





'''simple docstring'''






from __future__ import annotations

import unittest
from collections.abc import Iterator




class    _A   :

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


					"""simple docstring"""

					__snake_case				:			Optional[Any]       			=    label
					__snake_case				:			Optional[Any]       			=    parent
					__snake_case				:			Node | None       			=    None
					__snake_case				:			Node | None       			=    None





class    _A   :

		def __init__(      self				:      Optional[Any] )				->						None:


					"""simple docstring"""

					__snake_case				:			Node | None       			=    None

		def   lowercase__    (      self				:      Tuple )				->						None:


					"""simple docstring"""

					__snake_case				:			Optional[Any]       			=    None

		def   lowercase__    (      self				:      str )				->						bool:


					"""simple docstring"""

					return self.root is None

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


					"""simple docstring"""

					__snake_case				:			List[str]       			=    self._put(self.root     ,			__magic_name__ )

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


					"""simple docstring"""

					if node is None:
								__snake_case				:			Dict       			=    Node(__magic_name__     ,			__magic_name__ )
					else:
								if label < node.label:
											__snake_case				:			Dict       			=    self._put(node.left     ,			__magic_name__     ,			__magic_name__ )
								elif label > node.label:
											__snake_case				:			List[Any]       			=    self._put(node.right     ,			__magic_name__     ,			__magic_name__ )
								else:
											__snake_case				:			Optional[Any]       			=    f'''Node with label {label} already exists'''
											raise Exception(__magic_name__ )

					return node

		def   lowercase__    (      self				:      str     ,			__magic_name__				:      int )				->						Node:


					"""simple docstring"""

					return self._search(self.root     ,			__magic_name__ )

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


					"""simple docstring"""

					if node is None:
								__snake_case				:			Optional[Any]       			=    f'''Node with label {label} does not exist'''
								raise Exception(__magic_name__ )
					else:
								if label < node.label:
											__snake_case				:			List[Any]       			=    self._search(node.left     ,			__magic_name__ )
								elif label > node.label:
											__snake_case				:			int       			=    self._search(node.right     ,			__magic_name__ )

					return node

		def   lowercase__    (      self				:      Any     ,			__magic_name__				:      int )				->						None:


					"""simple docstring"""

					__snake_case				:			Optional[int]       			=    self.search(__magic_name__ )
					if node.right and node.left:
								__snake_case				:			Dict       			=    self._get_lowest_node(node.right )
								__snake_case				:			Union[str, Any]       			=    node.left
								__snake_case				:			List[str]       			=    node.right
								__snake_case				:			str       			=    lowest_node
								if node.right:
											__snake_case				:			Optional[int]       			=    lowest_node
								self._reassign_nodes(__magic_name__     ,			__magic_name__ )
					elif not node.right and node.left:
								self._reassign_nodes(__magic_name__     ,			node.left )
					elif node.right and not node.left:
								self._reassign_nodes(__magic_name__     ,			node.right )
					else:
								self._reassign_nodes(__magic_name__     ,			__magic_name__ )

		def   lowercase__    (      self				:      List[str]     ,			__magic_name__				:      Node     ,			__magic_name__				:      Node | None )				->						None:


					"""simple docstring"""

					if new_children:
								__snake_case				:			Optional[int]       			=    node.parent

					if node.parent:
								if node.parent.right == node:
											__snake_case				:			Tuple       			=    new_children
								else:
											__snake_case				:			List[Any]       			=    new_children
					else:
								__snake_case				:			List[str]       			=    new_children

		def   lowercase__    (      self				:      int     ,			__magic_name__				:      Node )				->						Node:


					"""simple docstring"""

					if node.left:
								__snake_case				:			str       			=    self._get_lowest_node(node.left )
					else:
								__snake_case				:			str       			=    node
								self._reassign_nodes(__magic_name__     ,			node.right )

					return lowest_node

		def   lowercase__    (      self				:      Any     ,			__magic_name__				:      int )				->						bool:


					"""simple docstring"""

					try:
								self.search(__magic_name__ )
								return True
					except Exception:
								return False

		def   lowercase__    (      self				:      str )				->						int:


					"""simple docstring"""

					if self.root is None:
								raise Exception("""Binary search tree is empty""" )

					__snake_case				:			str       			=    self.root
					while node.right is not None:
								__snake_case				:			Tuple       			=    node.right

					return node.label

		def   lowercase__    (      self				:      Optional[Any] )				->						int:


					"""simple docstring"""

					if self.root is None:
								raise Exception("""Binary search tree is empty""" )

					__snake_case				:			str       			=    self.root
					while node.left is not None:
								__snake_case				:			Union[str, Any]       			=    node.left

					return node.label

		def   lowercase__    (      self				:      Union[str, Any] )				->						Iterator[Node]:


					"""simple docstring"""

					return self._inorder_traversal(self.root )

		def   lowercase__    (      self				:      Optional[Any]     ,			__magic_name__				:      Node | None )				->						Iterator[Node]:


					"""simple docstring"""

					if node is not None:
								yield from self._inorder_traversal(node.left )
								yield node
								yield from self._inorder_traversal(node.right )

		def   lowercase__    (      self				:      Dict )				->						Iterator[Node]:


					"""simple docstring"""

					return self._preorder_traversal(self.root )

		def   lowercase__    (      self				:      Union[str, Any]     ,			__magic_name__				:      Node | None )				->						Iterator[Node]:


					"""simple docstring"""

					if node is not None:
								yield node
								yield from self._preorder_traversal(node.left )
								yield from self._preorder_traversal(node.right )





class    _A   (				unittest.TestCase		):

		@staticmethod
		def   lowercase__    (      )				->						BinarySearchTree:


					"""simple docstring"""

					__snake_case				:			Any       			=    BinarySearchTree()
					t.put(8 )
					t.put(3 )
					t.put(6 )
					t.put(1 )
					t.put(10 )
					t.put(14 )
					t.put(13 )
					t.put(4 )
					t.put(7 )
					t.put(5 )

					return t

		def   lowercase__    (      self				:      Any )				->						None:


					"""simple docstring"""

					__snake_case				:			Optional[Any]       			=    BinarySearchTree()
					assert t.is_empty()

					t.put(8 )
					assert t.root is not None
					assert t.root.parent is None
					assert t.root.label == 8

					t.put(10 )
					assert t.root.right is not None
					assert t.root.right.parent == t.root
					assert t.root.right.label == 10

					t.put(3 )
					assert t.root.left is not None
					assert t.root.left.parent == t.root
					assert t.root.left.label == 3

					t.put(6 )
					assert t.root.left.right is not None
					assert t.root.left.right.parent == t.root.left
					assert t.root.left.right.label == 6

					t.put(1 )
					assert t.root.left.left is not None
					assert t.root.left.left.parent == t.root.left
					assert t.root.left.left.label == 1

					with self.assertRaises(__magic_name__ ):  # noqa: B017
								t.put(1 )

		def   lowercase__    (      self				:      Union[str, Any] )				->						None:


					"""simple docstring"""

					__snake_case				:			List[str]       			=    self._get_binary_search_tree()

					__snake_case				:			Any       			=    t.search(6 )
					assert node.label == 6

					__snake_case				:			Tuple       			=    t.search(13 )
					assert node.label == 13

					with self.assertRaises(__magic_name__ ):  # noqa: B017
								t.search(2 )

		def   lowercase__    (      self				:      Tuple )				->						None:


					"""simple docstring"""

					__snake_case				:			int       			=    self._get_binary_search_tree()

					t.remove(13 )
					assert t.root is not None
					assert t.root.right is not None
					assert t.root.right.right is not None
					assert t.root.right.right.right is None
					assert t.root.right.right.left is None

					t.remove(7 )
					assert t.root.left is not None
					assert t.root.left.right is not None
					assert t.root.left.right.left is not None
					assert t.root.left.right.right is None
					assert t.root.left.right.left.label == 4

					t.remove(6 )
					assert t.root.left.left is not None
					assert t.root.left.right.right is not None
					assert t.root.left.left.label == 1
					assert t.root.left.right.label == 4
					assert t.root.left.right.right.label == 5
					assert t.root.left.right.left is None
					assert t.root.left.left.parent == t.root.left
					assert t.root.left.right.parent == t.root.left

					t.remove(3 )
					assert t.root is not None
					assert t.root.left.label == 4
					assert t.root.left.right.label == 5
					assert t.root.left.left.label == 1
					assert t.root.left.parent == t.root
					assert t.root.left.left.parent == t.root.left
					assert t.root.left.right.parent == t.root.left

					t.remove(4 )
					assert t.root.left is not None
					assert t.root.left.left is not None
					assert t.root.left.label == 5
					assert t.root.left.right is None
					assert t.root.left.left.label == 1
					assert t.root.left.parent == t.root
					assert t.root.left.left.parent == t.root.left

		def   lowercase__    (      self				:      List[str] )				->						None:


					"""simple docstring"""

					__snake_case				:			Dict       			=    self._get_binary_search_tree()

					t.remove(3 )
					assert t.root is not None
					assert t.root.left is not None
					assert t.root.left.left is not None
					assert t.root.left.right is not None
					assert t.root.left.right.left is not None
					assert t.root.left.right.right is not None
					assert t.root.left.label == 4
					assert t.root.left.right.label == 6
					assert t.root.left.left.label == 1
					assert t.root.left.right.right.label == 7
					assert t.root.left.right.left.label == 5
					assert t.root.left.parent == t.root
					assert t.root.left.right.parent == t.root.left
					assert t.root.left.left.parent == t.root.left
					assert t.root.left.right.left.parent == t.root.left.right

		def   lowercase__    (      self				:      Optional[Any] )				->						None:


					"""simple docstring"""

					__snake_case				:			Optional[Any]       			=    self._get_binary_search_tree()
					t.empty()
					assert t.root is None

		def   lowercase__    (      self				:      Dict )				->						None:


					"""simple docstring"""

					__snake_case				:			Tuple       			=    self._get_binary_search_tree()
					assert not t.is_empty()

					t.empty()
					assert t.is_empty()

		def   lowercase__    (      self				:      Dict )				->						None:


					"""simple docstring"""

					__snake_case				:			int       			=    self._get_binary_search_tree()

					assert t.exists(6 )
					assert not t.exists(-1 )

		def   lowercase__    (      self				:      List[Any] )				->						None:


					"""simple docstring"""

					__snake_case				:			Any       			=    self._get_binary_search_tree()

					assert t.get_max_label() == 14

					t.empty()
					with self.assertRaises(__magic_name__ ):  # noqa: B017
								t.get_max_label()

		def   lowercase__    (      self				:      List[Any] )				->						None:


					"""simple docstring"""

					__snake_case				:			str       			=    self._get_binary_search_tree()

					assert t.get_min_label() == 1

					t.empty()
					with self.assertRaises(__magic_name__ ):  # noqa: B017
								t.get_min_label()

		def   lowercase__    (      self				:      List[Any] )				->						None:


					"""simple docstring"""

					__snake_case				:			List[str]       			=    self._get_binary_search_tree()

					__snake_case				:			Any       			=    [i.label for i in t.inorder_traversal()]
					assert inorder_traversal_nodes == [1, 3, 4, 5, 6, 7, 8, 10, 13, 14]

		def   lowercase__    (      self				:      int )				->						None:


					"""simple docstring"""

					__snake_case				:			List[str]       			=    self._get_binary_search_tree()

					__snake_case				:			List[str]       			=    [i.label for i in t.preorder_traversal()]
					assert preorder_traversal_nodes == [8, 3, 1, 6, 4, 5, 7, 10, 14, 13]







def 				_a	(					)   ->							None:



			"""simple docstring"""


			__snake_case				:			Any       			=    BinarySearchTree()
			t.put(8   )
			t.put(3   )
			t.put(6   )
			t.put(1   )
			t.put(10   )
			t.put(14   )
			t.put(13   )
			t.put(4   )
			t.put(7   )
			t.put(5   )

			print(
			    """
            8
           / \\
          3   10
         / \\    \\
        1   6    14
           / \\   /
          4   7 13
           \\
            5
        """   )

			print("""Label 6 exists:"""						,  t.exists(6   )   )
			print("""Label 13 exists:"""						,  t.exists(13   )   )
			print("""Label -1 exists:"""						,  t.exists(-1   )   )
			print("""Label 12 exists:"""						,  t.exists(12   )   )

			# Prints all the elements of the list in inorder traversal
			__snake_case				:			Dict       			=    [i.label for i in t.inorder_traversal()]
			print("""Inorder traversal:"""						,  _lowerCamelCase   )

			# Prints all the elements of the list in preorder traversal
			__snake_case				:			Optional[int]       			=    [i.label for i in t.preorder_traversal()]
			print("""Preorder traversal:"""						,  _lowerCamelCase   )

			print("""Max. label:"""						,  t.get_max_label()   )
			print("""Min. label:"""						,  t.get_min_label()   )

			# Delete elements
			print("""\nDeleting elements 13, 10, 8, 3, 6, 14"""   )
			print(
			    """
          4
         / \\
        1   7
             \\
              5
        """   )
			t.remove(13   )
			t.remove(10   )
			t.remove(8   )
			t.remove(3   )
			t.remove(6   )
			t.remove(14   )

			# Prints all the elements of the list in inorder traversal after delete
			__snake_case				:			Any       			=    [i.label for i in t.inorder_traversal()]
			print("""Inorder traversal after delete:"""						,  _lowerCamelCase   )

			# Prints all the elements of the list in preorder traversal after delete
			__snake_case				:			Tuple       			=    [i.label for i in t.preorder_traversal()]
			print("""Preorder traversal after delete:"""						,  _lowerCamelCase   )

			print("""Max. label:"""						,  t.get_max_label()   )
			print("""Min. label:"""						,  t.get_min_label()   )


if __name__ == "__main__":
	binary_search_tree_example()









'''simple docstring'''






import torch
from torch import autograd




class    _A   (				autograd.Function		):

		@staticmethod
		def   lowercase__    (      __magic_name__				:      List[Any]     ,			__magic_name__				:      torch.tensor     ,			__magic_name__				:      float     ,			__magic_name__				:      bool )				->						Optional[int]:


					"""simple docstring"""

					__snake_case				:			List[Any]       			=    inputs.numel()
					__snake_case				:			List[Any]       			=    int(0.005 * nb_elems ) + 1
					if sigmoid:
								__snake_case				:			Dict       			=    (torch.sigmoid(__magic_name__ ) > threshold).type(inputs.type() )
					else:
								__snake_case				:			Tuple       			=    (inputs > threshold).type(inputs.type() )
					if mask.sum() < nb_min:
								# We limit the pruning so that at least 0.5% (half a percent) of the weights are remaining
								__snake_case				:			Tuple       			=    inputs.flatten().kthvalue(max(nb_elems - nb_min     ,			1 ) ).values
								__snake_case				:			Union[str, Any]       			=    (inputs > k_threshold).type(inputs.type() )
					return mask

		@staticmethod
		def   lowercase__    (      __magic_name__				:      int     ,			__magic_name__				:      Any )				->						Tuple:


					"""simple docstring"""

					return gradOutput, None, None





class    _A   (				autograd.Function		):

		@staticmethod
		def   lowercase__    (      __magic_name__				:      Tuple     ,			__magic_name__				:      torch.tensor     ,			__magic_name__				:      float )				->						int:


					"""simple docstring"""

					__snake_case				:			Tuple       			=    inputs.clone()
					__snake_case			,    __snake_case				:			Dict       			=    inputs.flatten().sort(descending=__magic_name__ )
					__snake_case				:			List[Any]       			=    int(threshold * inputs.numel() )

					# flat_out and mask access the same memory.
					__snake_case				:			Optional[Any]       			=    mask.flatten()
					__snake_case				:			List[str]       			=    0
					__snake_case				:			Any       			=    1
					return mask

		@staticmethod
		def   lowercase__    (      __magic_name__				:      List[str]     ,			__magic_name__				:      Any )				->						Optional[Any]:


					"""simple docstring"""

					return gradOutput, None





class    _A   (				__lowercase		):

		@staticmethod
		def   lowercase__    (      __magic_name__				:      torch.tensor     ,			__magic_name__				:      float )				->						List[str]:


					"""simple docstring"""

					__snake_case				:			List[str]       			=    inputs.clone()
					__snake_case			,    __snake_case				:			Tuple       			=    inputs.abs().flatten().sort(descending=__magic_name__ )
					__snake_case				:			Any       			=    int(threshold * inputs.numel() )

					# flat_out and mask access the same memory.
					__snake_case				:			Union[str, Any]       			=    mask.flatten()
					__snake_case				:			Tuple       			=    0
					__snake_case				:			int       			=    1
					return mask


