Dijkstra算法的Python实现

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将图上的顶点分为已访问visited和未访问node两个集合.
每次从visited向外拓展一个点,拓展规则是在可更新的点里是距离最小的.

算法伪代码:

def dijkstra():
    初始化 visited 和 node 集合,distance[]
    visited 加入源节点
    node 移除源节点
    while node 非空:
        最短路径长度 = inf
        for each visited:
            for each 相邻节点:
                if 长度<最短路径长度:
                    更新最短路径长度
                    维护 distance
                    保存此节点
        visited 加入更新节点
        node 移除更新节点
    return distance

具体实现:

'''
dijkstra algorithm demo
graph size:6*6
node index start from 0
'''
import numpy as np

graph_list = [[0, 2, 1, 4, 5, 1],
              [1, 0, 4, 2, 3, 4],
              [2, 1, 0, 1, 2, 4],
              [3, 5, 2, 0, 3, 3],
              [2, 4, 3, 4, 0, 1],
              [3, 4, 7, 3, 1, 0]]


def dijkstra(graph, src):
    # init
    visited = []
    distance = {src: 0}
    node = list(range(len(graph[0])))
    if src in node:
        node.remove(src)
        visited.append(src)
    else:
        return None
    for i in node:
        distance[i] = graph[src][i]
    prefer = src
    while node:
        _distance = float('inf')
        for i in visited:
            for j in node:
                if graph[i][j] > 0:
                    if _distance > distance[i] + graph[i][j]:
                        _distance = distance[j] = distance[i] + graph[i][j]
                        prefer = j
        visited.append(prefer)
        node.remove(prefer)
    return distance


if __name__ == '__main__':
    distance = dijkstra(graph_list, 0)
    print(distance)