最小路径覆盖 python
时间: 2024-07-23 14:01:33 浏览: 93
最小路径覆盖是指在一个加权有向图中找到一条从源节点(起始点)到目标节点(结束点)的路径,该路径恰好经过图中的每一条边一次。在Python中,可以使用迪杰斯特拉算法(Dijkstra's Algorithm)或者贝尔曼-福特算法(Bellman-Ford Algorithm)作为基础,结合贪心策略来找出这样的路径。
这里是一个基本的使用迪杰斯特拉算法实现最小路径覆盖的例子:
```python
from heapq import heappop, heappush
def shortest_path_with_coverage(graph, start, end):
INF = float('inf') # 定义无穷大
dists = {node: INF for node in graph} # 初始化距离字典
prev_nodes = {node: None for node in graph} # 初始化前驱节点字典
dists[start] = 0 # 设置起点的距离为0
queue = [(0, start)] # 使用堆来存储节点及其距离
while queue:
curr_dist, curr_node = heappop(queue) # 取出距离最小的节点
# 如果已经访问过更短路径,则跳过当前节点
if dists[curr_node] < curr_dist:
continue
# 更新相邻节点的距离和前驱节点
for neighbor, weight in graph[curr_node].items():
new_dist = curr_dist + weight
if new_dist < dists[neighbor]:
dists[neighbor] = new_dist
prev_nodes[neighbor] = curr_node
heappush(queue, (new_dist, neighbor)) # 将更新后的节点加入堆
# 从终点开始构建路径
path = []
curr_node = end
while curr_node is not None:
path.append(curr_node)
curr_node = prev_nodes[curr_node]
path.reverse() # 路径需要从终点反向
return path, dists[end] # 返回路径和总距离
# 示例图,假设这是一个有向图
graph = {
'A': {'B': 1, 'C': 4},
'B': {'A': 1, 'D': 5},
'C': {'A': 4, 'D': 1},
'D': {'B': 5, 'C': 1, 'E': 6},
'E': {}
}
start = 'A'
end = 'E'
result = shortest_path_with_coverage(graph, start, end)
path, total_cost = result
print("最小路径覆盖:", path)
print("总覆盖成本:", total_cost)
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