Python实现最短路径Dijkstra算法_python使用dijkstra算法计算从源点出发到达每个其他结点的最短路径

Dijkstra算法Python实现

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求结点1到各个结点的最短路径

def Dijkstra(G, start):
    """
    """
    nodes_num = len(G)
    start = start - 1
    inf = float('inf')
    visited = [0] * nodes_num
    # 初始dis为初始点到各结点的距离
    dis = {node: G[start][node] for node in range(nodes_num)}
    # 初始parents为初始结点到本结点寻找最短路径时，本节点的上一个最优结点
    parents = {node: [-1] for node in range(nodes_num)}
    visited[start] = 1
    last_point = start


    for i in range(nodes_num - 1):
        min_dis = inf
        for j in range(nodes_num):
            if visited[j] == 0 and dis[j] < min_dis:
                min_dis = dis[j]
                last_point = j

        visited[last_point] = 1

        if i == 0:
            parents[last_point][0] = start + 1

        for k in range(nodes_num):

            if G[last_point][k] < inf:
                if dis[k] > G[last_point][k] + dis[last_point]:
                    parents[k] = [last_point + 1]
                    dis[k] = G[last_point][k] + dis[last_point]
                elif G[last_point][k] != 0 and dis[k] == G[last_point][k] + dis[last_point]:
                    parents[k].append(last_point + 1)

    return {key + 1: val for key, val in dis.items()}, {key + 1: val for key, val in parents.items()}


if __name__ == '__main__':
    # 二维数组
    # 设初始顶点为pe1
    #     pe1  pe4  pe6  pe2  pe5  pe3
    #     1    4    6    2    5    3
    # 1   0    inf  inf  1    inf  12
    # 4   inf  0    15   inf  9    4
    # 6   inf  inf  0    inf  inf  inf
    # 2   inf  3    inf   0   inf   9
    # 5   inf  inf  4    inf  0     inf
    # 3   inf  inf  inf  inf  5    0
    vals = {
        -1: 'pe1',
        1: 'pe1',
        2: 'pe4',
        3: 'pe6',
        4: 'pe2',
        5: 'pe5',
        6: 'pe3'
    }

    inf = float('inf')
    G = [[0, inf, inf, 1, inf, 12],  # pe1
        [inf, 0, 15, inf, 9, 4],  # pe4
        [inf, inf, 0, inf, inf, inf],  # pe6
        [inf, 3, inf, 0, inf, 9],  # pe2
        [inf, inf, 4, inf, 0, inf],  # pe5
        [inf, inf, inf, inf, 5, 0]  # pe3
        ]
    # 二维数组的初始结点到各个结点的出发顺序为1， 4， 6， 2， 5， 3
    dis, parents = Dijkstra(G, 1)
    # print(parents)

    # 初始点到各个结点的最短距离
    print({vals[key]: val for key, val in dis.items()})

    print({vals[key]: [vals[v] for v in val ] for key, val in parents.items()})
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