





import torch
from torch import nn

class  __A(						nn.Module ):

     def __init__(      self,       A,       A,       A,       A,       A=1,       A=False      ):





            """simple docstring"""

            super().__init__()

            _UpperCamelCase              =						n_token
            _UpperCamelCase              =						d_embed
            _UpperCamelCase              =						d_proj

            _UpperCamelCase              =						cutoffs + [n_token]
            _UpperCamelCase              =						[0] + self.cutoffs
            _UpperCamelCase              =						div_val

            _UpperCamelCase              =						self.cutoffs[0]
            _UpperCamelCase              =						len(self.cutoffs      ) - 1
            _UpperCamelCase              =						self.shortlist_size + self.n_clusters

            if self.n_clusters > 0:
                   _UpperCamelCase              =						nn.Parameter(torch.zeros(self.n_clusters,       self.d_embed      )      )
                   _UpperCamelCase              =						nn.Parameter(torch.zeros(self.n_clusters      )      )

            _UpperCamelCase              =						nn.ModuleList()
            _UpperCamelCase              =						nn.ParameterList()

            if div_val == 1:
                   for i in range(len(self.cutoffs      )      ):
                          if d_proj != d_embed:
                                 self.out_projs.append(nn.Parameter(torch.FloatTensor(A,       A      )      )      )
                          else:
                                 self.out_projs.append(A      )

                   self.out_layers.append(nn.Linear(A,       A      )      )
            else:
                   for i in range(len(self.cutoffs      )      ):
                          _UpperCamelCase       ,		_UpperCamelCase              =						self.cutoff_ends[i], self.cutoff_ends[i + 1]
                          _UpperCamelCase              =						d_embed // (div_val**i)

                          self.out_projs.append(nn.Parameter(torch.FloatTensor(A,       A      )      )      )

                          self.out_layers.append(nn.Linear(A,       r_idx - l_idx      )      )

            _UpperCamelCase              =						keep_order

     def 	_UpperCamelCase     (      self,       A,       A,       A,       A      ):





            """simple docstring"""

            if proj is None:
                   _UpperCamelCase              =						nn.functional.linear(A,       A,       bias=A      )
            else:
                   # if CUDA_MAJOR <= 9 and CUDA_MINOR <= 1:
                   _UpperCamelCase              =						nn.functional.linear(A,       proj.t().contiguous()      )
                   _UpperCamelCase              =						nn.functional.linear(A,       A,       bias=A      )
                   # else:
                   #     logit = torch.einsum('bd,de,ev->bv', (hidden, proj, weight.t()))
                   #     if bias is not None:
                   #         logit = logit + bias

            return logit

     def 	_UpperCamelCase     (      self,       A,       A=None,       A=False      ):





            """simple docstring"""

            if labels is not None:
                   # Shift so that tokens < n predict n
                   _UpperCamelCase              =						hidden[..., :-1, :].contiguous()
                   _UpperCamelCase              =						labels[..., 1:].contiguous()
                   _UpperCamelCase              =						hidden.view(-1,       hidden.size(-1      )      )
                   _UpperCamelCase              =						labels.view(-1      )
                   if hidden.size(0      ) != labels.size(0      ):
                          raise RuntimeError('''Input and labels should have the same size in the batch dimension.'''      )
            else:
                   _UpperCamelCase              =						hidden.view(-1,       hidden.size(-1      )      )

            if self.n_clusters == 0:
                   _UpperCamelCase              =						self._compute_logit(A,       self.out_layers[0].weight,       self.out_layers[0].bias,       self.out_projs[0]      )
                   if labels is not None:
                          _UpperCamelCase              =						labels != -100
                          _UpperCamelCase              =						torch.zeros_like(A,       dtype=hidden.dtype,       device=hidden.device      )
                          _UpperCamelCase              =						(
                              -nn.functional.log_softmax(A,       dim=-1      )[mask].gather(1,       labels[mask].unsqueeze(1      )      ).squeeze(1      )
                          )
                   else:
                          _UpperCamelCase              =						nn.functional.log_softmax(A,       dim=-1      )
            else:
                   # construct weights and biases
                   _UpperCamelCase       ,		_UpperCamelCase              =						[], []
                   for i in range(len(self.cutoffs      )      ):
                          if self.div_val == 1:
                                 _UpperCamelCase       ,		_UpperCamelCase              =						self.cutoff_ends[i], self.cutoff_ends[i + 1]
                                 _UpperCamelCase              =						self.out_layers[0].weight[l_idx:r_idx]
                                 _UpperCamelCase              =						self.out_layers[0].bias[l_idx:r_idx]
                          else:
                                 _UpperCamelCase              =						self.out_layers[i].weight
                                 _UpperCamelCase              =						self.out_layers[i].bias

                          if i == 0:
                                 _UpperCamelCase              =						torch.cat([weight_i, self.cluster_weight],       dim=0      )
                                 _UpperCamelCase              =						torch.cat([bias_i, self.cluster_bias],       dim=0      )

                          weights.append(A      )
                          biases.append(A      )

                   _UpperCamelCase       ,		_UpperCamelCase       ,		_UpperCamelCase              =						weights[0], biases[0], self.out_projs[0]

                   _UpperCamelCase              =						self._compute_logit(A,       A,       A,       A      )
                   _UpperCamelCase              =						nn.functional.log_softmax(A,       dim=1      )

                   if labels is None:
                          _UpperCamelCase              =						hidden.new_empty((head_logit.size(0      ), self.n_token)      )
                   else:
                          _UpperCamelCase              =						torch.zeros_like(A,       dtype=hidden.dtype,       device=hidden.device      )

                   _UpperCamelCase              =						0
                   _UpperCamelCase              =						[0] + self.cutoffs
                   for i in range(len(A      ) - 1      ):
                          _UpperCamelCase       ,		_UpperCamelCase              =						cutoff_values[i], cutoff_values[i + 1]

                          if labels is not None:
                                 _UpperCamelCase              =						(labels >= l_idx) & (labels < r_idx)
                                 _UpperCamelCase              =						mask_i.nonzero().squeeze()

                                 if indices_i.numel() == 0:
                                        continue

                                 _UpperCamelCase              =						labels.index_select(0,       A      ) - l_idx
                                 _UpperCamelCase              =						head_logprob.index_select(0,       A      )
                                 _UpperCamelCase              =						hidden.index_select(0,       A      )
                          else:
                                 _UpperCamelCase              =						hidden

                          if i == 0:
                                 if labels is not None:
                                        _UpperCamelCase              =						head_logprob_i.gather(1,       target_i[:, None]      ).squeeze(1      )
                                 else:
                                        _UpperCamelCase              =						head_logprob[:, : self.cutoffs[0]]
                          else:
                                 _UpperCamelCase       ,		_UpperCamelCase       ,		_UpperCamelCase              =						weights[i], biases[i], self.out_projs[i]

                                 _UpperCamelCase              =						self._compute_logit(A,       A,       A,       A      )
                                 _UpperCamelCase              =						nn.functional.log_softmax(A,       dim=1      )
                                 _UpperCamelCase              =						self.cutoffs[0] + i - 1  # No probability for the head cluster
                                 if labels is not None:
                                        _UpperCamelCase              =						head_logprob_i[:, cluster_prob_idx] + tail_logprob_i.gather(
                                            1,       target_i[:, None]      ).squeeze(1      )
                                 else:
                                        _UpperCamelCase              =						head_logprob[:, cluster_prob_idx, None] + tail_logprob_i
                                        _UpperCamelCase              =						logprob_i

                          if labels is not None:
                                 if (hasattr(self,       '''keep_order'''      ) and self.keep_order) or keep_order:
                                        out.index_copy_(0,       A,       -logprob_i      )
                                 else:
                                        out[offset : offset + logprob_i.size(0      )].copy_(-logprob_i      )
                                 offset += logprob_i.size(0      )

            return out



     def 	_UpperCamelCase     (      self,       A      ):





            """simple docstring"""

            if self.n_clusters == 0:
                   _UpperCamelCase              =						self._compute_logit(A,       self.out_layers[0].weight,       self.out_layers[0].bias,       self.out_projs[0]      )
                   return nn.functional.log_softmax(A,       dim=-1      )
            else:
                   # construct weights and biases
                   _UpperCamelCase       ,		_UpperCamelCase              =						[], []
                   for i in range(len(self.cutoffs      )      ):
                          if self.div_val == 1:
                                 _UpperCamelCase       ,		_UpperCamelCase              =						self.cutoff_ends[i], self.cutoff_ends[i + 1]
                                 _UpperCamelCase              =						self.out_layers[0].weight[l_idx:r_idx]
                                 _UpperCamelCase              =						self.out_layers[0].bias[l_idx:r_idx]
                          else:
                                 _UpperCamelCase              =						self.out_layers[i].weight
                                 _UpperCamelCase              =						self.out_layers[i].bias

                          if i == 0:
                                 _UpperCamelCase              =						torch.cat([weight_i, self.cluster_weight],       dim=0      )
                                 _UpperCamelCase              =						torch.cat([bias_i, self.cluster_bias],       dim=0      )

                          weights.append(A      )
                          biases.append(A      )

                   _UpperCamelCase       ,		_UpperCamelCase       ,		_UpperCamelCase              =						weights[0], biases[0], self.out_projs[0]
                   _UpperCamelCase              =						self._compute_logit(A,       A,       A,       A      )

                   _UpperCamelCase              =						hidden.new_empty((head_logit.size(0      ), self.n_token)      )
                   _UpperCamelCase              =						nn.functional.log_softmax(A,       dim=1      )

                   _UpperCamelCase              =						[0] + self.cutoffs
                   for i in range(len(A      ) - 1      ):
                          _UpperCamelCase       ,		_UpperCamelCase              =						cutoff_values[i], cutoff_values[i + 1]

                          if i == 0:
                                 _UpperCamelCase              =						head_logprob[:, : self.cutoffs[0]]
                          else:
                                 _UpperCamelCase       ,		_UpperCamelCase       ,		_UpperCamelCase              =						weights[i], biases[i], self.out_projs[i]

                                 _UpperCamelCase              =						self._compute_logit(A,       A,       A,       A      )
                                 _UpperCamelCase              =						nn.functional.log_softmax(A,       dim=1      )

                                 _UpperCamelCase              =						head_logprob[:, -i] + tail_logprob_i
                                 _UpperCamelCase              =						logprob_i

                   return out













from __future__ import annotations

lowercase    : int    	=  {
    """A""": ["""B""", """C""", """E"""],
    """B""": ["""A""", """D""", """E"""],
    """C""": ["""A""", """F""", """G"""],
    """D""": ["""B"""],
    """E""": ["""A""", """B""", """D"""],
    """F""": ["""C"""],
    """G""": ["""C"""],
}

class  __A:

     def __init__(      self,       A,       A      ):





            """simple docstring"""

            _UpperCamelCase              =						graph
            # mapping node to its parent in resulting breadth first tree
            _UpperCamelCase              =						{}
            _UpperCamelCase              =						source_vertex

     def 	_UpperCamelCase     (      self      ):





            """simple docstring"""

            _UpperCamelCase              =						{self.source_vertex}
            _UpperCamelCase              =						None
            _UpperCamelCase              =						[self.source_vertex]  # first in first out queue

            while queue:
                   _UpperCamelCase              =						queue.pop(0      )
                   for adjacent_vertex in self.graph[vertex]:
                          if adjacent_vertex not in visited:
                                 visited.add(A      )
                                 _UpperCamelCase              =						vertex
                                 queue.append(A      )



     def 	_UpperCamelCase     (      self,       A      ):





            """simple docstring"""

            if target_vertex == self.source_vertex:
                   return self.source_vertex

            _UpperCamelCase              =						self.parent.get(A      )
            if target_vertex_parent is None:
                   _UpperCamelCase              =						(
                       F'''No path from vertex: {self.source_vertex} to vertex: {target_vertex}'''
                   )
                   raise ValueError(A      )

            return self.shortest_path(A      ) + F'''->{target_vertex}'''


if __name__ == "__main__":
       lowercase    : Tuple    	=  Graph(graph, """G""")
       g.breath_first_search()
       print(g.shortest_path("""D"""))
       print(g.shortest_path("""G"""))
       print(g.shortest_path("""Foo"""))






