



"""simple docstring"""





from __future__ import annotations

from random import random
from typing import Generic, TypeVar

__lowerCAmelCase							:       int          =       TypeVar('''KT''')
__lowerCAmelCase							:       Union[str, Any]          =       TypeVar('''VT''')



class  _lowerCAmelCase     (					Generic[KT, VT]		):





		"""simple docstring"""






		def __init__(       self				,     _lowercase = "root"				,     _lowercase = None )			->    Union[str, Any]:







								'''simple docstring'''

								snake_case_ :			Tuple            =      key
								snake_case_ :			Tuple            =      value
								snake_case_ :			list[Node[KT, VT]]            =      []





		def __repr__(       self )			->    str:







								'''simple docstring'''

								return f'Node({self.key}: {self.value})'





		@property
		def  UpperCAmelCase__				(       self )			->    int:







								'''simple docstring'''

								return len(self.forward )




class  _lowerCAmelCase     (					Generic[KT, VT]		):





		"""simple docstring"""






		def __init__(       self				,     _lowercase = 0.5				,     _lowercase = 1_6 )			->    int:







								'''simple docstring'''

								snake_case_ :			Node[KT, VT]            =      Node[KT, VT]()
								snake_case_ :			Union[str, Any]            =      0
								snake_case_ :			Optional[int]            =      p
								snake_case_ :			Any            =      max_level





		def __str__(       self )			->    str:







								'''simple docstring'''

								snake_case_ :			str            =      list(self )

								if len(_lowercase ) == 0:
														return f'SkipList(level={self.level})'

								snake_case_ :			List[Any]            =      max((len(str(_lowercase ) ) for item in items)				,     default=4 )
								snake_case_ :			str            =      max(_lowercase				,     4 ) + 4

								snake_case_ :			Union[str, Any]            =      self.head
								snake_case_ :			Dict            =      []

								snake_case_ :			List[str]            =      node.forward.copy()
								lines.append(f'[{node.key}]'.ljust(_lowercase				,     """-""" ) + """* """ * len(_lowercase ) )
								lines.append(""" """ * label_size + """| """ * len(_lowercase ) )

								while len(node.forward ) != 0:
														snake_case_ :			Optional[Any]            =      node.forward[0]

														lines.append(
														    f'[{node.key}]'.ljust(_lowercase				,     """-""" )
														    + """ """.join(str(n.key ) if n.key == node.key else """|""" for n in forwards ) )
														lines.append(""" """ * label_size + """| """ * len(_lowercase ) )
														snake_case_ :			List[str]            =      node.forward

								lines.append("""None""".ljust(_lowercase ) + """* """ * len(_lowercase ) )
								return f'SkipList(level={self.level})\n' + "\n".join(_lowercase )





		def __iter__(       self )			->    Optional[int]:







								'''simple docstring'''

								snake_case_ :			Dict            =      self.head

								while len(node.forward ) != 0:
														yield node.forward[0].key
														snake_case_ :			Dict            =      node.forward[0]





		def  UpperCAmelCase__				(       self )			->    int:







								'''simple docstring'''

								snake_case_ :			Optional[int]            =      1
								while random() < self.p and level < self.max_level:
														level += 1

								return level





		def  UpperCAmelCase__				(       self				,     _lowercase )			->    tuple[Node[KT, VT] | None, list[Node[KT, VT]]]:







								'''simple docstring'''

								snake_case_ :			Optional[Any]            =      []

								snake_case_ :			int            =      self.head

								for i in reversed(range(self.level ) ):
														# i < node.level - When node level is lesser than `i` decrement `i`.
														# node.forward[i].key < key - Jumping to node with key value higher
														#                             or equal to searched key would result
														#                             in skipping searched key.
														while i < node.level and node.forward[i].key < key:
																				snake_case_ :			List[Any]            =      node.forward[i]
														# Each leftmost node (relative to searched node) will potentially have to
														# be updated.
														update_vector.append(_lowercase )

								update_vector.reverse()  # Note that we were inserting values in reverse order.

								# len(node.forward) != 0 - If current node doesn't contain any further
								#                          references then searched key is not present.
								# node.forward[0].key == key - Next node key should be equal to search key
								#                              if key is present.
								if len(node.forward ) != 0 and node.forward[0].key == key:
														return node.forward[0], update_vector
								else:
														return None, update_vector





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







								'''simple docstring'''

								snake_case_      ,		snake_case_ :			Dict            =      self._locate_node(_lowercase )

								if node is not None:
														for i, update_node in enumerate(_lowercase ):
																				# Remove or replace all references to removed node.
																				if update_node.level > i and update_node.forward[i].key == key:
																										if node.level > i:
																																snake_case_ :			List[str]            =      node.forward[i]
																										else:
																																snake_case_ :			Tuple            =      update_node.forward[:i]





		def  UpperCAmelCase__				(       self				,     _lowercase				,     _lowercase )			->    str:







								'''simple docstring'''

								snake_case_      ,		snake_case_ :			Dict            =      self._locate_node(_lowercase )
								if node is not None:
														snake_case_ :			List[Any]            =      value
								else:
														snake_case_ :			Optional[int]            =      self.random_level()

														if level > self.level:
																				# After level increase we have to add additional nodes to head.
																				for _ in range(self.level - 1				,     _lowercase ):
																										update_vector.append(self.head )
																				snake_case_ :			Any            =      level

														snake_case_ :			Optional[int]            =      Node(_lowercase				,     _lowercase )

														for i, update_node in enumerate(update_vector[:level] ):
																				# Change references to pass through new node.
																				if update_node.level > i:
																										new_node.forward.append(update_node.forward[i] )

																				if update_node.level < i + 1:
																										update_node.forward.append(_lowercase )
																				else:
																										snake_case_ :			Optional[Any]            =      new_node





		def  UpperCAmelCase__				(       self				,     _lowercase )			->    VT | None:







								'''simple docstring'''

								snake_case_      ,		snake_case_ :			Dict            =      self._locate_node(_lowercase )

								if node is not None:
														return node.value

								return None




def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						snake_case_ :			List[str]            =      SkipList()
						skip_list.insert("""Key1"""       ,			3     )
						skip_list.insert("""Key2"""       ,			1_2     )
						skip_list.insert("""Key3"""       ,			4_1     )
						skip_list.insert("""Key4"""       ,			-1_9     )

						snake_case_ :			Optional[int]            =      skip_list.head
						snake_case_ :			List[Any]            =      {}
						while node.level != 0:
												snake_case_ :			List[str]            =      node.forward[0]
												snake_case_ :			Union[str, Any]            =      node.value

						assert len(__UpperCamelCase     ) == 4
						assert all_values["Key1"] == 3
						assert all_values["Key2"] == 1_2
						assert all_values["Key3"] == 4_1
						assert all_values["Key4"] == -1_9
def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						snake_case_ :			Optional[int]            =      SkipList()
						skip_list.insert("""Key1"""       ,			1_0     )
						skip_list.insert("""Key1"""       ,			1_2     )

						skip_list.insert("""Key5"""       ,			7     )
						skip_list.insert("""Key7"""       ,			1_0     )
						skip_list.insert("""Key10"""       ,			5     )

						skip_list.insert("""Key7"""       ,			7     )
						skip_list.insert("""Key5"""       ,			5     )
						skip_list.insert("""Key10"""       ,			1_0     )

						snake_case_ :			str            =      skip_list.head
						snake_case_ :			str            =      {}
						while node.level != 0:
												snake_case_ :			Optional[Any]            =      node.forward[0]
												snake_case_ :			int            =      node.value

						if len(__UpperCamelCase     ) != 4:
												print()
						assert len(__UpperCamelCase     ) == 4
						assert all_values["Key1"] == 1_2
						assert all_values["Key7"] == 7
						assert all_values["Key5"] == 5
						assert all_values["Key10"] == 1_0
def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						snake_case_ :			str            =      SkipList()
						assert skip_list.find("""Some key"""     ) is None
def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						snake_case_ :			Optional[Any]            =      SkipList()

						skip_list.insert("""Key2"""       ,			2_0     )
						assert skip_list.find("""Key2"""     ) == 2_0

						skip_list.insert("""Some Key"""       ,			1_0     )
						skip_list.insert("""Key2"""       ,			8     )
						skip_list.insert("""V"""       ,			1_3     )

						assert skip_list.find("""Y"""     ) is None
						assert skip_list.find("""Key2"""     ) == 8
						assert skip_list.find("""Some Key"""     ) == 1_0
						assert skip_list.find("""V"""     ) == 1_3
def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						snake_case_ :			Any            =      SkipList()
						skip_list.delete("""Some key"""     )

						assert len(skip_list.head.forward     ) == 0
def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						snake_case_ :			Tuple            =      SkipList()

						skip_list.insert("""Key1"""       ,			1_2     )
						skip_list.insert("""V"""       ,			1_3     )
						skip_list.insert("""X"""       ,			1_4     )
						skip_list.insert("""Key2"""       ,			1_5     )

						skip_list.delete("""V"""     )
						skip_list.delete("""Key2"""     )

						assert skip_list.find("""V"""     ) is None
						assert skip_list.find("""Key2"""     ) is None
def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						snake_case_ :			Optional[int]            =      SkipList()

						skip_list.insert("""Key1"""       ,			1_2     )
						skip_list.insert("""V"""       ,			1_3     )
						skip_list.insert("""X"""       ,			1_4     )
						skip_list.insert("""Key2"""       ,			1_5     )

						skip_list.delete("""V"""     )
						assert skip_list.find("""V"""     ) is None
						assert skip_list.find("""X"""     ) == 1_4
						assert skip_list.find("""Key1"""     ) == 1_2
						assert skip_list.find("""Key2"""     ) == 1_5

						skip_list.delete("""X"""     )
						assert skip_list.find("""V"""     ) is None
						assert skip_list.find("""X"""     ) is None
						assert skip_list.find("""Key1"""     ) == 1_2
						assert skip_list.find("""Key2"""     ) == 1_5

						skip_list.delete("""Key1"""     )
						assert skip_list.find("""V"""     ) is None
						assert skip_list.find("""X"""     ) is None
						assert skip_list.find("""Key1"""     ) is None
						assert skip_list.find("""Key2"""     ) == 1_5

						skip_list.delete("""Key2"""     )
						assert skip_list.find("""V"""     ) is None
						assert skip_list.find("""X"""     ) is None
						assert skip_list.find("""Key1"""     ) is None
						assert skip_list.find("""Key2"""     ) is None
def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						snake_case_ :			Union[str, Any]            =      SkipList()

						skip_list.insert("""Key1"""       ,			1_2     )
						skip_list.insert("""V"""       ,			1_3     )
						skip_list.insert("""X"""       ,			1_4_2     )
						skip_list.insert("""Key2"""       ,			1_5     )

						skip_list.delete("""X"""     )

						def traverse_keys(__UpperCamelCase   :      str     ):
												yield node.key
												for forward_node in node.forward:
																		yield from traverse_keys(__UpperCamelCase     )

						assert len(set(traverse_keys(skip_list.head     )     )     ) == 4
def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						def is_sorted(__UpperCamelCase   :      List[Any]     ):
												return all(next_item >= item for item, next_item in zip(__UpperCamelCase       ,			lst[1:]     )     )

						snake_case_ :			str            =      SkipList()
						for i in range(1_0     ):
												skip_list.insert(__UpperCamelCase       ,			__UpperCamelCase     )
						assert is_sorted(list(__UpperCamelCase     )     )
						skip_list.delete(5     )
						skip_list.delete(8     )
						skip_list.delete(2     )
						assert is_sorted(list(__UpperCamelCase     )     )
						skip_list.insert(-1_2       ,			-1_2     )
						skip_list.insert(7_7       ,			7_7     )
						assert is_sorted(list(__UpperCamelCase     )     )
def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						for _ in range(1_0_0     ):
												# Repeat test 100 times due to the probabilistic nature of skip list
												# random values == random bugs
												test_insert()
												test_insert_overrides_existing_value()

												test_searching_empty_list_returns_none()
												test_search()

												test_deleting_item_from_empty_list_do_nothing()
												test_deleted_items_are_not_founded_by_find_method()
												test_delete_removes_only_given_key()
												test_delete_doesnt_leave_dead_nodes()

												test_iter_always_yields_sorted_values()
def 						__lowerCAmelCase    (		):


						'''simple docstring'''






						snake_case_ :			Dict            =      SkipList()
						skip_list.insert(2       ,			"""2"""     )
						skip_list.insert(4       ,			"""4"""     )
						skip_list.insert(6       ,			"""4"""     )
						skip_list.insert(4       ,			"""5"""     )
						skip_list.insert(8       ,			"""4"""     )
						skip_list.insert(9       ,			"""4"""     )

						skip_list.delete(4     )

						print(__UpperCamelCase     )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()








_lowercase		:  Optional[Any]			       ="""
# Transformers installation
! pip install transformers datasets
# To install from source instead of the last release, comment the command above and uncomment the following one.
# ! pip install git+https://github.com/huggingface/transformers.git
"""

_lowercase		:  Union[str, Any]			       =[{"""type""": """code""", """content""": INSTALL_CONTENT}]
_lowercase		:  List[Any]			       ={
    """{processor_class}""": """FakeProcessorClass""",
    """{model_class}""": """FakeModelClass""",
    """{object_class}""": """FakeObjectClass""",
}
