



'''simple docstring'''





class 							lowerCAmelCase_		:





				def __init__(    self    :    List[Any],    _snake_case    :    Tuple     ):



							'''simple docstring'''







							snake_case   :							str						  =val
							# Number of nodes in left subtree
							snake_case   :							List[str]						  =0
							snake_case   :							Any						  =None
							snake_case   :							Any						  =None
							snake_case   :							List[str]						  =None






				def 					__snake_case       (    self    :    Optional[Any],    _snake_case    :    Optional[int]     ):



							'''simple docstring'''







							assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

							if self.val < other.val:
										snake_case   :							Any						  =self.right
										snake_case   :							List[str]						  =None
										if self.right:
													snake_case   :							List[str]						  =other
										snake_case   :							List[str]						  =other
										snake_case   :							Optional[int]						  =self.left_tree_size * 2 + 1
										return self
							else:
										snake_case   :							List[str]						  =other.right
										snake_case   :							str						  =None
										if other.right:
													snake_case   :							str						  =self
										snake_case   :							Any						  =self
										snake_case   :							List[str]						  =other.left_tree_size * 2 + 1
										return other





class 							lowerCAmelCase_		:





				def __init__(    self    :    Any,    _snake_case    :    Dict=None,    _snake_case    :    Dict=None,    _snake_case    :    List[Any]=0     ):



							'''simple docstring'''







							snake_case   :							Tuple						  =heap_size
							snake_case   :							int						  =bottom_root
							snake_case   :							List[str]						  =min_node





				def 					__snake_case       (    self    :    Optional[int],    _snake_case    :    Optional[Any]     ):



							'''simple docstring'''







							if other.size == 0:
										return None
							if self.size == 0:
										snake_case   :							Dict						  =other.size
										snake_case   :							int						  =other.bottom_root
										snake_case   :							Union[str, Any]						  =other.min_node
										return None
							# Update size
							snake_case   :							int						  =self.size + other.size

							# Update min.node
							if self.min_node.val > other.min_node.val:
										snake_case   :							List[str]						  =other.min_node
							# Merge

							# Order roots by left_subtree_size
							snake_case   :							Optional[int]						  =[]
							snake_case  ,    snake_case   :							Union[str, Any]						  =self.bottom_root, other.bottom_root
							while i or j:
										if i and ((not j) or i.left_tree_size < j.left_tree_size):
													combined_roots_list.append((i, True)     )
													snake_case   :							List[Any]						  =i.parent
										else:
													combined_roots_list.append((j, False)     )
													snake_case   :							Dict						  =j.parent
        # Insert links between them
							for i in range(len(__lowerCAmelCase     ) - 1     ):
										if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
													snake_case   :							List[str]						  =combined_roots_list[i + 1][0]
													snake_case   :							Union[str, Any]						  =combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
							snake_case   :							Tuple						  =combined_roots_list[0][0]
							while i.parent:
										if (
										    (i.left_tree_size == i.parent.left_tree_size) and (not i.parent.parent)
										) or (
										    i.left_tree_size == i.parent.left_tree_size
										    and i.left_tree_size != i.parent.parent.left_tree_size
										):
													# Neighbouring Nodes
													snake_case   :							Dict						  =i.left
													snake_case   :							List[Any]						  =i.parent.parent

													# Merging trees
													snake_case   :							int						  =i.merge_trees(i.parent     )

													# Updating links
													snake_case   :							int						  =previous_node
													snake_case   :							Dict						  =next_node
													if previous_node:
																snake_case   :							str						  =i
													if next_node:
																snake_case   :							List[str]						  =i
										else:
													snake_case   :							Optional[Any]						  =i.parent
        # Updating self.bottom_root
							while i.left:
										snake_case   :							str						  =i.left
							snake_case   :							Optional[Any]						  =i

							# Update other
							snake_case   :							List[Any]						  =self.size
							snake_case   :							List[str]						  =self.bottom_root
							snake_case   :							Optional[int]						  =self.min_node

							# Return the merged heap
							return self





				def 					__snake_case       (    self    :    List[str],    _snake_case    :    str     ):



							'''simple docstring'''







							if self.size == 0:
										snake_case   :							str						  =Node(__lowerCAmelCase     )
										snake_case   :							List[str]						  =1
										snake_case   :							List[str]						  =self.bottom_root
							else:
										# Create new node
										snake_case   :							Optional[int]						  =Node(__lowerCAmelCase     )

										# Update size
										self.size += 1

										# update min_node
										if val < self.min_node.val:
													snake_case   :							int						  =new_node
										# Put new_node as a bottom_root in heap
										snake_case   :							Any						  =new_node
										snake_case   :							Dict						  =self.bottom_root
										snake_case   :							Tuple						  =new_node

										# Consecutively merge roots with same left_tree_size
										while (
										    self.bottom_root.parent
										    and self.bottom_root.left_tree_size
										    == self.bottom_root.parent.left_tree_size
										):
													# Next node
													snake_case   :							Optional[Any]						  =self.bottom_root.parent.parent

													# Merge
													snake_case   :							int						  =self.bottom_root.merge_trees(self.bottom_root.parent     )

													# Update Links
													snake_case   :							str						  =next_node
													snake_case   :							Dict						  =None
													if next_node:
																snake_case   :							Dict						  =self.bottom_root





				def 					__snake_case       (    self    :    Union[str, Any]     ):



							'''simple docstring'''







							return self.min_node.val





				def 					__snake_case       (    self    :    Any     ):



							'''simple docstring'''







							return self.size == 0





				def 					__snake_case       (    self    :    Tuple     ):



							'''simple docstring'''







							snake_case   :							List[str]						  =self.min_node.val

							# Last element in heap corner case
							if self.size == 1:
										# Update size
										snake_case   :							Optional[int]						  =0

										# Update bottom root
										snake_case   :							str						  =None

										# Update min_node
										snake_case   :							Tuple						  =None

										return min_value
							# No right subtree corner case
							# The structure of the tree implies that this should be the bottom root
							# and there is at least one other root
							if self.min_node.right is None:
										# Update size
										self.size -= 1

										# Update bottom root
										snake_case   :							Any						  =self.bottom_root.parent
										snake_case   :							Tuple						  =None

										# Update min_node
										snake_case   :							Tuple						  =self.bottom_root
										snake_case   :							int						  =self.bottom_root.parent
										while i:
													if i.val < self.min_node.val:
																snake_case   :							Tuple						  =i
													snake_case   :							int						  =i.parent
										return min_value
							# General case
							# Find the BinomialHeap of the right subtree of min_node
							snake_case   :							List[Any]						  =self.min_node.right
							snake_case   :							Dict						  =None
							snake_case   :							Any						  =bottom_of_new
							snake_case   :							Optional[int]						  =1

							# Size, min_node and bottom_root
							while bottom_of_new.left:
										snake_case   :							Dict						  =size_of_new * 2 + 1
										snake_case   :							Optional[int]						  =bottom_of_new.left
										if bottom_of_new.val < min_of_new.val:
													snake_case   :							Any						  =bottom_of_new
        # Corner case of single root on top left path
							if (not self.min_node.left) and (not self.min_node.parent):
										snake_case   :							List[str]						  =size_of_new
										snake_case   :							Optional[Any]						  =bottom_of_new
										snake_case   :							Any						  =min_of_new
										# print("Single root, multiple nodes case")
										return min_value
							# Remaining cases
							# Construct heap of right subtree
							snake_case   :							Any						  =BinomialHeap(
							    bottom_root=__lowerCAmelCase,    min_node=__lowerCAmelCase,    heap_size=__lowerCAmelCase     )

							# Update size
							snake_case   :							int						  =self.size - 1 - size_of_new

							# Neighbour nodes
							snake_case   :							Optional[int]						  =self.min_node.left
							snake_case   :							Optional[int]						  =self.min_node.parent

							# Initialize new bottom_root and min_node
							snake_case   :							List[Any]						  =previous_node or next_node
							snake_case   :							Dict						  =next_node

							# Update links of previous_node and search below for new min_node and
							# bottom_root
							if previous_node:
										snake_case   :							List[str]						  =next_node

										# Update bottom_root and search for min_node below
										snake_case   :							int						  =previous_node
										snake_case   :							str						  =previous_node
										while self.bottom_root.left:
													snake_case   :							Optional[int]						  =self.bottom_root.left
													if self.bottom_root.val < self.min_node.val:
																snake_case   :							Dict						  =self.bottom_root
							if next_node:
										snake_case   :							Dict						  =previous_node

										# Search for new min_node above min_node
										snake_case   :							Optional[Any]						  =next_node
										while i:
													if i.val < self.min_node.val:
																snake_case   :							List[str]						  =i
													snake_case   :							Optional[Any]						  =i.parent
        # Merge heaps
							self.merge_heaps(__lowerCAmelCase     )

							return min_value





				def 					__snake_case       (    self    :    Union[str, Any]     ):



							'''simple docstring'''







							snake_case   :							Optional[Any]						  =self.bottom_root
							while top_root.parent:
										snake_case   :							List[str]						  =top_root.parent
							# preorder
							snake_case   :							Optional[Any]						  =[]
							self.__traversal(__lowerCAmelCase,    __lowerCAmelCase     )
							return heap_pre_order





				def 					__snake_case       (    self    :    Tuple,    _snake_case    :    Dict,    _snake_case    :    Union[str, Any],    _snake_case    :    Dict=0     ):



							'''simple docstring'''







							if curr_node:
										preorder.append((curr_node.val, level)     )
										self.__traversal(curr_node.left,    __lowerCAmelCase,    level + 1     )
										self.__traversal(curr_node.right,    __lowerCAmelCase,    level + 1     )
							else:
										preorder.append(('''#''', level)     )






				def __str__(    self    :    List[str]     ):



							'''simple docstring'''







							if self.is_empty():
										return ""
							snake_case   :							List[str]						  =self.pre_order()

							return "\n".join(('''-''' * level + str(__lowerCAmelCase     )) for value, level in preorder_heap     )


# Unit Tests
if __name__ == "__main__":
						import doctest

						doctest.testmod()










'''simple docstring'''





import os
import unittest

from transformers import is_torch_available
from transformers.testing_utils import require_sentencepiece, require_tokenizers, require_torch, slow, torch_device


if is_torch_available():
      import torch

      from transformers import GPTaLMHeadModel





@require_torch
@require_sentencepiece
@require_tokenizers
class 							lowerCAmelCase_		(	unittest.TestCase						):





    @slow
    @unittest.skip('''Model is not available.'''     )
    def 					__snake_case       (    self    :    List[Any]     ):



       '''simple docstring'''







       snake_case   :							Any						  ='''nvidia/megatron-gpt2-345m/'''
       if "MYDIR" in os.environ:
          snake_case   :							Any						  =os.path.join(os.environ['''MYDIR'''],    _snake_case     )
       snake_case   :							Optional[Any]						  =GPTaLMHeadModel.from_pretrained(_snake_case     )
       model.to(_snake_case     )
       model.half()

       snake_case   :							int						  =torch.tensor(
           [[101, 7_110, 1_005, 1_056, 2_023, 11_333, 17_413, 1_029, 102]],    device=_snake_case,    dtype=torch.long,    )

       with torch.no_grad():
          snake_case   :							Dict						  =model(_snake_case     ).logits

       snake_case   :							Dict						  =torch.Size((1, 9, 50_257)     )
       self.assertEqual(output.shape,    _snake_case     )

       snake_case   :							str						  =torch.tensor(
           [
               4.9414,
               -0.2920,
               -1.2148,
               -4.0273,
               -0.5161,
               -5.2109,
               -1.2412,
               -1.8301,
               -1.7734,
               -4.7148,
               -0.2317,
               -1.0811,
               -2.1777,
               0.4141,
               -3.7969,
               -4.0586,
               -2.5332,
               -3.3809,
               4.3867,
           ],    device=_snake_case,    dtype=torch.half,    )

       for i in range(19     ):
          snake_case  ,    snake_case   :							Tuple						  =8 * i // 17, 2_792 * i  # along the diagonal
          snake_case  ,    snake_case   :							List[str]						  =output[0, r, c], expected_diag[i]
          snake_case   :							Optional[int]						  =f'''row={r} col={c} computed={computed} expected={expected}'''
          self.assertAlmostEqual(_snake_case,    _snake_case,    delta=1E-4,    msg=_snake_case     )





