迪杰斯特拉算法 python代码实现有向图

迪杰斯特拉(Dijkstra's Algorithm)是一种用于寻找图中两点之间最短路径的算法，通常应用于带权重的有向图或无向图。以下是Python中使用邻接矩阵表示的有向图实现Dijkstra算法的一个简单示例：

import heapq

def dijkstra(graph, start):
    distances = {node: float('inf') for node in graph}
    distances[start] = 0
    queue = [(0, start)]
    
    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
                heapq.heappush(queue, (distance, neighbor))
                
    return distances

# 示例：有向图的邻接矩阵表示，其中weights是从start到end的距离
graph = {
    'A': {'B': 1, 'C': 4},
    'B': {'A': 1, 'C': 2, 'D': 5},
    'C': {'A': 4, 'B': 2, 'D': 1},
    'D': {'B': 5, 'C': 1}
}

start = 'A'
shortest_distances = dijkstra(graph, start)
print("从{}到各个节点的最短距离: {}".format(start, shortest_distances))