修复有向图以确保最顶层的父级始终是第一级,通常涉及到图的拓扑排序和重新排列节点。以下是详细的步骤和相关概念:
from collections import defaultdict, deque
class Graph:
def __init__(self, vertices):
self.graph = defaultdict(list)
self.V = vertices
def add_edge(self, u, v):
self.graph[u].append(v)
def topological_sort(self):
in_degree = [0] * self.V
for i in self.graph:
for j in self.graph[i]:
in_degree[j] += 1
queue = deque()
for i in range(self.V):
if in_degree[i] == 0:
queue.append(i)
topo_order = []
while queue:
u = queue.popleft()
topo_order.append(u)
for i in self.graph[u]:
in_degree[i] -= 1
if in_degree[i] == 0:
queue.append(i)
return topo_order
def fix_graph(self):
topo_order = self.topological_sort()
# Reconstruct the graph based on the topological order
new_graph = {i: [] for i in range(self.V)}
for i in topo_order:
for j in self.graph[i]:
new_graph[i].append(j)
self.graph = new_graph
return topo_order
# Example usage
g = Graph(6)
g.add_edge(5, 2)
g.add_edge(5, 0)
g.add_edge(4, 0)
g.add_edge(4, 1)
g.add_edge(2, 3)
g.add_edge(3, 1)
print("Original graph:", g.graph)
fixed_order = g.fix_graph()
print("Fixed topological order:", fixed_order)
print("Fixed graph:", g.graph)
通过这种方式,可以确保有向图的最顶层父级始终是第一级,从而简化图的层次结构和处理逻辑。
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