_=inf=999999#inf
 
def Dijkstra_all_minpath(start,matrix):
 length=len(matrix)#该图的节点数
 path_array=[]
 temp_array=[]
 path_array.extend(matrix[start])#深复制
 temp_array.extend(matrix[start])#深复制
 temp_array[start] = inf#临时数组会把处理过的节点的值变成inf，表示不是最小权值的节点了
 already_traversal=[start]#start已处理
 path_parent=[start]*length#用于画路径，记录此路径中该节点的父节点
 while(len(already_traversal)<length):
  i= temp_array.index(min(temp_array))#找最小权值的节点的坐标
  temp_array[i]=inf
  path=[]#用于画路径
  path.append(str(i))
  k=i
  while(path_parent[k]!=start):#找该节点的父节点添加到path，直到父节点是start
   path.append(str(path_parent[k]))
   k=path_parent[k]
  path.append(str(start))
  path.reverse()#path反序产生路径
  print(str(i)+':','->'.join(path))#打印路径
  already_traversal.append(i)#该索引已经处理了
  for j in range(length):#这个不用多说了吧
   if j not in already_traversal:
    if (path_array[i]+matrix[i][j])<path_array[j]:
     path_array[j] = temp_array[j] =path_array[i]+matrix[i][j]
     path_parent[j]=i#说明父节点是i
 return path_array
 
#领接矩阵
adjacency_matrix=[[0,10,_,30,100],
     [10,0,50,_,_],
     [_,50,0,20,10],
     [30,_,20,0,60],
     [100,_,10,60,0]
     ]
print(Dijkstra_all_minpath(4,adjacency_matrix))

def Dijkstra_all_minpath_for_graph(start,graph):
 inf = 999999 # inf
 length=len(graph)
 path_graph={k:inf for k in graph.keys()}
 already_traversal=set()
 path_graph[start]=0
 min_node=start#初始化最小权值点
 already_traversal.add(min_node)#把找到的最小节点添加进去
 path_parent={k:start for k in graph.keys()}
 while(len(already_traversal)<=length):
  p = min_node
  if p!=start:
   path = []
   path.append(str(p))
   while (path_parent[p] != start):#找该节点的父节点添加到path，直到父节点是start
    path.append(str(path_parent[p]))
    p=path_parent[p]
   path.append(str(start))
   path.reverse()#反序
   print(str(min_node) + ':', '->'.join(path))#打印
  if(len(already_traversal)==length):break
  for k in path_graph.keys():#更新距离
   if k not in already_traversal:
    if k in graph[min_node].keys() and (path_graph[min_node]+graph[min_node][k])<path_graph[k]:
     path_graph[k]=path_graph[min_node]+graph[min_node][k]
     path_parent[k]=min_node
  min_value=inf
  for k in path_graph.keys():#找最小节点
   if k not in already_traversal:
    if path_graph[k]<min_value:
     min_node=k
     min_value=path_graph[k]
  already_traversal.add(min_node)#把找到最小节点添加进去
 return path_graph
adjacency_graph={0:{1:10,3:30,4:100},
     1:{0:10,2:50},
     2:{1:50,3:20,4:10},
     3:{0:30,2:20,4:60},
     4:{0:100,2:10,3:60}}
print(Dijkstra_all_minpath_for_graph(4,adjacency_graph))