


'''simple docstring'''


class 					lowercase__						:





	'''simple docstring'''


	def __init__(					self					,      __snake_case						):
					_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   val
					# Number of nodes in left subtree
					_SCREAMING_SNAKE_CASE				: Any  	=   0
					_SCREAMING_SNAKE_CASE				: List[str]  	=   None
					_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   None
					_SCREAMING_SNAKE_CASE				: str  	=   None






	def UpperCAmelCase_			(					self					,      __snake_case						):
					assert self.left_tree_size == other.left_tree_size, "Unequal Sizes of Blocks"

					if self.val < other.val:
									_SCREAMING_SNAKE_CASE				: str  	=   self.right
									_SCREAMING_SNAKE_CASE				: Any  	=   None
									if self.right:
													_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   other
									_SCREAMING_SNAKE_CASE				: str  	=   other
									_SCREAMING_SNAKE_CASE				: str  	=   self.left_tree_size * 2 + 1
									return self
					else:
									_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   other.right
									_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   None
									if other.right:
													_SCREAMING_SNAKE_CASE				: Tuple  	=   self
									_SCREAMING_SNAKE_CASE				: Dict  	=   self
									_SCREAMING_SNAKE_CASE				: Tuple  	=   other.left_tree_size * 2 + 1
									return other





class 					lowercase__						:





	'''simple docstring'''


	def __init__(					self					,      __snake_case=None					,      __snake_case=None					,      __snake_case=0						):
					_SCREAMING_SNAKE_CASE				: List[Any]  	=   heap_size
					_SCREAMING_SNAKE_CASE				: List[Any]  	=   bottom_root
					_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   min_node






	def UpperCAmelCase_			(					self					,      __snake_case						):

					# Empty heaps corner cases
					if other.size == 0:
									return None
					if self.size == 0:
									_SCREAMING_SNAKE_CASE				: Dict  	=   other.size
									_SCREAMING_SNAKE_CASE				: Dict  	=   other.bottom_root
									_SCREAMING_SNAKE_CASE				: int  	=   other.min_node
									return None
					# Update size
					_SCREAMING_SNAKE_CASE				: Any  	=   self.size + other.size

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

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

													# Merging trees
													_SCREAMING_SNAKE_CASE				: Tuple  	=   i.merge_trees(i.parent						)

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

					# Update other
					_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   self.size
					_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   self.bottom_root
					_SCREAMING_SNAKE_CASE				: Any  	=   self.min_node

					# Return the merged heap
					return self






	def UpperCAmelCase_			(					self					,      __snake_case						):
					if self.size == 0:
									_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   Node(__snake_case						)
									_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   1
									_SCREAMING_SNAKE_CASE				: Optional[int]  	=   self.bottom_root
					else:
									# Create new node
									_SCREAMING_SNAKE_CASE				: Tuple  	=   Node(__snake_case						)

									# Update size
									self.size += 1

									# update min_node
									if val < self.min_node.val:
													_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   new_node
									# Put new_node as a bottom_root in heap
									_SCREAMING_SNAKE_CASE				: Tuple  	=   new_node
									_SCREAMING_SNAKE_CASE				: str  	=   self.bottom_root
									_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   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
													_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   self.bottom_root.parent.parent

													# Merge
													_SCREAMING_SNAKE_CASE				: Any  	=   self.bottom_root.merge_trees(self.bottom_root.parent						)

													# Update Links
													_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   next_node
													_SCREAMING_SNAKE_CASE				: Dict  	=   None
													if next_node:
																	_SCREAMING_SNAKE_CASE				: List[str]  	=   self.bottom_root






	def UpperCAmelCase_			(					self						):
					return self.min_node.val






	def UpperCAmelCase_			(					self						):
					return self.size == 0






	def UpperCAmelCase_			(					self						):
					_SCREAMING_SNAKE_CASE				: str  	=   self.min_node.val

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

									# Update bottom root
									_SCREAMING_SNAKE_CASE				: List[Any]  	=   None

									# Update min_node
									_SCREAMING_SNAKE_CASE				: Any  	=   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
									_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   self.bottom_root.parent
									_SCREAMING_SNAKE_CASE				: Tuple  	=   None

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

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

					# Update size
					_SCREAMING_SNAKE_CASE				: Optional[int]  	=   self.size - 1 - size_of_new

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

					# Initialize new bottom_root and min_node
					_SCREAMING_SNAKE_CASE				: Union[str, Any]  	=   previous_node or next_node
					_SCREAMING_SNAKE_CASE				: Optional[Any]  	=   next_node

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

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

									# Search for new min_node above min_node
									_SCREAMING_SNAKE_CASE				: Tuple  	=   next_node
									while i:
													if i.val < self.min_node.val:
																	_SCREAMING_SNAKE_CASE				: str  	=   i
													_SCREAMING_SNAKE_CASE				: Optional[int]  	=   i.parent
        # Merge heaps
					self.merge_heaps(__snake_case						)

					return min_value






	def UpperCAmelCase_			(					self						):
					_SCREAMING_SNAKE_CASE				: Optional[int]  	=   self.bottom_root
					while top_root.parent:
									_SCREAMING_SNAKE_CASE				: Any  	=   top_root.parent
					# preorder
					_SCREAMING_SNAKE_CASE				: Tuple  	=   []
					self.__traversal(__snake_case					,      __snake_case						)
					return heap_pre_order






	def UpperCAmelCase_			(					self					,      __snake_case					,      __snake_case					,      __snake_case=0						):
					if curr_node:
									preorder.append((curr_node.val, level)						)
									self.__traversal(curr_node.left					,      __snake_case					,      level + 1						)
									self.__traversal(curr_node.right					,      __snake_case					,      level + 1						)
					else:
									preorder.append(("""#""", level)						)






	def __str__(					self						):
					if self.is_empty():
									return ""
					_SCREAMING_SNAKE_CASE				: List[str]  	=   self.pre_order()

					return "\n".join(("""-""" * level + str(__snake_case						)) 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_torch_available


UpperCAmelCase_	:     Any							     =	{
    'configuration_musicgen': [
        'MUSICGEN_PRETRAINED_CONFIG_ARCHIVE_MAP',
        'MusicgenConfig',
        'MusicgenDecoderConfig',
    ],
    'processing_musicgen': ['MusicgenProcessor'],
}

try:
				if not is_torch_available():
								raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
				pass
else:
				UpperCAmelCase_	:     Any							     =	[
				    'MUSICGEN_PRETRAINED_MODEL_ARCHIVE_LIST',
				    'MusicgenForConditionalGeneration',
				    'MusicgenForCausalLM',
				    'MusicgenModel',
				    'MusicgenPreTrainedModel',
				]

if TYPE_CHECKING:
				from .configuration_musicgen import (
				    MUSICGEN_PRETRAINED_CONFIG_ARCHIVE_MAP,
				    MusicgenConfig,
				    MusicgenDecoderConfig,
				)
				from .processing_musicgen import MusicgenProcessor

				try:
								if not is_torch_available():
												raise OptionalDependencyNotAvailable()
				except OptionalDependencyNotAvailable:
								pass
				else:
								from .modeling_musicgen import (
								    MUSICGEN_PRETRAINED_MODEL_ARCHIVE_LIST,
								    MusicgenForCausalLM,
								    MusicgenForConditionalGeneration,
								    MusicgenModel,
								    MusicgenPreTrainedModel,
								)

else:
				import sys

				UpperCAmelCase_	:     Tuple							     =	_LazyModule(__name__, globals()['__file__'], _import_structure, module_spec=__spec__)




