





'''simple docstring'''







import logging
import math
from functools import partial
from typing import Any, Callable, Dict, Iterable, List, Optional, Sequence, Tuple, Union

import torch

from .tensor_utils import tensor_tree_map, tree_map





def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			Any   ) ->	List[Tuple[int, ...]]:
							UpperCAmelCase_			:      Union[str, Any]     						=  []
							if isinstance(__snake_case,			__snake_case   ):
														for v in tree.values():
																					shapes.extend(_fetch_dims(__snake_case   )   )
							elif isinstance(__snake_case,			(list, tuple)   ):
														for t in tree:
																					shapes.extend(_fetch_dims(__snake_case   )   )
							elif isinstance(__snake_case,			torch.Tensor   ):
														shapes.append(tree.shape   )
							else:
														raise ValueError('''Not supported'''   )

							return shapes





@torch.jit.ignore
def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			Dict,			SCREAMING_SNAKE_CASE__      :			List[Any]   ) ->	Tuple[int, ...]:
							UpperCAmelCase_			:      Any     						=  []
							for d in reversed(__snake_case   ):
														idx.append(flat_idx % d   )
														UpperCAmelCase_			:      Any     						=  flat_idx // d

							return tuple(reversed(__snake_case   )   )





@torch.jit.ignore
def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			Optional[int],			SCREAMING_SNAKE_CASE__      :			int,			SCREAMING_SNAKE_CASE__      :			Tuple,			SCREAMING_SNAKE_CASE__      :			Tuple = None,			SCREAMING_SNAKE_CASE__      :			Union[str, Any] = None,			) ->	List[Tuple[slice, ...]]:





							def reduce_edge_list(SCREAMING_SNAKE_CASE__      :			int   ) -> None:
														UpperCAmelCase_			:      str     						=  True
														for i in range(len(__snake_case   )   ):
																					UpperCAmelCase_			:      Union[str, Any]     						=  -1 * (i + 1)
																					l[reversed_idx] &= tally
																					UpperCAmelCase_			:      Tuple     						=  l[reversed_idx]

							if start_edges is None:
														UpperCAmelCase_			:      Union[str, Any]     						=  [s == 0 for s in start]
														reduce_edge_list(__snake_case   )
							if end_edges is None:
														UpperCAmelCase_			:      Any     						=  [e == (d - 1) for e, d in zip(__snake_case,			__snake_case   )]
														reduce_edge_list(__snake_case   )

							# Base cases. Either start/end are empty and we're done, or the final,
							# one-dimensional tensor can be simply sliced
							if len(__snake_case   ) == 0:
														return [()]
							elif len(__snake_case   ) == 1:
														return [(slice(start[0],			end[0] + 1   ),)]

							UpperCAmelCase_			:      List[str]     						=  []
							UpperCAmelCase_			:      Any     						=  []

							# Dimensions common to start and end can be selected directly
							for s, e in zip(__snake_case,			__snake_case   ):
														if s == e:
																					path_list.append(slice(__snake_case,			s + 1   )   )
														else:
																					break

							UpperCAmelCase_			:      Union[str, Any]     						=  tuple(__snake_case   )
							UpperCAmelCase_			:      Dict     						=  len(__snake_case   )

							# start == end, and we're done
							if divergence_idx == len(__snake_case   ):
														return [path]

							def upper() -> Tuple[Tuple[slice, ...], ...]:
														assert start_edges is not None
														assert end_edges is not None

														UpperCAmelCase_			:      Union[str, Any]     						=  start[divergence_idx]
														return tuple(
														    path + (slice(__snake_case,			sdi + 1   ),) + s
														    for s in _get_minimal_slice_set(
														        start[divergence_idx + 1 :],			[d - 1 for d in dims[divergence_idx + 1 :]],			dims[divergence_idx + 1 :],			start_edges=start_edges[divergence_idx + 1 :],			end_edges=[True for _ in end_edges[divergence_idx + 1 :]],			)   )

							def lower() -> Tuple[Tuple[slice, ...], ...]:
														assert start_edges is not None
														assert end_edges is not None

														UpperCAmelCase_			:      List[Any]     						=  end[divergence_idx]
														return tuple(
														    path + (slice(__snake_case,			edi + 1   ),) + s
														    for s in _get_minimal_slice_set(
														        [0 for _ in start[divergence_idx + 1 :]],			end[divergence_idx + 1 :],			dims[divergence_idx + 1 :],			start_edges=[True for _ in start_edges[divergence_idx + 1 :]],			end_edges=end_edges[divergence_idx + 1 :],			)   )

							# If both start and end are at the edges of the subtree rooted at
							# divergence_idx, we can just select the whole subtree at once
							if start_edges[divergence_idx] and end_edges[divergence_idx]:
														slices.append(path + (slice(start[divergence_idx],			end[divergence_idx] + 1   ),)   )
							# If just start is at the edge, we can grab almost all of the subtree,
							# treating only the ragged bottom edge as an edge case
							elif start_edges[divergence_idx]:
														slices.append(path + (slice(start[divergence_idx],			end[divergence_idx]   ),)   )
														slices.extend(lower()   )
							# Analogous to the previous case, but the top is ragged this time
							elif end_edges[divergence_idx]:
														slices.extend(upper()   )
														slices.append(path + (slice(start[divergence_idx] + 1,			end[divergence_idx] + 1   ),)   )
							# If both sides of the range are ragged, we need to handle both sides
							# separately. If there's contiguous meat in between them, we can index it
							# in one big chunk
							else:
														slices.extend(upper()   )
														UpperCAmelCase_			:      str     						=  end[divergence_idx] - start[divergence_idx]
														if middle_ground > 1:
																					slices.append(path + (slice(start[divergence_idx] + 1,			end[divergence_idx]   ),)   )
														slices.extend(lower()   )

							return slices





@torch.jit.ignore
def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			Tuple,			SCREAMING_SNAKE_CASE__      :			Any,			SCREAMING_SNAKE_CASE__      :			Optional[int],			SCREAMING_SNAKE_CASE__      :			Dict   ) ->	torch.Tensor:
							UpperCAmelCase_			:      str     						=  t.shape[:no_batch_dims]
							UpperCAmelCase_			:      Union[str, Any]     						=  list(_flat_idx_to_idx(__snake_case,			__snake_case   )   )
							# _get_minimal_slice_set is inclusive
							UpperCAmelCase_			:      Tuple     						=  list(_flat_idx_to_idx(flat_end - 1,			__snake_case   )   )

							# Get an ordered list of slices to perform
							UpperCAmelCase_			:      Optional[int]     						=  _get_minimal_slice_set(
							    __snake_case,			__snake_case,			__snake_case,			)

							UpperCAmelCase_			:      Union[str, Any]     						=  [t[s] for s in slices]

							return torch.cat([s.view((-1,) + t.shape[no_batch_dims:]   ) for s in sliced_tensors]   )





def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			str,			SCREAMING_SNAKE_CASE__      :			int,			SCREAMING_SNAKE_CASE__      :			str,			SCREAMING_SNAKE_CASE__      :			Union[str, Any],			SCREAMING_SNAKE_CASE__      :			Optional[Any] = False,			SCREAMING_SNAKE_CASE__      :			Union[str, Any] = None,			SCREAMING_SNAKE_CASE__      :			List[Any] = False,			) ->	Any:





							if not (len(__snake_case   ) > 0):
														raise ValueError('''Must provide at least one input'''   )

							UpperCAmelCase_			:      List[Any]     						=  [shape[:no_batch_dims] for shape in _fetch_dims(__snake_case   )]
							UpperCAmelCase_			:      Union[str, Any]     						=  tuple([max(__snake_case   ) for s in zip(*__snake_case   )]   )

							def _prep_inputs(SCREAMING_SNAKE_CASE__      :			Dict   ) -> torch.Tensor:
														if not low_mem:
																					if not sum(t.shape[:no_batch_dims]   ) == no_batch_dims:
																												UpperCAmelCase_			:      int     						=  t.expand(orig_batch_dims + t.shape[no_batch_dims:]   )
																					UpperCAmelCase_			:      Optional[Any]     						=  t.reshape(-1,			*t.shape[no_batch_dims:]   )
														else:
																					UpperCAmelCase_			:      Optional[Any]     						=  t.expand(orig_batch_dims + t.shape[no_batch_dims:]   )
														return t

							UpperCAmelCase_			:      str     						=  tensor_tree_map(_prep_inputs,			__snake_case   )
							UpperCAmelCase_			:      Optional[int]     						=  None
							if _out is not None:
														UpperCAmelCase_			:      int     						=  tensor_tree_map(lambda SCREAMING_SNAKE_CASE__   : t.view([-1] + list(t.shape[no_batch_dims:]   )   ),			_out   )

							UpperCAmelCase_			:      Optional[Any]     						=  1
							for d in orig_batch_dims:
														flat_batch_dim *= d

							UpperCAmelCase_			:      Dict     						=  flat_batch_dim // chunk_size + (flat_batch_dim % chunk_size != 0)

							def _select_chunk(SCREAMING_SNAKE_CASE__      :			str   ) -> torch.Tensor:
														return t[i : i + chunk_size] if t.shape[0] != 1 else t

							UpperCAmelCase_			:      List[Any]     						=  0
							UpperCAmelCase_			:      Optional[Any]     						=  prepped_outputs
							for _ in range(__snake_case   ):
														# Chunk the input
														if not low_mem:
																					UpperCAmelCase_			:      Optional[Any]     						=  _select_chunk
														else:
																					UpperCAmelCase_			:      Union[str, Any]     						=  partial(
																					    _chunk_slice,			flat_start=__snake_case,			flat_end=min(__snake_case,			i + chunk_size   ),			no_batch_dims=len(__snake_case   ),			)

														UpperCAmelCase_			:      List[str]     						=  tensor_tree_map(__snake_case,			__snake_case   )

														# Run the layer on the chunk
														UpperCAmelCase_			:      int     						=  layer(**__snake_case   )

														# Allocate space for the output
														if out is None:
																					UpperCAmelCase_			:      Union[str, Any]     						=  tensor_tree_map(lambda SCREAMING_SNAKE_CASE__   : t.new_zeros((flat_batch_dim,) + t.shape[1:]   ),			__snake_case   )

														# Put the chunk in its pre-allocated space
														if isinstance(__snake_case,			__snake_case   ):

																					def assign(SCREAMING_SNAKE_CASE__      :			Any,			SCREAMING_SNAKE_CASE__      :			Dict   ) -> None:
																												for k, v in da.items():
																																			if isinstance(__snake_case,			__snake_case   ):
																																										assign(__snake_case,			da[k]   )
																																			else:
																																										if _add_into_out:
																																																	v[i : i + chunk_size] += da[k]
																																										else:
																																																	UpperCAmelCase_			:      List[Any]     						=  da[k]

																					assign(__snake_case,			__snake_case   )
														elif isinstance(__snake_case,			__snake_case   ):
																					for xa, xa in zip(__snake_case,			__snake_case   ):
																												if _add_into_out:
																																			xa[i : i + chunk_size] += xa
																												else:
																																			UpperCAmelCase_			:      int     						=  xa
														elif isinstance(__snake_case,			torch.Tensor   ):
																					if _add_into_out:
																												out[i : i + chunk_size] += output_chunk
																					else:
																												UpperCAmelCase_			:      Union[str, Any]     						=  output_chunk
														else:
																					raise ValueError('''Not supported'''   )

														i += chunk_size

							UpperCAmelCase_			:      Optional[int]     						=  tensor_tree_map(lambda SCREAMING_SNAKE_CASE__   : t.view(orig_batch_dims + t.shape[1:]   ),			__snake_case   )

							return out


class 					__a      :

							def __init__(							self							:     Optional[Any]       ,     __magic_name__							:     int = 5_12       ,     )					->       List[Any]:







														"""simple docstring"""
														UpperCAmelCase_			:      List[str]     						=  max_chunk_size
														UpperCAmelCase_			:      Optional[int]     						=  None
														UpperCAmelCase_			:      Union[str, Any]     						=  None

							def     UpperCAmelCase__	(							self							:     Any       ,     __magic_name__							:     Tuple       ,     __magic_name__							:     List[Any]       ,     __magic_name__							:     Optional[int]   )					->       int:







														"""simple docstring"""
														logging.info('''Tuning chunk size...'''   )

														if min_chunk_size >= self.max_chunk_size:
																					return min_chunk_size

														UpperCAmelCase_			:      Optional[int]     						=  [2**l for l in range(int(math.log(self.max_chunk_size       ,     2   )   ) + 1   )]
														UpperCAmelCase_			:      Any     						=  [c for c in candidates if c > min_chunk_size]
														UpperCAmelCase_			:      Dict     						=  [min_chunk_size] + candidates
														candidates[-1] += 4

														def test_chunk_size(__magic_name__							:     Dict   ) -> bool:
																					try:
																												with torch.no_grad():
																																			fn(*__a       ,     chunk_size=__a   )
																												return True
																					except RuntimeError:
																												return False

														UpperCAmelCase_			:      Tuple     						=  0
														UpperCAmelCase_			:      str     						=  len(__a   ) - 1
														while i > min_viable_chunk_size_index:
																					UpperCAmelCase_			:      Any     						=  test_chunk_size(candidates[i]   )
																					if not viable:
																												UpperCAmelCase_			:      str     						=  (min_viable_chunk_size_index + i) // 2
																					else:
																												UpperCAmelCase_			:      Any     						=  i
																												UpperCAmelCase_			:      int     						=  (i + len(__a   ) - 1) // 2

														return candidates[min_viable_chunk_size_index]

							def     UpperCAmelCase__	(							self							:     Union[str, Any]       ,     __magic_name__							:     List[Any]       ,     __magic_name__							:     Union[str, Any]   )					->       bool:







														"""simple docstring"""
														UpperCAmelCase_			:      Dict     						=  True
														for aa, aa in zip(__a       ,     __a   ):
																					assert type(__a   ) == type(__a   )
																					if isinstance(__a       ,     (list, tuple)   ):
																												consistent &= self._compare_arg_caches(__a       ,     __a   )
																					elif isinstance(__a       ,     __a   ):
																												UpperCAmelCase_			:      List[Any]     						=  [v for _, v in sorted(aa.items()       ,     key=lambda __magic_name__   : x[0]   )]
																												UpperCAmelCase_			:      Tuple     						=  [v for _, v in sorted(aa.items()       ,     key=lambda __magic_name__   : x[0]   )]
																												consistent &= self._compare_arg_caches(__a       ,     __a   )
																					else:
																												consistent &= aa == aa

														return consistent



							def     UpperCAmelCase__	(							self							:     Optional[int]       ,     __magic_name__							:     Optional[int]       ,     __magic_name__							:     int       ,     __magic_name__							:     Optional[int]       ,     )					->       int:







														"""simple docstring"""
														UpperCAmelCase_			:      Any     						=  True
														UpperCAmelCase_			:      Optional[Any]     						=  tree_map(lambda __magic_name__   : a.shape if isinstance(__a       ,     torch.Tensor   ) else a       ,     __a       ,     __a   )
														if self.cached_arg_data is not None:
																					# If args have changed shape/value, we need to re-tune
																					assert len(self.cached_arg_data   ) == len(__a   )
																					UpperCAmelCase_			:      Optional[Any]     						=  self._compare_arg_caches(self.cached_arg_data       ,     __a   )
														else:
																					# Otherwise, we can reuse the precomputed value
																					UpperCAmelCase_			:      Tuple     						=  False

														if not consistent:
																					UpperCAmelCase_			:      Union[str, Any]     						=  self._determine_favorable_chunk_size(
																					    __a       ,     __a       ,     __a       ,     )
																					UpperCAmelCase_			:      Optional[Any]     						=  arg_data

														assert self.cached_chunk_size is not None

														return self.cached_chunk_size












'''simple docstring'''







from collections.abc import Iterable
from typing import Any


class 					__a      :

							def __init__(							self							:     Optional[Any]       ,     __magic_name__							:     int | None = None   )					->       Tuple:







													"""simple docstring"""
													UpperCAmelCase_			:      List[str]     						=  value
													UpperCAmelCase_			:      Node | None     						=  None  # Added in order to delete a node easier
													UpperCAmelCase_			:      Node | None     						=  None
													UpperCAmelCase_			:      Node | None     						=  None



							def __repr__(							self							:     List[str]   )					->       str:







													"""simple docstring"""
													from pprint import pformat

													if self.left is None and self.right is None:
																			return str(self.value   )
													return pformat({F"""{self.value}""": (self.left, self.right)}       ,     indent=1   )





class 					__a      :

							def __init__(							self							:     int       ,     __magic_name__							:     Node | None = None   )					->       Optional[int]:







													"""simple docstring"""
													UpperCAmelCase_			:      str     						=  root

							def __str__(							self							:     Any   )					->       str:







													"""simple docstring"""
													return str(self.root   )

							def     UpperCAmelCase__	(							self							:     Any       ,     __magic_name__							:     Node       ,     __magic_name__							:     Node | None   )					->       None:







													"""simple docstring"""
													if new_children is not None:  # reset its kids
																			UpperCAmelCase_			:      Dict     						=  node.parent
													if node.parent is not None:  # reset its parent
																			if self.is_right(__magic_name__   ):  # If it is the right children
																									UpperCAmelCase_			:      Optional[Any]     						=  new_children
																			else:
																									UpperCAmelCase_			:      Optional[int]     						=  new_children
													else:
																			UpperCAmelCase_			:      List[str]     						=  new_children

							def     UpperCAmelCase__	(							self							:     List[str]       ,     __magic_name__							:     Node   )					->       bool:







													"""simple docstring"""
													if node.parent and node.parent.right:
																			return node == node.parent.right
													return False

							def     UpperCAmelCase__	(							self							:     Union[str, Any]   )					->       bool:







													"""simple docstring"""
													return self.root is None

							def     UpperCAmelCase__	(							self							:     Any       ,     __magic_name__							:     str   )					->       None:







													"""simple docstring"""
													UpperCAmelCase_			:      Tuple     						=  Node(__magic_name__   )  # create a new Node
													if self.empty():  # if Tree is empty
																			UpperCAmelCase_			:      List[Any]     						=  new_node  # set its root
													else:  # Tree is not empty
																			UpperCAmelCase_			:      str     						=  self.root  # from root
																			if parent_node is None:
																									return
																			while True:  # While we don't get to a leaf
																									if value < parent_node.value:  # We go left
																															if parent_node.left is None:
																																					UpperCAmelCase_			:      Union[str, Any]     						=  new_node  # We insert the new node in a leaf
																																					break
																															else:
																																					UpperCAmelCase_			:      List[Any]     						=  parent_node.left
																									else:
																															if parent_node.right is None:
																																					UpperCAmelCase_			:      List[Any]     						=  new_node
																																					break
																															else:
																																					UpperCAmelCase_			:      Union[str, Any]     						=  parent_node.right
																			UpperCAmelCase_			:      Union[str, Any]     						=  parent_node

							def     UpperCAmelCase__	(							self							:     Optional[Any]       ,     *__magic_name__							:     List[str]   )					->       None:







													"""simple docstring"""
													for value in values:
																			self.__insert(__magic_name__   )

							def     UpperCAmelCase__	(							self							:     Dict       ,     __magic_name__							:     int   )					->       Node | None:







													"""simple docstring"""
													if self.empty():
																			raise IndexError('''Warning: Tree is empty! please use another.'''   )
													else:
																			UpperCAmelCase_			:      str     						=  self.root
																			# use lazy evaluation here to avoid NoneType Attribute error
																			while node is not None and node.value is not value:
																									UpperCAmelCase_			:      List[str]     						=  node.left if value < node.value else node.right
																			return node

							def     UpperCAmelCase__	(							self							:     Optional[int]       ,     __magic_name__							:     Node | None = None   )					->       Node | None:







													"""simple docstring"""
													if node is None:
																			if self.root is None:
																									return None
																			UpperCAmelCase_			:      Dict     						=  self.root

													if not self.empty():
																			while node.right is not None:
																									UpperCAmelCase_			:      Any     						=  node.right
													return node

							def     UpperCAmelCase__	(							self							:     Dict       ,     __magic_name__							:     Node | None = None   )					->       Node | None:







													"""simple docstring"""
													if node is None:
																			UpperCAmelCase_			:      Optional[int]     						=  self.root
													if self.root is None:
																			return None
													if not self.empty():
																			UpperCAmelCase_			:      Union[str, Any]     						=  self.root
																			while node.left is not None:
																									UpperCAmelCase_			:      Dict     						=  node.left
													return node

							def     UpperCAmelCase__	(							self							:     Tuple       ,     __magic_name__							:     int   )					->       None:







													"""simple docstring"""
													UpperCAmelCase_			:      List[str]     						=  self.search(__magic_name__   )  # Look for the node with that label
													if node is not None:
																			if node.left is None and node.right is None:  # If it has no children
																									self.__reassign_nodes(__magic_name__       ,     __magic_name__   )
																			elif node.left is None:  # Has only right children
																									self.__reassign_nodes(__magic_name__       ,     node.right   )
																			elif node.right is None:  # Has only left children
																									self.__reassign_nodes(__magic_name__       ,     node.left   )
																			else:
																									UpperCAmelCase_			:      List[str]     						=  self.get_max(
																									    node.left   )  # Gets the max value of the left branch
																									self.remove(tmp_node.value   )  # type: ignore
																									UpperCAmelCase_			:      Optional[int]     						=  (
																									    tmp_node.value  # type: ignore
																									)  # Assigns the value to the node to delete and keep tree structure

							def     UpperCAmelCase__	(							self							:     List[Any]       ,     __magic_name__							:     Node | None   )					->       Iterable:







													"""simple docstring"""
													if node is not None:
																			yield node  # Preorder Traversal
																			yield from self.preorder_traverse(node.left   )
																			yield from self.preorder_traverse(node.right   )

							def     UpperCAmelCase__	(							self							:     List[Any]       ,     __magic_name__							:     List[Any]=None   )					->       Any:







													"""simple docstring"""
													if traversal_function is None:
																			return self.preorder_traverse(self.root   )
													else:
																			return traversal_function(self.root   )

							def     UpperCAmelCase__	(							self							:     Optional[int]       ,     __magic_name__							:     list       ,     __magic_name__							:     Node | None   )					->       None:







													"""simple docstring"""
													if node:
																			self.inorder(__magic_name__       ,     node.left   )
																			arr.append(node.value   )
																			self.inorder(__magic_name__       ,     node.right   )



							def     UpperCAmelCase__	(							self							:     Tuple       ,     __magic_name__							:     int       ,     __magic_name__							:     Node   )					->       int:







													"""simple docstring"""
													UpperCAmelCase_			:      list[int]     						=  []
													self.inorder(__magic_name__       ,     __magic_name__   )  # append all values to list using inorder traversal
													return arr[k - 1]





def        lowerCamelCase_      (  SCREAMING_SNAKE_CASE__      :			Node | None   ) ->	list[Node]:
						UpperCAmelCase_			:      Any     						=  []
						if curr_node is not None:
												UpperCAmelCase_			:      Any     						=  postorder(curr_node.left   ) + postorder(curr_node.right   ) + [curr_node]
						return node_list





def        lowerCamelCase_      (  ) ->	None:
						UpperCAmelCase_			:      str     						=  (8, 3, 6, 1, 10, 14, 13, 4, 7)
						UpperCAmelCase_			:      Tuple     						=  BinarySearchTree()
						for i in testlist:
												t.insert(SCREAMING_SNAKE_CASE__   )

						# Prints all the elements of the list in order traversal
						print(SCREAMING_SNAKE_CASE__   )

						if t.search(6   ) is not None:
												print('''The value 6 exists'''   )
						else:
												print('''The value 6 doesn\'t exist'''   )

						if t.search(-1   ) is not None:
												print('''The value -1 exists'''   )
						else:
												print('''The value -1 doesn\'t exist'''   )

						if not t.empty():
												print('''Max Value: ''',			t.get_max().value   )  # type: ignore
												print('''Min Value: ''',			t.get_min().value   )  # type: ignore

						for i in testlist:
												t.remove(SCREAMING_SNAKE_CASE__   )
												print(SCREAMING_SNAKE_CASE__   )


if __name__ == "__main__":
					import doctest

					doctest.testmod(verbose=True)





