

"""simple docstring"""


from __future__ import annotations

from random import random
from typing import Generic, TypeVar

__A						       =      TypeVar("KT")
__A						       =      TypeVar("VT")





class    snake_case     (    Generic[KT, VT]  ):

				def __init__(     self							:    Any					,  UpperCamelCase__							:    KT | str = "root"					,  UpperCamelCase__							:    VT | None = None)->       str:



						'''simple docstring'''


						__lowerCAmelCase:	Tuple   				=      key
						__lowerCAmelCase:	List[str]   				=      value
						__lowerCAmelCase:	list[Node[KT, VT]]   				=      []

				def __repr__(     self							:    Optional[Any])->       str:



						'''simple docstring'''


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




				@property
				def 							lowercase_					(     self							:    List[Any])->       int:



						'''simple docstring'''


						return len(self.forward)





class    snake_case     (    Generic[KT, VT]  ):

				def __init__(     self							:    Optional[Any]					,  UpperCamelCase__							:    float = 0.5					,  UpperCamelCase__							:    int = 1_6)->       str:



						'''simple docstring'''


						__lowerCAmelCase:	Node[KT, VT]   				=      Node[KT, VT]()
						__lowerCAmelCase:	List[str]   				=      0
						__lowerCAmelCase:	Dict   				=      p
						__lowerCAmelCase:	str   				=      max_level

				def __str__(     self							:    Dict)->       str:



						'''simple docstring'''


						__lowerCAmelCase:	Optional[Any]   				=      list(self)

						if len(UpperCamelCase__) == 0:
								return f"SkipList(level={self.level})"

						__lowerCAmelCase:	Tuple   				=      max((len(str(UpperCamelCase__)) for item in items)					,  default=4)
						__lowerCAmelCase:	Optional[int]   				=      max(UpperCamelCase__					,  4) + 4

						__lowerCAmelCase:	Tuple   				=      self.head
						__lowerCAmelCase:	int   				=      []

						__lowerCAmelCase:	Dict   				=      node.forward.copy()
						lines.append(f"[{node.key}]".ljust(UpperCamelCase__					,  "-") + "* " * len(UpperCamelCase__))
						lines.append(" " * label_size + "| " * len(UpperCamelCase__))

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

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

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

				def __iter__(     self							:    Optional[Any])->       str:



						'''simple docstring'''


						__lowerCAmelCase:	Union[str, Any]   				=      self.head

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

				def 							lowercase_					(     self							:    List[Any])->       int:



						'''simple docstring'''


						__lowerCAmelCase:	Tuple   				=      1
						while random() < self.p and level < self.max_level:
								level += 1

						return level

				def 							lowercase_					(     self							:    Optional[int]					,  UpperCamelCase__							:    Any)->       tuple[Node[KT, VT] | None, list[Node[KT, VT]]]:



						'''simple docstring'''


						__lowerCAmelCase:	List[str]   				=      []

						__lowerCAmelCase:	List[Any]   				=      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:
										__lowerCAmelCase:	Union[str, Any]   				=      node.forward[i]
								# Each leftmost node (relative to searched node) will potentially have to
								# be updated.
								update_vector.append(UpperCamelCase__)

						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 							lowercase_					(     self							:    List[str]					,  UpperCamelCase__							:    KT)->       str:



						'''simple docstring'''


						__lowerCAmelCase:	Optional[Any]   				=      self._locate_node(UpperCamelCase__)

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

				def 							lowercase_					(     self							:    Any					,  UpperCamelCase__							:    KT					,  UpperCamelCase__							:    VT)->       Optional[int]:



						'''simple docstring'''


						__lowerCAmelCase:	Union[str, Any]   				=      self._locate_node(UpperCamelCase__)
						if node is not None:
								__lowerCAmelCase:	str   				=      value
						else:
								__lowerCAmelCase:	Tuple   				=      self.random_level()

								if level > self.level:
										# After level increase we have to add additional nodes to head.
										for _ in range(self.level - 1					,  UpperCamelCase__):
												update_vector.append(self.head)
										__lowerCAmelCase:	Optional[int]   				=      level

								__lowerCAmelCase:	Tuple   				=      Node(UpperCamelCase__					,  UpperCamelCase__)

								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(UpperCamelCase__)
										else:
												__lowerCAmelCase:	int   				=      new_node




				def 							lowercase_					(     self							:    Tuple					,  UpperCamelCase__							:    VT)->       VT | None:



						'''simple docstring'''


						__lowerCAmelCase:	Dict   				=      self._locate_node(UpperCamelCase__)

						if node is not None:
								return node.value

						return None






def    a__   (   )     ->     Tuple:
		__lowerCAmelCase:	Optional[int]   				=      SkipList()
		skip_list.insert("Key1" ,			3			)
		skip_list.insert("Key2" ,			1_2			)
		skip_list.insert("Key3" ,			4_1			)
		skip_list.insert("Key4" ,			-1_9			)

		__lowerCAmelCase:	Tuple   				=      skip_list.head
		__lowerCAmelCase:	Optional[int]   				=      {}
		while node.level != 0:
				__lowerCAmelCase:	Dict   				=      node.forward[0]
				__lowerCAmelCase:	Dict   				=      node.value

		assert len(__SCREAMING_SNAKE_CASE			) == 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    a__   (   )     ->     Tuple:
		__lowerCAmelCase:	Dict   				=      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			)

		__lowerCAmelCase:	Optional[Any]   				=      skip_list.head
		__lowerCAmelCase:	Tuple   				=      {}
		while node.level != 0:
				__lowerCAmelCase:	Optional[int]   				=      node.forward[0]
				__lowerCAmelCase:	List[Any]   				=      node.value

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






def    a__   (   )     ->     Any:
		__lowerCAmelCase:	List[Any]   				=      SkipList()
		assert skip_list.find("Some key"			) is None






def    a__   (   )     ->     Union[str, Any]:
		__lowerCAmelCase:	List[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    a__   (   )     ->     Union[str, Any]:
		__lowerCAmelCase:	List[str]   				=      SkipList()
		skip_list.delete("Some key"			)

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






def    a__   (   )     ->     List[Any]:
		__lowerCAmelCase:	str   				=      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    a__   (   )     ->     Any:
		__lowerCAmelCase:	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    a__   (   )     ->     List[str]:
		__lowerCAmelCase:	Dict   				=      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(__SCREAMING_SNAKE_CASE			):
				yield node.key
				for forward_node in node.forward:
						yield from traverse_keys(__SCREAMING_SNAKE_CASE			)

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






def    a__   (   )     ->     Optional[int]:
		def is_sorted(__SCREAMING_SNAKE_CASE			):
				return all(next_item >= item for item, next_item in zip(__SCREAMING_SNAKE_CASE ,			lst[1:]			)			)

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






def    a__   (   )     ->     Optional[Any]:
		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    a__   (   )     ->     Optional[Any]:
		__lowerCAmelCase:	Tuple   				=      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(__SCREAMING_SNAKE_CASE			)


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()





"""simple docstring"""


from __future__ import annotations

from math import pi






def    a__   (   __SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE ,			__SCREAMING_SNAKE_CASE			)     ->     dict[str, float]:

		if (inductance, frequency, reactance).count(0			) != 1:
				raise ValueError("One and only one argument must be 0"			)
		if inductance < 0:
				raise ValueError("Inductance cannot be negative"			)
		if frequency < 0:
				raise ValueError("Frequency cannot be negative"			)
		if reactance < 0:
				raise ValueError("Inductive reactance cannot be negative"			)
		if inductance == 0:
				return {"inductance": reactance / (2 * pi * frequency)}
		elif frequency == 0:
				return {"frequency": reactance / (2 * pi * inductance)}
		elif reactance == 0:
				return {"reactance": 2 * pi * frequency * inductance}
		else:
				raise ValueError("Exactly one argument must be 0"			)


if __name__ == "__main__":
			import doctest

			doctest.testmod()


