dijkstra标号法python

Dijkstra算法是一种用于解决带权图的单源最短路径问题的贪心算法。其中标号法是一种实现Dijkstra算法的方法之一，下面是一个使用Python实现Dijkstra标号法的示例代码：

import heapq

def dijkstra(graph, start):
    # 初始化距离字典和堆
    distances = {vertex: float('infinity') for vertex in graph}
    distances[start] = 0
    heap = [(0, start)]
    
    while heap:
        # 弹出堆中距离最小的节点
        current_distance, current_vertex = heapq.heappop(heap)
        
        # 如果当前节点已经被处理过，则跳过
        if current_distance > distances[current_vertex]:
            continue
        
        # 遍历当前节点的邻居节点
        for neighbor, weight in graph[current_vertex].items():
            distance = current_distance + weight
            
            # 如果新的距离比原来的距离更短，则更新距离字典和堆
            if distance < distances[neighbor]:
                distances[neighbor] = distance
                heapq.heappush(heap, (distance, neighbor))
    
    return distances

# 示例图
graph = {
    'A': {'B': 1, 'C': 4},
    'B': {'D': 3},
    'C': {'D': 2},
    'D': {'E': 1},
    'E': {}
}

# 计算从节点A出发到其他节点的最短距离
distances = dijkstra(graph, 'A')
print(distances)

# 输出：{'A': 0, 'B': 1, 'C': 4, 'D': 4, 'E': 5}