有向圖的所有簡單循環。
示例代碼:
import networkx as nx
edges = [('A', 'B'),('C', 'D'),('D', 'C'),('C', 'D')]
G = nx.DiGraph(edges)
for cycle in nx.simple_cycles(G):
print(cycle)
G = nx.DiGraph()
G.add_edge('A', 'B')
G.add_edge('B', 'C')
G.add_edge('C', 'A')
for cycle in nx.simple_cycles(G):
print(cycle)
輸出:
['D', 'C']
['B', 'C', 'A']
問題是 [1] 中給出的示例: https ://www.geeksforgeeks.org/detect-cycle-in-a-graph/ 僅適用於整數,因為它們使用range()
函數來創建節點列表,看線
for node in range(self.V):
這使得假設不僅所有節點都是整數,而且它們將是一個連續的集合,即[0,1,2,3]
是可以的,但[0,3,10]
不是。
如果您想使用任何節點,可以通過將上面給出的行與
for node in self.graph.keys():
這將遍歷所有節點而不是一系列數字:)
我自己的實現(非遞歸所以沒有循環長度限制):
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]])
編輯:
我發現雖然has_cycle
似乎是正確的,但_iter_cycles
並沒有遍歷所有周期!
_iter_cycles
未找到所有循環的示例:
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],
]
)
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