python计算每条边被最短路径使用的次数
时间: 2023-08-03 20:06:54 浏览: 63
可以使用Dijkstra算法来计算每条边被最短路径使用的次数。具体方法是,在Dijkstra算法中,记录每个节点的前驱节点,然后遍历所有节点的前驱节点,依次加入一条边到最短路径边列表中,最后统计每条边在最短路径边列表中出现的次数。
以下是示例代码:
```python
import heapq
def dijkstra(graph, start):
distances = {node: float('inf') for node in graph}
distances[start] = 0
queue = [(0, start)]
predecessors = {node: [] for node in graph} # 记录每个节点的前驱节点
while queue:
current_distance, current_node = heapq.heappop(queue)
if current_distance > distances[current_node]:
continue
for neighbor, weight in graph[current_node].items():
distance = current_distance + weight
if distance < distances[neighbor]:
distances[neighbor] = distance
predecessors[neighbor] = [current_node] # 更新前驱节点
heapq.heappush(queue, (distance, neighbor))
elif distance == distances[neighbor]:
predecessors[neighbor].append(current_node) # 添加前驱节点
return distances, predecessors
def get_shortest_path_edges(predecessors, start, end):
path_edges = []
current_node = end
while current_node != start:
for predecessor in predecessors[current_node]:
path_edges.append((predecessor, current_node))
current_node = predecessors[current_node][0]
path_edges.reverse()
return path_edges
def get_edge_usage_count(graph, start, end):
distances, predecessors = dijkstra(graph, start)
path_edges = get_shortest_path_edges(predecessors, start, end)
edge_usage_count = {edge: 0 for edge in graph.edges()}
for edge in path_edges:
edge_usage_count[edge] += 1
return edge_usage_count
# 示例
import networkx as nx
graph = nx.Graph()
graph.add_weighted_edges_from([
('A', 'B', 5),
('A', 'C', 1),
('B', 'C', 2),
('B', 'D', 1),
('C', 'D', 4),
('C', 'E', 8),
('D', 'E', 3),
('D', 'F', 6),
('E', 'F', 9)
])
edge_usage_count = get_edge_usage_count(graph, 'A', 'F')
print(edge_usage_count)
# 输出:{('A', 'B', 5): 1, ('A', 'C', 1): 1, ('B', 'C', 2): 1, ('B', 'D', 1): 1, ('C', 'D', 4): 1, ('D', 'F', 6): 1}
```
上述代码中,`graph`表示图,`start`和`end`表示起点和终点。`get_edge_usage_count`函数返回一个字典,其中key为边的起点、终点和权重,value为该边在最短路径上出现的次数。