





import torch
from torch import nn






class       __A					(					nn.Module				):

			'''simple docstring'''







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



				'''simple docstring'''







				super().__init__()

				lowerCamelCase__              =	n_token
				lowerCamelCase__              =	d_embed
				lowerCamelCase__              =	d_proj

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

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

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

				lowerCamelCase__              =	nn.ModuleList()
				lowerCamelCase__              =	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(__lowerCAmelCase ,						__lowerCAmelCase							)							)							)
						else:
							self.out_projs.append(__lowerCAmelCase							)

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

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

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

				lowerCamelCase__              =	keep_order





			def 	__lowerCamelCase       (					self ,						__lowerCAmelCase ,						__lowerCAmelCase ,						__lowerCAmelCase ,						__lowerCAmelCase							):



				'''simple docstring'''







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

				return logit





			def 	__lowerCamelCase       (					self ,						__lowerCAmelCase ,						__lowerCAmelCase=None ,						__lowerCAmelCase=False							):



				'''simple docstring'''







				if labels is not None:
					# Shift so that tokens < n predict n
					lowerCamelCase__              =	hidden[..., :-1, :].contiguous()
					lowerCamelCase__              =	labels[..., 1:].contiguous()
					lowerCamelCase__              =	hidden.view(-1 ,						hidden.size(-1							)							)
					lowerCamelCase__              =	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:
					lowerCamelCase__              =	hidden.view(-1 ,						hidden.size(-1							)							)

				if self.n_clusters == 0:
					lowerCamelCase__              =	self._compute_logit(__lowerCAmelCase ,						self.out_layers[0].weight ,						self.out_layers[0].bias ,						self.out_projs[0]							)
					if labels is not None:
						lowerCamelCase__              =	labels != -1_0_0
						lowerCamelCase__              =	torch.zeros_like(__lowerCAmelCase ,						dtype=hidden.dtype ,						device=hidden.device							)
						lowerCamelCase__              =	(
						    -nn.functional.log_softmax(__lowerCAmelCase ,						dim=-1							)[mask].gather(1 ,						labels[mask].unsqueeze(1							)							).squeeze(1							)
						)
					else:
						lowerCamelCase__              =	nn.functional.log_softmax(__lowerCAmelCase ,						dim=-1							)
				else:
					# construct weights and biases
					lowerCamelCase__       ,			lowerCamelCase__              =	[], []
					for i in range(len(self.cutoffs							)							):
						if self.div_val == 1:
							lowerCamelCase__       ,			lowerCamelCase__              =	self.cutoff_ends[i], self.cutoff_ends[i + 1]
							lowerCamelCase__              =	self.out_layers[0].weight[l_idx:r_idx]
							lowerCamelCase__              =	self.out_layers[0].bias[l_idx:r_idx]
						else:
							lowerCamelCase__              =	self.out_layers[i].weight
							lowerCamelCase__              =	self.out_layers[i].bias

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

						weights.append(__lowerCAmelCase							)
						biases.append(__lowerCAmelCase							)

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

					lowerCamelCase__              =	self._compute_logit(__lowerCAmelCase ,						__lowerCAmelCase ,						__lowerCAmelCase ,						__lowerCAmelCase							)
					lowerCamelCase__              =	nn.functional.log_softmax(__lowerCAmelCase ,						dim=1							)

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

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

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

							if indices_i.numel() == 0:
								continue

							lowerCamelCase__              =	labels.index_select(0 ,						__lowerCAmelCase							) - l_idx
							lowerCamelCase__              =	head_logprob.index_select(0 ,						__lowerCAmelCase							)
							lowerCamelCase__              =	hidden.index_select(0 ,						__lowerCAmelCase							)
						else:
							lowerCamelCase__              =	hidden

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

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

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

				return out





			def 	__lowerCamelCase       (					self ,						__lowerCAmelCase							):



				'''simple docstring'''







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

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

						weights.append(__lowerCAmelCase							)
						biases.append(__lowerCAmelCase							)

					lowerCamelCase__       ,			lowerCamelCase__       ,			lowerCamelCase__              =	weights[0], biases[0], self.out_projs[0]
					lowerCamelCase__              =	self._compute_logit(__lowerCAmelCase ,						__lowerCAmelCase ,						__lowerCAmelCase ,						__lowerCAmelCase							)

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

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

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

							lowerCamelCase__              =	self._compute_logit(__lowerCAmelCase ,						__lowerCAmelCase ,						__lowerCAmelCase ,						__lowerCAmelCase							)
							lowerCamelCase__              =	nn.functional.log_softmax(__lowerCAmelCase ,						dim=1							)

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

					return out










from queue import PriorityQueue
from typing import Any

import numpy as np





def lowerCAmelCase__(__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,)       ->   float | int:







	'''simple docstring'''







	for nxt, d in graph[v]:
		if nxt in visited_forward:
			continue
		lowerCamelCase__              =	cst_fwd.get(__snake_case ,np.inf							)
		lowerCamelCase__              =	cst_fwd[v] + d
		if new_cost_f < old_cost_f:
			queue.put((new_cost_f, nxt)							)
			lowerCamelCase__              =	new_cost_f
			lowerCamelCase__              =	v
		if nxt in visited_backward:
			if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
				lowerCamelCase__              =	cst_fwd[v] + d + cst_bwd[nxt]
	return shortest_distance





def lowerCAmelCase__(__snake_case ,__snake_case ,__snake_case ,__snake_case							)       ->   int:







	'''simple docstring'''







	lowerCamelCase__              =	-1

	lowerCamelCase__              =	set()
	lowerCamelCase__              =	set()
	lowerCamelCase__              =	{source: 0}
	lowerCamelCase__              =	{destination: 0}
	lowerCamelCase__              =	{source: None}
	lowerCamelCase__              =	{destination: None}
	lowerCamelCase__              =	PriorityQueue()
	lowerCamelCase__              =	PriorityQueue()

	lowerCamelCase__              =	np.inf

	queue_forward.put((0, source)							)
	queue_backward.put((0, destination)							)

	if source == destination:
		return 0

	while not queue_forward.empty() and not queue_backward.empty():
		lowerCamelCase__       ,			lowerCamelCase__              =	queue_forward.get()
		visited_forward.add(__snake_case							)

		lowerCamelCase__       ,			lowerCamelCase__              =	queue_backward.get()
		visited_backward.add(__snake_case							)

		lowerCamelCase__              =	pass_and_relaxation(
		    __snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,)

		lowerCamelCase__              =	pass_and_relaxation(
		    __snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,__snake_case ,)

		if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
			break

	if shortest_distance != np.inf:
		lowerCamelCase__              =	shortest_distance
	return shortest_path_distance


_a						=   {
    "B": [["C", 1]],
    "C": [["D", 1]],
    "D": [["F", 1]],
    "E": [["B", 1], ["G", 2]],
    "F": [],
    "G": [["F", 1]],
}
_a						=   {
    "B": [["E", 1]],
    "C": [["B", 1]],
    "D": [["C", 1]],
    "F": [["D", 1], ["G", 1]],
    "E": [[None, np.inf]],
    "G": [["E", 2]],
}

if __name__ == "__main__":
			import doctest

			doctest.testmod()



