迪杰斯特拉算法(网上找的)

"""
输入
graph 输入的图
src 原点
返回
dis 记录源点到其他点的最短距离
path 路径
"""
import json


def dijkstra(graph, src):
    if graph == None:
        return None
    # 定点集合
    nodes = [i for i in range(len(graph))]  # 获取顶点列表，用邻接矩阵存储图
    # 顶点是否被访问
    visited = []
    visited.append(src)
    # 初始化dis
    dis = {src: 0}  # 源点到自身的距离为0
    for i in nodes:
        dis[i] = graph[src][i]
    path = {src: {src: []}}  # 记录源节点到每个节点的路径
    k = pre = src
    while nodes:
        temp_k = k
        mid_distance = float('inf')  # 设置中间距离无穷大
        for v in visited:
            for d in nodes:
                if graph[src][v] != float('inf') and graph[v][d] != float('inf'):  # 有边
                    new_distance = graph[src][v] + graph[v][d]
                    if new_distance <= mid_distance:
                        mid_distance = new_distance
                        graph[src][d] = new_distance  # 进行距离更新
                        k = d
                        pre = v
        if k != src and temp_k == k:
            break
        dis[k] = mid_distance  # 最短路径
        path[src][k] = [i for i in path[src][pre]]
        path[src][k].append(k)

        visited.append(k)
        nodes.remove(k)
        print(nodes)
    return dis, path


if __name__ == '__main__':
    # 输入的有向图,有边存储的就是边的权值，无边就是float('inf')，顶点到自身就是0
    graph = [
        [0, float('inf'), 10, float('inf'), 30, 100],
        [float('inf'), 0, 5, float('inf'), float('inf'), float('inf')],
        [float('inf'), float('inf'), 0, 50, float('inf'), float('inf')],
        [float('inf'), float('inf'), float('inf'), 0, float('inf'), 10],
        [float('inf'), float('inf'), float('inf'), 20, 0, 60],
        [float('inf'), float('inf'), float('inf'), float('inf'), float('inf'), 0]]
    dis, path = dijkstra(graph, 0)  # 查找从源点0开始带其他节点的最短路径
    print(dis)
    print(json.dumps(path, indent=4))

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2020-05-08