用python写最小斯坦纳树的代码
时间: 2023-12-14 09:38:34 浏览: 27
下面是用Python写的最小斯坦纳树的代码:
```python
import heapq
def prim(graph, start):
visited = {start}
heap = [(cost, start, to) for to, cost in graph[start].items()]
heapq.heapify(heap)
mst = []
while heap:
cost, frm, to = heapq.heappop(heap)
if to not in visited:
visited.add(to)
mst.append((frm, to, cost))
for to_next, cost in graph[to].items():
if to_next not in visited:
heapq.heappush(heap, (cost, to, to_next))
return mst
def kruskal(graph):
uf = {}
edges = []
for frm, to_dict in graph.items():
for to, cost in to_dict.items():
uf[frm] = frm
uf[to] = to
edges.append((cost, frm, to))
edges.sort()
mst = []
for cost, frm, to in edges:
if find(uf, frm) != find(uf, to):
mst.append((frm, to, cost))
union(uf, frm, to)
return mst
def find(uf, x):
if uf[x] != x:
uf[x] = find(uf, uf[x])
return uf[x]
def union(uf, x, y):
uf[find(uf, x)] = find(uf, y)
def build_digraph(graph):
digraph = {}
for frm, to_dict in graph.items():
for to, cost in to_dict.items():
if frm not in digraph:
digraph[frm] = {}
digraph[frm][to] = cost
return digraph
def steiner_tree(graph, terminals):
subgraph = {}
for term in terminals:
if term not in graph:
return None
mst = build_digraph({term: prim(graph, term)})
for frm, to_dict in mst.items():
if frm not in subgraph:
subgraph[frm] = {}
for to, cost in to_dict.items():
subgraph[frm][to] = min(subgraph[frm].get(to, float('inf')), cost)
return kruskal(subgraph)
graph = {
'A': {'B': 1, 'C': 2},
'B': {'A': 1, 'C': 3},
'C': {'A': 2, 'B': 3}
}
terminals = ['A', 'B']
mst = steiner_tree(graph, terminals)
print(mst)
```
这段代码实现了最小斯坦纳树的算法。其中,`prim`函数和`kruskal`函数分别实现了Prim和Kruskal算法,`build_digraph`函数将无向图转换为有向图,`steiner_tree`函数实现了最小斯坦纳树的算法。在这段代码中,我们可以通过修改`graph`和`terminals`来生成不同的最小斯坦纳树。