


import heapq
def 	_lowerCamelCase  (		A_  :	int							,  A_  :	str							,  A_  :	List[Any]      )			->			Any:

   '''simple docstring'''






   UpperCamelCase__ :			Dict 						=[(0, start)]  # cost from start node,end node
   UpperCamelCase__ :			Union[str, Any] 						=set()
   while heap:
      (UpperCamelCase__) :			int 						=heapq.heappop(lowerCamelCase__      )
      if u in visited:
         continue
      visited.add(lowerCamelCase__      )
      if u == end:
         return cost
      for v, c in graph[u]:
         if v in visited:
            continue
         UpperCamelCase__ :			List[Any] 						=cost + c
         heapq.heappush(lowerCamelCase__							,  (next_item, v)      )
   return -1


__UpperCAmelCase      			=  {
    """A""": [["""B""", 2], ["""C""", 5]],
    """B""": [["""A""", 2], ["""D""", 3], ["""E""", 1], ["""F""", 1]],
    """C""": [["""A""", 5], ["""F""", 3]],
    """D""": [["""B""", 3]],
    """E""": [["""B""", 4], ["""F""", 3]],
    """F""": [["""C""", 3], ["""E""", 3]],
}
__UpperCAmelCase      			=  {
    """B""": [["""C""", 1]],
    """C""": [["""D""", 1]],
    """D""": [["""F""", 1]],
    """E""": [["""B""", 1], ["""F""", 3]],
    """F""": [],
}
__UpperCAmelCase      			=  {
    """B""": [["""C""", 1]],
    """C""": [["""D""", 1]],
    """D""": [["""F""", 1]],
    """E""": [["""B""", 1], ["""G""", 2]],
    """F""": [],
    """G""": [["""F""", 1]],
}

__UpperCAmelCase      			=  dijkstra(G, """E""", """C""")
print(short_distance)  # E -- 3 --> F -- 3 --> C == 6

__UpperCAmelCase      			=  dijkstra(Ga, """E""", """F""")
print(short_distance)  # E -- 3 --> F == 3

__UpperCAmelCase      			=  dijkstra(Ga, """E""", """F""")
print(short_distance)  # E -- 2 --> G -- 1 --> F == 3

if __name__ == "__main__":
     import doctest

     doctest.testmod()









from functools import partial
from typing import Any, Callable, Dict, List, Type, TypeVar, Union, overload

import torch
import torch.nn as nn
import torch.types




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      torch.Tensor:
 # The first operation in a checkpoint can't be in-place, but it's
 # nice to have in-place addition during inference. Thus...
 if not inplace:
  lowerCamelCase_							:    Tuple							=     ma + ma
 else:
  ma += ma

 return ma




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      torch.Tensor:
 lowerCamelCase_							:    Union[str, Any]							=     -1 * len(lowerCamelCase__				)
 lowerCamelCase_							:    Optional[Any]							=     list(range(len(tensor.shape[:zero_index]				)				)				)
 return tensor.permute(first_inds + [zero_index + i for i in inds]				)




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      torch.Tensor:
 return t.reshape(t.shape[:-no_dims] + (-1,)				)




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ = 1e-4				)  ->      torch.Tensor:
 lowerCamelCase_							:    Optional[int]							=     mask.expand(*value.shape				)
 return torch.sum(mask * value ,			dim=lowerCamelCase__				) / (eps + torch.sum(lowerCamelCase__ ,			dim=lowerCamelCase__				))




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ = 2.3125 ,			lowerCamelCase__ = 21.6875 ,			lowerCamelCase__ = 64				)  ->      torch.Tensor:
 lowerCamelCase_							:    int							=     torch.linspace(lowerCamelCase__ ,			lowerCamelCase__ ,			no_bins - 1 ,			device=pts.device				)
 lowerCamelCase_							:    Tuple							=     torch.sqrt(torch.sum((pts.unsqueeze(-2				) - pts.unsqueeze(-3				)) ** 2 ,			dim=-1				)				)
 return torch.bucketize(lowerCamelCase__ ,			lowerCamelCase__				)




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      dict:
 lowerCamelCase_							:    Optional[Any]							=     dicts[0]
 lowerCamelCase_							:    Optional[Any]							=     {}
 for k, v in first.items():
  lowerCamelCase_							:    Tuple							=     [d[k] for d in dicts]
  if isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
   lowerCamelCase_							:    Optional[int]							=     dict_multimap(lowerCamelCase__ ,			lowerCamelCase__				)
  else:
   lowerCamelCase_							:    List[Any]							=     fn(lowerCamelCase__				)

 return new_dict




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__				)  ->      torch.Tensor:
 lowerCamelCase_							:    str							=     v_bins.view(((1,) * len(x.shape				)) + (len(lowerCamelCase__				),)				)
 lowerCamelCase_							:    List[Any]							=     x[..., None] - reshaped_bins
 lowerCamelCase_							:    List[Any]							=     torch.argmin(torch.abs(lowerCamelCase__				) ,			dim=-1				)
 return nn.functional.one_hot(lowerCamelCase__ ,			num_classes=len(lowerCamelCase__				)				).float()




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__ = 0 ,			lowerCamelCase__ = 0				)  ->      torch.Tensor:
 lowerCamelCase_							:    List[Union[slice, torch.Tensor]]							=     []
 for i, s in enumerate(data.shape[:no_batch_dims]				):
  lowerCamelCase_							:    int							=     torch.arange(lowerCamelCase__				)
  lowerCamelCase_							:    Any							=     r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape				) - i - 1)))				)
  ranges.append(lowerCamelCase__				)

 lowerCamelCase_							:    List[Union[slice, torch.Tensor]]							=     [slice(lowerCamelCase__				) for _ in range(len(data.shape				) - no_batch_dims				)]
 lowerCamelCase_							:    Optional[int]							=     inds
 ranges.extend(lowerCamelCase__				)
 # Matt note: Editing this to get around the behaviour of using a list as an array index changing
 # in recent Numpy versions
 return data[tuple(lowerCamelCase__				)]


UpperCamelCase											=      TypeVar('''T''')




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      Dict[Any, Union[dict, list, tuple, Any]]:
 lowerCamelCase_							:    Dict[Any, Union[dict, list, tuple, Any]]							=     {}
 for k, v in dic.items():
  if isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
   lowerCamelCase_							:    Optional[Any]							=     dict_map(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)
  else:
   lowerCamelCase_							:    Dict							=     tree_map(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)

 return new_dict




@overload
def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      Any:
 ...




@overload
def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      dict:
 ...




@overload
def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      list:
 ...




@overload
def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      tuple:
 ...




def       _a   (							lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)  ->      Any:
 if isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
  return dict_map(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				)
 elif isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
  return [tree_map(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				) for x in tree]
 elif isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
  return tuple(tree_map(lowerCamelCase__ ,			lowerCamelCase__ ,			lowerCamelCase__				) for x in tree				)
 elif isinstance(lowerCamelCase__ ,			lowerCamelCase__				):
  return fn(lowerCamelCase__				)
 else:
  print(type(lowerCamelCase__				)				)
  raise ValueError('Not supported'				)





UpperCamelCase											=      partial(tree_map, leaf_type=torch.Tensor)
