Python实现迪杰斯特拉算法及最短路径生成详解

def Dijkstra(network,s,d):#迪杰斯特拉算法算s-d的最短路径，并返回该路径和代价
  print("Start Dijstra Path……")
  path=[]#s-d的最短路径
  n=len(network)#邻接矩阵维度，即节点个数
  fmax=999
  w=[[0 for i in range(n)]for j in range(n)]#邻接矩阵转化成维度矩阵，即0→max
  book=[0 for i in range(n)]#是否已经是最小的标记列表
  dis=[fmax for i in range(n)]#s到其他节点的最小距离
  book[s-1]=1#节点编号从1开始，列表序号从0开始
  midpath=[-1 for i in range(n)]#上一跳列表
  for i in range(n):
    for j in range(n):
      if network[i][j]!=0:
        w[i][j]=network[i][j]#0→max
      else:
        w[i][j]=fmax
      if i==s-1 and network[i][j]!=0:#直连的节点最小距离就是network[i][j]
        dis[j]=network[i][j]
  for i in range(n-1):#n-1次遍历，除了s节点
    min=fmax
    for j in range(n):
      if book[j]==0 and dis[j]<min:#如果未遍历且距离最小
        min=dis[j]
        u=j
    book[u]=1
    for v in range(n):#u直连的节点遍历一遍
      if dis[v]>dis[u]+w[u][v]:
        dis[v]=dis[u]+w[u][v]
        midpath[v]=u+1#上一跳更新
  j=d-1#j是序号
  path.append(d)#因为存储的是上一跳，所以先加入目的节点d，最后倒置
  while(midpath[j]!=-1):
    path.append(midpath[j])
    j=midpath[j]-1
  path.append(s)
  path.reverse()#倒置列表
  print(path)
  #print(midpath)
  print(dis)
  #return path

network=[[0,1,0,2,0,0],
     [1,0,2,4,3,0],
     [0,2,0,0,1,4],
     [2,4,0,0,6,0],
     [0,3,1,6,0,2],
     [0,0,4,0,2,0]]
Dijkstra(network,1,6)