


"""simple docstring"""







from __future__ import annotations

from random import random
from typing import Generic, TypeVar

a__    :							List[str]            =					TypeVar('''KT''')
a__    :							str            =					TypeVar('''VT''')




class 			UpperCamelCase_     (			Generic[KT, VT]):

	"""simple docstring"""





	def __init__(			self      :    Union[str, Any]      ,      UpperCAmelCase__      :    KT | str = "root"      ,      UpperCAmelCase__      :    VT | None = None       )	->     Tuple:
						__SCREAMING_SNAKE_CASE						       =    key
						__SCREAMING_SNAKE_CASE						       =    value
						__SCREAMING_SNAKE_CASE						       =    []




	def __repr__(			self      :    Union[str, Any]       )	->     int:
						return F"""Node({self.key}: {self.value})"""




	@property
	def   UpperCAmelCase_				(			self      :    str       )	->     Any:
						return len(self.forward       )




class 			UpperCamelCase_     (			Generic[KT, VT]):

	"""simple docstring"""





	def __init__(			self      :    str      ,      UpperCAmelCase__      :    float = 0.5      ,      UpperCAmelCase__      :    int = 1_6       )	->     Tuple:
						__SCREAMING_SNAKE_CASE						       =    Node[KT, VT]()
						__SCREAMING_SNAKE_CASE						       =    0
						__SCREAMING_SNAKE_CASE						       =    p
						__SCREAMING_SNAKE_CASE						       =    max_level




	def __str__(			self      :    Optional[Any]       )	->     Any:
						__SCREAMING_SNAKE_CASE						       =    list(self       )

						if len(__A       ) == 0:
											return F"""SkipList(level={self.level})"""

						__SCREAMING_SNAKE_CASE						       =    max((len(str(__A       )       ) for item in items)      ,      default=4       )
						__SCREAMING_SNAKE_CASE						       =    max(__A      ,      4       ) + 4

						__SCREAMING_SNAKE_CASE						       =    self.head
						__SCREAMING_SNAKE_CASE						       =    []

						__SCREAMING_SNAKE_CASE						       =    node.forward.copy()
						lines.append(F"""[{node.key}]""".ljust(__A      ,      "-"       ) + "* " * len(__A       )       )
						lines.append(" " * label_size + "| " * len(__A       )       )

						while len(node.forward       ) != 0:
											__SCREAMING_SNAKE_CASE						       =    node.forward[0]

											lines.append(
											    F"""[{node.key}]""".ljust(__A      ,      "-"       )
											    + " ".join(str(n.key       ) if n.key == node.key else "|" for n in forwards       )       )
											lines.append(" " * label_size + "| " * len(__A       )       )
											__SCREAMING_SNAKE_CASE						       =    node.forward

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




	def __iter__(			self      :    Dict       )	->     int:
						__SCREAMING_SNAKE_CASE						       =    self.head

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




	def   UpperCAmelCase_				(			self      :    str       )	->     Optional[int]:
						__SCREAMING_SNAKE_CASE						       =    1
						while random() < self.p and level < self.max_level:
											level += 1

						return level




	def   UpperCAmelCase_				(			self      :    Union[str, Any]      ,      UpperCAmelCase__      :    List[str]       )	->     Union[str, Any]:
						__SCREAMING_SNAKE_CASE						       =    []

						__SCREAMING_SNAKE_CASE						       =    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:
																__SCREAMING_SNAKE_CASE						       =    node.forward[i]
											# Each leftmost node (relative to searched node) will potentially have to
											# be updated.
											update_vector.append(__A       )

						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      :    Tuple      ,      UpperCAmelCase__      :    KT       )	->     int:
						__SCREAMING_SNAKE_CASE						       =    self._locate_node(__A       )

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




	def   UpperCAmelCase_				(			self      :    int      ,      UpperCAmelCase__      :    KT      ,      UpperCAmelCase__      :    VT       )	->     int:
						__SCREAMING_SNAKE_CASE						       =    self._locate_node(__A       )
						if node is not None:
											__SCREAMING_SNAKE_CASE						       =    value
						else:
											__SCREAMING_SNAKE_CASE						       =    self.random_level()

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

											__SCREAMING_SNAKE_CASE						       =    Node(__A      ,      __A       )

											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(__A       )
																else:
																					__SCREAMING_SNAKE_CASE						       =    new_node




	def   UpperCAmelCase_				(			self      :    Tuple      ,      UpperCAmelCase__      :    VT       )	->     List[Any]:
						__SCREAMING_SNAKE_CASE						       =    self._locate_node(__A       )

						if node is not None:
											return node.value

						return None




def        UpperCAmelCase__	():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    SkipList()
					skip_list.insert("Key1"  ,						3       )
					skip_list.insert("Key2"  ,						12       )
					skip_list.insert("Key3"  ,						41       )
					skip_list.insert("Key4"  ,						-19       )

					__SCREAMING_SNAKE_CASE						       =    skip_list.head
					__SCREAMING_SNAKE_CASE						       =    {}
					while node.level != 0:
										__SCREAMING_SNAKE_CASE						       =    node.forward[0]
										__SCREAMING_SNAKE_CASE						       =    node.value

					assert len(lowerCAmelCase_       ) == 4
					assert all_values["Key1"] == 3
					assert all_values["Key2"] == 12
					assert all_values["Key3"] == 41
					assert all_values["Key4"] == -19




def        UpperCAmelCase__	():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    SkipList()
					skip_list.insert("Key1"  ,						10       )
					skip_list.insert("Key1"  ,						12       )

					skip_list.insert("Key5"  ,						7       )
					skip_list.insert("Key7"  ,						10       )
					skip_list.insert("Key10"  ,						5       )

					skip_list.insert("Key7"  ,						7       )
					skip_list.insert("Key5"  ,						5       )
					skip_list.insert("Key10"  ,						10       )

					__SCREAMING_SNAKE_CASE						       =    skip_list.head
					__SCREAMING_SNAKE_CASE						       =    {}
					while node.level != 0:
										__SCREAMING_SNAKE_CASE						       =    node.forward[0]
										__SCREAMING_SNAKE_CASE						       =    node.value

					if len(lowerCAmelCase_       ) != 4:
										print()
					assert len(lowerCAmelCase_       ) == 4
					assert all_values["Key1"] == 12
					assert all_values["Key7"] == 7
					assert all_values["Key5"] == 5
					assert all_values["Key10"] == 10




def        UpperCAmelCase__	():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    SkipList()
					assert skip_list.find("Some key"       ) is None




def        UpperCAmelCase__	():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    SkipList()

					skip_list.insert("Key2"  ,						20       )
					assert skip_list.find("Key2"       ) == 20

					skip_list.insert("Some Key"  ,						10       )
					skip_list.insert("Key2"  ,						8       )
					skip_list.insert("V"  ,						13       )

					assert skip_list.find("Y"       ) is None
					assert skip_list.find("Key2"       ) == 8
					assert skip_list.find("Some Key"       ) == 10
					assert skip_list.find("V"       ) == 13




def        UpperCAmelCase__	():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    SkipList()
					skip_list.delete("Some key"       )

					assert len(skip_list.head.forward       ) == 0




def        UpperCAmelCase__	():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    SkipList()

					skip_list.insert("Key1"  ,						12       )
					skip_list.insert("V"  ,						13       )
					skip_list.insert("X"  ,						14       )
					skip_list.insert("Key2"  ,						15       )

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

					assert skip_list.find("V"       ) is None
					assert skip_list.find("Key2"       ) is None




def        UpperCAmelCase__	():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    SkipList()

					skip_list.insert("Key1"  ,						12       )
					skip_list.insert("V"  ,						13       )
					skip_list.insert("X"  ,						14       )
					skip_list.insert("Key2"  ,						15       )

					skip_list.delete("V"       )
					assert skip_list.find("V"       ) is None
					assert skip_list.find("X"       ) == 14
					assert skip_list.find("Key1"       ) == 12
					assert skip_list.find("Key2"       ) == 15

					skip_list.delete("X"       )
					assert skip_list.find("V"       ) is None
					assert skip_list.find("X"       ) is None
					assert skip_list.find("Key1"       ) == 12
					assert skip_list.find("Key2"       ) == 15

					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"       ) == 15

					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        UpperCAmelCase__	():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    SkipList()

					skip_list.insert("Key1"  ,						12       )
					skip_list.insert("V"  ,						13       )
					skip_list.insert("X"  ,						142       )
					skip_list.insert("Key2"  ,						15       )

					skip_list.delete("X"       )

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

					assert len(set(traverse_keys(skip_list.head       )       )       ) == 4




def        UpperCAmelCase__	():




					'''simple docstring'''


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

					__SCREAMING_SNAKE_CASE						       =    SkipList()
					for i in range(10       ):
										skip_list.insert(lowerCAmelCase_  ,						lowerCAmelCase_       )
					assert is_sorted(list(lowerCAmelCase_       )       )
					skip_list.delete(5       )
					skip_list.delete(8       )
					skip_list.delete(2       )
					assert is_sorted(list(lowerCAmelCase_       )       )
					skip_list.insert(-12  ,						-12       )
					skip_list.insert(77  ,						77       )
					assert is_sorted(list(lowerCAmelCase_       )       )




def        UpperCAmelCase__	():




					'''simple docstring'''


					for _ in range(100       ):
										# 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        UpperCAmelCase__	():




					'''simple docstring'''


					__SCREAMING_SNAKE_CASE						       =    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(lowerCAmelCase_       )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()




"""simple docstring"""







def        UpperCAmelCase__	(lowerCAmelCase_       ):




					'''simple docstring'''


					return " ".join(
					    "".join(word[::-1]       ) if len(lowerCAmelCase_       ) > 4 else word for word in sentence.split()       )


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		print(reverse_long_words('''Hey wollef sroirraw'''))
