




from __future__ import annotations

from random import random
from typing import Generic, TypeVar

lowercase__							:	List[str]											=		TypeVar("KT")
lowercase__							:	int											=		TypeVar("VT")
class 						UpperCAmelCase  (							Generic[KT, VT]     ):







						'''simple docstring'''





						def __init__(		self				:	Optional[int]			,      __lowercase				:	KT | str = "root"			,      __lowercase				:	VT | None = None		):






							"""simple docstring"""






							snake_case_						       =	key
							snake_case_						       =	value
							snake_case_						       =	[]






						def __repr__(		self				:	int		):






							"""simple docstring"""






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






						@property
						def 			snake_case__		(		self				:	List[Any]		):






							"""simple docstring"""






							return len(self.forward		)







class 						UpperCAmelCase  (							Generic[KT, VT]     ):







						'''simple docstring'''





						def __init__(		self				:	Any			,      __lowercase				:	float = 0.5			,      __lowercase				:	int = 16		):






							"""simple docstring"""






							snake_case_						       =	Node[KT, VT]()
							snake_case_						       =	0
							snake_case_						       =	p
							snake_case_						       =	max_level






						def __str__(		self				:	List[Any]		):






							"""simple docstring"""






							snake_case_						       =	list(self		)

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

							snake_case_						       =	max((len(str(__lowercase		)		) for item in items)			,      default=4		)
							snake_case_						       =	max(__lowercase			,      4		) + 4

							snake_case_						       =	self.head
							snake_case_						       =	[]

							snake_case_						       =	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_						       =	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_						       =	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_						       =	self.head

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






						def 			snake_case__		(		self				:	Any		):






							"""simple docstring"""






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

							return level






						def 			snake_case__		(		self				:	Dict			,      __lowercase				:	Dict		):






							"""simple docstring"""






							snake_case_						       =	[]

							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:
									snake_case_						       =	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 			snake_case__		(		self				:	Tuple			,      __lowercase				:	KT		):






							"""simple docstring"""






							snake_case_       , snake_case_						       =	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_						       =	node.forward[i]
										else:
											snake_case_						       =	update_node.forward[:i]






						def 			snake_case__		(		self				:	str			,      __lowercase				:	KT			,      __lowercase				:	VT		):






							"""simple docstring"""






							snake_case_       , snake_case_						       =	self._locate_node(__lowercase		)
							if node is not None:
								snake_case_						       =	value
							else:
								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			,      __lowercase		):
										update_vector.append(self.head		)
									snake_case_						       =	level

								snake_case_						       =	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_						       =	new_node






						def 			snake_case__		(		self				:	str			,      __lowercase				:	VT		):






							"""simple docstring"""






							snake_case_       , snake_case_						       =	self._locate_node(__lowercase		)

							if node is not None:
								return node.value

							return None







def 		lowerCamelCase__       (						):







	'''simple docstring'''





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

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

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


def 		lowerCamelCase__       (						):







	'''simple docstring'''





	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				)

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

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


def 		lowerCamelCase__       (						):







	'''simple docstring'''





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


def 		lowerCamelCase__       (						):







	'''simple docstring'''





	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 		lowerCamelCase__       (						):







	'''simple docstring'''





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

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


def 		lowerCamelCase__       (						):







	'''simple docstring'''





	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 		lowerCamelCase__       (						):







	'''simple docstring'''





	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 		lowerCamelCase__       (						):







	'''simple docstring'''





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

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


def 		lowerCamelCase__       (						):







	'''simple docstring'''





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

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


def 		lowerCamelCase__       (						):







	'''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 		lowerCamelCase__       (						):







	'''simple docstring'''





	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(_A				)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		main()






def 		lowerCamelCase__       (						_A	,      _A				):







	'''simple docstring'''





	_validate_point(_A				)
	_validate_point(_A				)
	if len(_A				) != len(_A				):
		raise ValueError("Both points must be in the same n-dimensional space"				)

	return float(sum(abs(a - b				) for a, b in zip(_A	,      _A				)				)				)


def 		lowerCamelCase__       (						_A				):







	'''simple docstring'''





	if point:
		if isinstance(_A	,      _A				):
			for item in point:
				if not isinstance(_A	,      (int, float)				):
					snake_case_						       =	(
					    "Expected a list of numbers as input, found "
					    f"{type(_A				).__name__}"
					)
					raise TypeError(_A				)
		else:
			snake_case_						       =	f"Expected a list of numbers as input, found {type(_A				).__name__}"
			raise TypeError(_A				)
	else:
		raise ValueError("Missing an input"				)


def 		lowerCamelCase__       (						_A	,      _A				):







	'''simple docstring'''





	_validate_point(_A				)
	_validate_point(_A				)
	if len(_A				) != len(_A				):
		raise ValueError("Both points must be in the same n-dimensional space"				)

	return float(sum(abs(x - y				) for x, y in zip(_A	,      _A				)				)				)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
