christofides算法python
时间: 2023-06-24 15:04:19 浏览: 53
以下是一个Python实现的Christofides算法:
```python
import networkx as nx
def christofides(G):
# Step 1: Find minimum spanning tree
T = nx.minimum_spanning_tree(G)
# Step 2: Find set of vertices with odd degree
odd_degrees = [v for v, d in T.degree() if d % 2 == 1]
# Step 3: Find minimum weight perfect matching on subgraph induced by odd_degree vertices
odd_degrees_subgraph = G.subgraph(odd_degrees)
matching = nx.algorithms.matching.max_weight_matching(odd_degrees_subgraph)
# Step 4: Add matching edges to tree
for u, v in matching.items():
T.add_edge(u, v)
# Step 5: Find Eulerian tour
tour = list(nx.eulerian_circuit(T))
# Step 6: Remove duplicate vertices
tour = [tour[i][0] for i in range(len(tour))]
visited = set()
tour_without_duplicates = [v for v in tour if not (v in visited or visited.add(v))]
# Step 7: Compute total weight of tour
total_weight = sum([G[u][v]['weight'] for u, v in zip(tour_without_duplicates, tour_without_duplicates[1:] + [tour_without_duplicates[0]])])
return tour_without_duplicates, total_weight
```
其中,参数`G`是一个带权重的无向图,返回值是一个包含节点顺序和总权重的元组。这个实现使用了NetworkX库进行计算。
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