


"""simple docstring"""



class       __a	:







				def __init__(   self			,  UpperCAmelCase      ):

					'''simple docstring'''






					lowerCAmelCase_			       = val
					# Number of nodes in left subtree
					lowerCAmelCase_			       = 0
					lowerCAmelCase_			       = None
					lowerCAmelCase_			       = None
					lowerCAmelCase_			       = None







				def     lowerCamelCase_    (   self			,  UpperCAmelCase      ):

					'''simple docstring'''






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

					if self.val < other.val:
						lowerCAmelCase_			       = self.right
						lowerCAmelCase_			       = None
						if self.right:
							lowerCAmelCase_			       = other
						lowerCAmelCase_			       = other
						lowerCAmelCase_			       = self.left_tree_size * 2 + 1
						return self
					else:
						lowerCAmelCase_			       = other.right
						lowerCAmelCase_			       = None
						if other.right:
							lowerCAmelCase_			       = self
						lowerCAmelCase_			       = self
						lowerCAmelCase_			       = other.left_tree_size * 2 + 1
						return other







class       __a	:







				def __init__(   self			,  UpperCAmelCase=None			,  UpperCAmelCase=None			,  UpperCAmelCase=0      ):

					'''simple docstring'''






					lowerCAmelCase_			       = heap_size
					lowerCAmelCase_			       = bottom_root
					lowerCAmelCase_			       = min_node







				def     lowerCamelCase_    (   self			,  UpperCAmelCase      ):

					'''simple docstring'''






					if other.size == 0:
						return None
					if self.size == 0:
						lowerCAmelCase_			       = other.size
						lowerCAmelCase_			       = other.bottom_root
						lowerCAmelCase_			       = other.min_node
						return None
					# Update size
					lowerCAmelCase_			       = self.size + other.size

					# Update min.node
					if self.min_node.val > other.min_node.val:
						lowerCAmelCase_			       = other.min_node
					# Merge

					# Order roots by left_subtree_size
					lowerCAmelCase_			       = []
					lowerCAmelCase_       ,  lowerCAmelCase_			       = 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)      )
							lowerCAmelCase_			       = i.parent
						else:
							combined_roots_list.append((j, False)      )
							lowerCAmelCase_			       = j.parent
        # Insert links between them
					for i in range(len(UpperCAmelCase      ) - 1      ):
						if combined_roots_list[i][1] != combined_roots_list[i + 1][1]:
							lowerCAmelCase_			       = combined_roots_list[i + 1][0]
							lowerCAmelCase_			       = combined_roots_list[i][0]
        # Consecutively merge roots with same left_tree_size
					lowerCAmelCase_			       = 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
							lowerCAmelCase_			       = i.left
							lowerCAmelCase_			       = i.parent.parent

							# Merging trees
							lowerCAmelCase_			       = i.merge_trees(i.parent      )

							# Updating links
							lowerCAmelCase_			       = previous_node
							lowerCAmelCase_			       = next_node
							if previous_node:
								lowerCAmelCase_			       = i
							if next_node:
								lowerCAmelCase_			       = i
						else:
							lowerCAmelCase_			       = i.parent
        # Updating self.bottom_root
					while i.left:
						lowerCAmelCase_			       = i.left
					lowerCAmelCase_			       = i

					# Update other
					lowerCAmelCase_			       = self.size
					lowerCAmelCase_			       = self.bottom_root
					lowerCAmelCase_			       = self.min_node

					# Return the merged heap
					return self







				def     lowerCamelCase_    (   self			,  UpperCAmelCase      ):

					'''simple docstring'''






					if self.size == 0:
						lowerCAmelCase_			       = Node(UpperCAmelCase      )
						lowerCAmelCase_			       = 1
						lowerCAmelCase_			       = self.bottom_root
					else:
						# Create new node
						lowerCAmelCase_			       = Node(UpperCAmelCase      )

						# Update size
						self.size += 1

						# update min_node
						if val < self.min_node.val:
							lowerCAmelCase_			       = new_node
						# Put new_node as a bottom_root in heap
						lowerCAmelCase_			       = new_node
						lowerCAmelCase_			       = self.bottom_root
						lowerCAmelCase_			       = 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
							lowerCAmelCase_			       = self.bottom_root.parent.parent

							# Merge
							lowerCAmelCase_			       = self.bottom_root.merge_trees(self.bottom_root.parent      )

							# Update Links
							lowerCAmelCase_			       = next_node
							lowerCAmelCase_			       = None
							if next_node:
								lowerCAmelCase_			       = self.bottom_root







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					return self.min_node.val







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					return self.size == 0







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					lowerCAmelCase_			       = self.min_node.val

					# Last element in heap corner case
					if self.size == 1:
						# Update size
						lowerCAmelCase_			       = 0

						# Update bottom root
						lowerCAmelCase_			       = None

						# Update min_node
						lowerCAmelCase_			       = 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
						lowerCAmelCase_			       = self.bottom_root.parent
						lowerCAmelCase_			       = None

						# Update min_node
						lowerCAmelCase_			       = self.bottom_root
						lowerCAmelCase_			       = self.bottom_root.parent
						while i:
							if i.val < self.min_node.val:
								lowerCAmelCase_			       = i
							lowerCAmelCase_			       = i.parent
						return min_value
					# General case
					# Find the BinomialHeap of the right subtree of min_node
					lowerCAmelCase_			       = self.min_node.right
					lowerCAmelCase_			       = None
					lowerCAmelCase_			       = bottom_of_new
					lowerCAmelCase_			       = 1

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

					# Update size
					lowerCAmelCase_			       = self.size - 1 - size_of_new

					# Neighbour nodes
					lowerCAmelCase_			       = self.min_node.left
					lowerCAmelCase_			       = self.min_node.parent

					# Initialize new bottom_root and min_node
					lowerCAmelCase_			       = previous_node or next_node
					lowerCAmelCase_			       = next_node

					# Update links of previous_node and search below for new min_node and
					# bottom_root
					if previous_node:
						lowerCAmelCase_			       = next_node

						# Update bottom_root and search for min_node below
						lowerCAmelCase_			       = previous_node
						lowerCAmelCase_			       = previous_node
						while self.bottom_root.left:
							lowerCAmelCase_			       = self.bottom_root.left
							if self.bottom_root.val < self.min_node.val:
								lowerCAmelCase_			       = self.bottom_root
					if next_node:
						lowerCAmelCase_			       = previous_node

						# Search for new min_node above min_node
						lowerCAmelCase_			       = next_node
						while i:
							if i.val < self.min_node.val:
								lowerCAmelCase_			       = i
							lowerCAmelCase_			       = i.parent
        # Merge heaps
					self.merge_heaps(UpperCAmelCase      )

					return min_value







				def     lowerCamelCase_    (   self      ):

					'''simple docstring'''






					lowerCAmelCase_			       = self.bottom_root
					while top_root.parent:
						lowerCAmelCase_			       = top_root.parent
					# preorder
					lowerCAmelCase_			       = []
					self.__traversal(UpperCAmelCase			,  UpperCAmelCase      )
					return heap_pre_order







				def     lowerCamelCase_    (   self			,  UpperCAmelCase			,  UpperCAmelCase			,  UpperCAmelCase=0      ):

					'''simple docstring'''






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







				def __str__(   self      ):

					'''simple docstring'''






					if self.is_empty():
						return ""
					lowerCAmelCase_			       = self.pre_order()

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


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

		doctest.testmod()



"""simple docstring"""



from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_sentencepiece_available,
    is_tf_available,
    is_tokenizers_available,
    is_torch_available,
)


lowercase_							 =       {'configuration_pegasus': ['PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP', 'PegasusConfig']}

try:
		if not is_sentencepiece_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowercase_							 =       ['PegasusTokenizer']

try:
		if not is_tokenizers_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowercase_							 =       ['PegasusTokenizerFast']

try:
		if not is_torch_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowercase_							 =       [
		    'PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST',
		    'PegasusForCausalLM',
		    'PegasusForConditionalGeneration',
		    'PegasusModel',
		    'PegasusPreTrainedModel',
		]

try:
		if not is_tf_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowercase_							 =       [
		    'TFPegasusForConditionalGeneration',
		    'TFPegasusModel',
		    'TFPegasusPreTrainedModel',
		]

try:
		if not is_flax_available():
				raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
		pass
else:
		lowercase_							 =       [
		    'FlaxPegasusForConditionalGeneration',
		    'FlaxPegasusModel',
		    'FlaxPegasusPreTrainedModel',
		]


if TYPE_CHECKING:
		from .configuration_pegasus import PEGASUS_PRETRAINED_CONFIG_ARCHIVE_MAP, PegasusConfig

		try:
				if not is_sentencepiece_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .tokenization_pegasus import PegasusTokenizer

		try:
				if not is_tokenizers_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .tokenization_pegasus_fast import PegasusTokenizerFast

		try:
				if not is_torch_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_pegasus import (
				    PEGASUS_PRETRAINED_MODEL_ARCHIVE_LIST,
				    PegasusForCausalLM,
				    PegasusForConditionalGeneration,
				    PegasusModel,
				    PegasusPreTrainedModel,
				)

		try:
				if not is_tf_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_tf_pegasus import TFPegasusForConditionalGeneration, TFPegasusModel, TFPegasusPreTrainedModel

		try:
				if not is_flax_available():
						raise OptionalDependencyNotAvailable()
		except OptionalDependencyNotAvailable:
				pass
		else:
				from .modeling_flax_pegasus import (
				    FlaxPegasusForConditionalGeneration,
				    FlaxPegasusModel,
				    FlaxPegasusPreTrainedModel,
				)

else:
		import sys

		lowercase_							 =       _LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)