迪杰斯特拉 (Dijkstra)算法

以下是一个简单的迪杰斯特拉算法的实现，假设图是通过邻接矩阵表示：

import sys

def dijkstra(graph, start):
    # 初始化距离数组
    dist = [sys.maxsize] * len(graph)
    dist[start] = 0

    # 创建集合S，用于存储已经确定最短路径的顶点
    S = set()

    while len(S) < len(graph):
        # 从距离数组中选择最小值的顶点
        min_dist = sys.maxsize
        min_index = -1
        for i in range(len(graph)):
            if i not in S and dist[i] < min_dist:
                min_dist = dist[i]
                min_index = i

        # 将该顶点添加到集合S中
        S.add(min_index)

        # 更新与该顶点相邻的顶点的最短距离
        for i in range(len(graph)):
            if i not in S and graph[min_index][i] != 0:
                new_dist = dist[min_index] + graph[min_index][i]
                if new_dist < dist[i]:
                    dist[i] = new_dist

    return dist

使用示例：

# 定义邻接矩阵表示的图
graph = [
    [0, 4, 0, 0, 0, 0, 0, 8, 0],
    [4, 0, 8, 0, 0, 0, 0, 11, 0],
    [0, 8, 0, 7, 0, 4, 0, 0, 2],
    [0, 0, 7, 0, 9, 14, 0, 0, 0],
    [0, 0, 0, 9, 0, 10, 0, 0, 0],
    [0, 0, 4, 14, 10, 0, 2, 0, 0],
    [0, 0, 0, 0, 0, 2, 0, 1, 6],
    [8, 11, 0, 0, 0, 0, 1, 0, 7],
    [0, 0, 2, 0, 0, 0, 6, 7, 0]
]

start = 0
dist = dijkstra(graph, start)
print(dist)

输出结果为：[0, 4, 12, 19, 21, 11, 9, 8, 14]，表示从起始顶点到其他所有顶点的最短距离。

制作不易,请点赞加关注