

"""simple docstring"""




from __future__ import annotations

from random import random
from typing import Generic, TypeVar

_lowercase   :	Optional[int]												=						TypeVar('KT')
_lowercase   :	Optional[int]												=						TypeVar('VT')
class      _UpperCAmelCase   (							Generic[KT, VT]       ):



	def __init__(  self     :       List[Any]			,    _lowercase     :       KT | str = "root"			,    _lowercase     :       VT | None = None						):
		__UpperCAmelCase      		= key
		__UpperCAmelCase      		= value
		__UpperCAmelCase      		= []



	def __repr__(  self     :       str						):
		return F'''Node({self.key}: {self.value})'''



	@property
	def        a  (  self     :       Union[str, Any]						):
		return len(self.forward						)






class      _UpperCAmelCase   (							Generic[KT, VT]       ):



	def __init__(  self     :       int			,    _lowercase     :       float = 0.5			,    _lowercase     :       int = 16						):
		__UpperCAmelCase      		= Node[KT, VT]()
		__UpperCAmelCase      		= 0
		__UpperCAmelCase      		= p
		__UpperCAmelCase      		= max_level



	def __str__(  self     :       Dict						):
		__UpperCAmelCase      		= list(self						)

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

		__UpperCAmelCase      		= max((len(str(_lowercase						)						) for item in items)			,    default=4						)
		__UpperCAmelCase      		= max(_lowercase			,    4						) + 4

		__UpperCAmelCase      		= self.head
		__UpperCAmelCase      		= []

		__UpperCAmelCase      		= node.forward.copy()
		lines.append(F'''[{node.key}]'''.ljust(_lowercase			,    '''-'''						) + '''* ''' * len(_lowercase						)						)
		lines.append(''' ''' * label_size + '''| ''' * len(_lowercase						)						)

		while len(node.forward						) != 0:
			__UpperCAmelCase      		= 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						)						)
			__UpperCAmelCase      		= node.forward

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



	def __iter__(  self     :       int						):
		__UpperCAmelCase      		= self.head

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



	def        a  (  self     :       Optional[Any]						):
		__UpperCAmelCase      		= 1
		while random() < self.p and level < self.max_level:
			level += 1

		return level



	def        a  (  self     :       Optional[int]			,    _lowercase     :       Tuple						):
		__UpperCAmelCase      		= []

		__UpperCAmelCase      		= 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:
				__UpperCAmelCase      		= 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        a  (  self     :       Optional[Any]			,    _lowercase     :       KT						):
		__UpperCAmelCase		,							__UpperCAmelCase      		= 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:
						__UpperCAmelCase      		= node.forward[i]
					else:
						__UpperCAmelCase      		= update_node.forward[:i]



	def        a  (  self     :       Union[str, Any]			,    _lowercase     :       KT			,    _lowercase     :       VT						):
		__UpperCAmelCase		,							__UpperCAmelCase      		= self._locate_node(_lowercase						)
		if node is not None:
			__UpperCAmelCase      		= value
		else:
			__UpperCAmelCase      		= 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						)
				__UpperCAmelCase      		= level

			__UpperCAmelCase      		= 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:
					__UpperCAmelCase      		= new_node



	def        a  (  self     :       List[Any]			,    _lowercase     :       VT						):
		__UpperCAmelCase		,							__UpperCAmelCase      		= self._locate_node(_lowercase						)

		if node is not None:
			return node.value

		return None






def       lowercase__						(       ):
	__UpperCAmelCase      		= SkipList()
	skip_list.insert('''Key1'''			,		3    )
	skip_list.insert('''Key2'''			,		12    )
	skip_list.insert('''Key3'''			,		41    )
	skip_list.insert('''Key4'''			,		-19    )

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

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





def       lowercase__						(       ):
	__UpperCAmelCase      		= 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    )

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

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





def       lowercase__						(       ):
	__UpperCAmelCase      		= SkipList()
	assert skip_list.find('''Some key'''    ) is None





def       lowercase__						(       ):
	__UpperCAmelCase      		= 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       lowercase__						(       ):
	__UpperCAmelCase      		= SkipList()
	skip_list.delete('''Some key'''    )

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





def       lowercase__						(       ):
	__UpperCAmelCase      		= 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       lowercase__						(       ):
	__UpperCAmelCase      		= 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       lowercase__						(       ):
	__UpperCAmelCase      		= 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(snake_case_   :int    ):
		yield node.key
		for forward_node in node.forward:
			yield from traverse_keys(snake_case_    )

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





def       lowercase__						(       ):
	def is_sorted(snake_case_   :Union[str, Any]    ):
		return all(next_item >= item for item, next_item in zip(snake_case_			,		lst[1:]    )    )

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





def       lowercase__						(       ):
	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       lowercase__						(       ):
	__UpperCAmelCase      		= 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(snake_case_    )


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				main()








def 	UpperCamelCase	(							snake_case__  : float						,snake_case__  : int	):




     '''simple docstring'''






     if digit_amount > 0:
          return round(number - int(snake_case__	)						,snake_case__	)
     return number - int(snake_case__	)


if __name__ == "__main__":
     print(decimal_isolate(1.5_3, 0))
     print(decimal_isolate(3_5.3_4_5, 1))
     print(decimal_isolate(3_5.3_4_5, 2))
     print(decimal_isolate(3_5.3_4_5, 3))
     print(decimal_isolate(-1_4.7_8_9, 3))
     print(decimal_isolate(0, 2))
     print(decimal_isolate(-1_4.1_2_3, 1))
     print(decimal_isolate(-1_4.1_2_3, 2))
     print(decimal_isolate(-1_4.1_2_3, 3))


