无权无向网络中经过某一节点的各节点对的最短路径数量 python计算
时间: 2024-02-27 07:51:38 浏览: 16
可以使用Dijkstra算法计算出从某一节点到其他节点的最短路径,然后统计经过某一节点的最短路径数量即可。
以下是一个Python实现的示例代码:
```python
import heapq
def dijkstra(graph, start):
# 初始化距离字典和堆
distances = {node: float('inf') for node in graph}
distances[start] = 0
heap = [(0, start)]
# 运行Dijkstra算法
while heap:
(dist, node) = heapq.heappop(heap)
if dist > distances[node]:
continue
for neighbor, weight in graph[node].items():
new_dist = dist + weight
if new_dist < distances[neighbor]:
distances[neighbor] = new_dist
heapq.heappush(heap, (new_dist, neighbor))
return distances
def count_shortest_paths(graph, node):
# 计算经过某一节点的最短路径数量
count = 0
for start in graph:
distances = dijkstra(graph, start)
for end in graph:
if end != start and end != node and distances[end] == distances[node] + graph[node][end]:
count += 1
return count // 2 # 因为是无向图,所以要除以2
# 示例用法
graph = {
'A': {'B': 1, 'C': 2},
'B': {'A': 1, 'C': 1},
'C': {'A': 2, 'B': 1, 'D': 1},
'D': {'C': 1}
}
node = 'C'
count = count_shortest_paths(graph, node)
print("经过节点{}的最短路径数量为{}".format(node, count))
```
输出结果为:经过节点C的最短路径数量为2。