
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     UpperCamelCase      (					__lowerCamelCase  :				torch.Tensor       ,      __lowerCamelCase  :				torch.Tensor       ,      __lowerCamelCase  :				bool					):
       # 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:
              snake_case :     List[Any]           =   ma + ma
       else:
              ma += ma

       return ma


def     UpperCamelCase      (					__lowerCamelCase  :				torch.Tensor       ,      __lowerCamelCase  :				List[int]					):
       snake_case :     Union[str, Any]           =   -1 * len(__lowerCamelCase					)
       snake_case :     List[Any]           =   list(range(len(tensor.shape[:zero_index]					)					)					)
       return tensor.permute(first_inds + [zero_index + i for i in inds]					)


def     UpperCamelCase      (					__lowerCamelCase  :				torch.Tensor       ,      __lowerCamelCase  :				int					):
       return t.reshape(t.shape[:-no_dims] + (-1,)					)


def     UpperCamelCase      (					__lowerCamelCase  :				torch.Tensor       ,      __lowerCamelCase  :				torch.Tensor       ,      __lowerCamelCase  :				int       ,      __lowerCamelCase  :				float = 1E-4					):
       snake_case :     Tuple           =   mask.expand(*value.shape					)
       return torch.sum(mask * value       ,      dim=__lowerCamelCase					) / (eps + torch.sum(__lowerCamelCase       ,      dim=__lowerCamelCase					))


def     UpperCamelCase      (					__lowerCamelCase  :				torch.Tensor       ,      __lowerCamelCase  :				torch.types.Number = 2.3125       ,      __lowerCamelCase  :				torch.types.Number = 21.6875       ,      __lowerCamelCase  :				int = 64					):
       snake_case :     Optional[Any]           =   torch.linspace(__lowerCamelCase       ,      __lowerCamelCase       ,      no_bins - 1       ,      device=pts.device					)
       snake_case :     int           =   torch.sqrt(torch.sum((pts.unsqueeze(-2					) - pts.unsqueeze(-3					)) ** 2       ,      dim=-1					)					)
       return torch.bucketize(__lowerCamelCase       ,      __lowerCamelCase					)


def     UpperCamelCase      (					__lowerCamelCase  :				Callable[[list], Any]       ,      __lowerCamelCase  :				List[dict]					):
       snake_case :     Optional[int]           =   dicts[0]
       snake_case :     Optional[int]           =   {}
       for k, v in first.items():
              snake_case :     Optional[int]           =   [d[k] for d in dicts]
              if isinstance(__lowerCamelCase       ,      __lowerCamelCase					):
                     snake_case :     List[Any]           =   dict_multimap(__lowerCamelCase       ,      __lowerCamelCase					)
              else:
                     snake_case :     Optional[Any]           =   fn(__lowerCamelCase					)

       return new_dict


def     UpperCamelCase      (					__lowerCamelCase  :				torch.Tensor       ,      __lowerCamelCase  :				torch.Tensor					):
       snake_case :     Union[str, Any]           =   v_bins.view(((1,) * len(x.shape					)) + (len(__lowerCamelCase					),)					)
       snake_case :     Tuple           =   x[..., None] - reshaped_bins
       snake_case :     str           =   torch.argmin(torch.abs(__lowerCamelCase					)       ,      dim=-1					)
       return nn.functional.one_hot(__lowerCamelCase       ,      num_classes=len(__lowerCamelCase					)					).float()


def     UpperCamelCase      (					__lowerCamelCase  :				torch.Tensor       ,      __lowerCamelCase  :				torch.Tensor       ,      __lowerCamelCase  :				int = 0       ,      __lowerCamelCase  :				int = 0					):
       snake_case :     List[Union[slice, torch.Tensor]]           =   []
       for i, s in enumerate(data.shape[:no_batch_dims]					):
              snake_case :     Union[str, Any]           =   torch.arange(__lowerCamelCase					)
              snake_case :     Optional[Any]           =   r.view(*(*((1,) * i), -1, *((1,) * (len(inds.shape					) - i - 1)))					)
              ranges.append(__lowerCamelCase					)

       snake_case :     List[Union[slice, torch.Tensor]]           =   [slice(__lowerCamelCase					) for _ in range(len(data.shape					) - no_batch_dims					)]
       snake_case :     Optional[Any]           =   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					)]


__lowerCamelCase							= TypeVar("""T""")


def     UpperCamelCase      (					__lowerCamelCase  :				Callable[[T], Any]       ,      __lowerCamelCase  :				Dict[Any, Union[dict, list, tuple, T]]       ,      __lowerCamelCase  :				Type[T]					):
       snake_case :     Dict[Any, Union[dict, list, tuple, Any]]           =   {}
       for k, v in dic.items():
              if isinstance(__lowerCamelCase       ,      __lowerCamelCase					):
                     snake_case :     Any           =   dict_map(__lowerCamelCase       ,      __lowerCamelCase       ,      __lowerCamelCase					)
              else:
                     snake_case :     Dict           =   tree_map(__lowerCamelCase       ,      __lowerCamelCase       ,      __lowerCamelCase					)

       return new_dict


@overload
def     UpperCamelCase      (					__lowerCamelCase  :				Callable[[T], Any]       ,      __lowerCamelCase  :				T       ,      __lowerCamelCase  :				Type[T]					):
       ...


@overload
def     UpperCamelCase      (					__lowerCamelCase  :				Callable[[T], Any]       ,      __lowerCamelCase  :				dict       ,      __lowerCamelCase  :				Type[T]					):
       ...


@overload
def     UpperCamelCase      (					__lowerCamelCase  :				Callable[[T], Any]       ,      __lowerCamelCase  :				list       ,      __lowerCamelCase  :				Type[T]					):
       ...


@overload
def     UpperCamelCase      (					__lowerCamelCase  :				Callable[[T], Any]       ,      __lowerCamelCase  :				tuple       ,      __lowerCamelCase  :				Type[T]					):
       ...


def     UpperCamelCase      (					__lowerCamelCase  :				Dict       ,      __lowerCamelCase  :				List[Any]       ,      __lowerCamelCase  :				Tuple					):
       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"					)




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







from __future__ import annotations






class 						UpperCAmelCase	:



   def __init__(self	:      List[str]					,		snake_case__	:      int				)	->			None:


          '''simple docstring'''


          snake_case :     Any           =   vertices
          snake_case :     str           =   [[0] * vertices for _ in range(snake_case__				)]



   def        _SCREAMING_SNAKE_CASE     (self	:      str					,		snake_case__	:      list[int]				)	->			None:


          '''simple docstring'''


          print("Vertex \t Distance from Source"				)
          for vertex in range(self.vertices				):
                 print(snake_case__					,		"\t\t"					,		distances_from_source[vertex]				)



   def        _SCREAMING_SNAKE_CASE     (self	:      Optional[int]					,		snake_case__	:      list[int]					,		snake_case__	:      list[bool]				)	->			int:


          '''simple docstring'''


          snake_case :     Union[str, Any]           =   1e7
          snake_case :     Any           =   0

          # Search not nearest vertex not in the shortest path tree
          for vertex in range(self.vertices				):
                 if distances_from_source[vertex] < minimum and visited[vertex] is False:
                        snake_case :     Union[str, Any]           =   distances_from_source[vertex]
                        snake_case :     str           =   vertex
          return min_index



   def        _SCREAMING_SNAKE_CASE     (self	:      Optional[Any]					,		snake_case__	:      int				)	->			None:


          '''simple docstring'''


          snake_case :     Optional[int]           =   [int(1e7				)] * self.vertices  # distances from the source
          snake_case :     Dict           =   0
          snake_case :     Union[str, Any]           =   [False] * self.vertices

          for _ in range(self.vertices				):
                 snake_case :     Dict           =   self.minimum_distance(snake_case__					,		snake_case__				)
                 snake_case :     List[str]           =   True

                 # Update dist value of the adjacent vertices
                 # of the picked vertex only if the current
                 # distance is greater than new distance and
                 # the vertex in not in the shortest path tree
                 for v in range(self.vertices				):
                        if (
                            self.graph[u][v] > 0
                            and visited[v] is False
                            and distances[v] > distances[u] + self.graph[u][v]
                        ):
                               snake_case :     Union[str, Any]           =   distances[u] + self.graph[u][v]

          self.print_solution(snake_case__				)


if __name__ == "__main__":
   __lowerCamelCase							= Graph(9)
   __lowerCamelCase							= [
       [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],
   ]
   graph.dijkstra(0)





