
'''simple docstring'''







from __future__ import annotations

from random import random
from typing import Generic, TypeVar

_lowercase			:  Optional[Any]   							=	TypeVar("KT")
_lowercase			:  List[str]   							=	TypeVar("VT")






class 			lowerCAmelCase__       (  Generic[KT, VT]					):






					def __init__(       self    ,							__SCREAMING_SNAKE_CASE = "root"    ,							__SCREAMING_SNAKE_CASE = None		):


											"""simple docstring"""





											lowercase_     :					Tuple													=	key
											lowercase_     :					str													=	value
											lowercase_     :					Union[str, Any]													=	[]






					def __repr__(       self		):


											"""simple docstring"""





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






					@property
					def      _snake_case   (       self		):


											"""simple docstring"""





											return len(self.forward		)







class 			lowerCAmelCase__       (  Generic[KT, VT]					):






					def __init__(       self    ,							__SCREAMING_SNAKE_CASE = 0.5    ,							__SCREAMING_SNAKE_CASE = 16		):


											"""simple docstring"""





											lowercase_     :					Union[str, Any]													=	Node[KT, VT]()
											lowercase_     :					Union[str, Any]													=	0
											lowercase_     :					List[str]													=	p
											lowercase_     :					Union[str, Any]													=	max_level






					def __str__(       self		):


											"""simple docstring"""





											lowercase_     :					Dict													=	list(self		)

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

											lowercase_     :					str													=	max((len(str(__SCREAMING_SNAKE_CASE		)		) for item in items)    ,							default=4		)
											lowercase_     :					Optional[int]													=	max(__SCREAMING_SNAKE_CASE    ,							4		) + 4

											lowercase_     :					Any													=	self.head
											lowercase_     :					List[str]													=	[]

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

											while len(node.forward		) != 0:
																	lowercase_     :					List[str]													=	node.forward[0]

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

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






					def __iter__(       self		):


											"""simple docstring"""





											lowercase_     :					Optional[Any]													=	self.head

											while len(node.forward		) != 0:
																	yield node.forward[0].key
																	lowercase_     :					Union[str, Any]													=	node.forward[0]






					def      _snake_case   (       self		):


											"""simple docstring"""





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

											return level






					def      _snake_case   (       self    ,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_     :					Optional[int]													=	[]

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

											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    ,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_						,			lowercase_     :					Tuple													=	self._locate_node(__SCREAMING_SNAKE_CASE		)

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






					def      _snake_case   (       self    ,							__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_						,			lowercase_     :					List[Any]													=	self._locate_node(__SCREAMING_SNAKE_CASE		)
											if node is not None:
																	lowercase_     :					Any													=	value
											else:
																	lowercase_     :					str													=	self.random_level()

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

																	lowercase_     :					int													=	Node(__SCREAMING_SNAKE_CASE    ,							__SCREAMING_SNAKE_CASE		)

																	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(__SCREAMING_SNAKE_CASE		)
																							else:
																													lowercase_     :					List[Any]													=	new_node






					def      _snake_case   (       self    ,							__SCREAMING_SNAKE_CASE		):


											"""simple docstring"""





											lowercase_						,			lowercase_     :					Optional[Any]													=	self._locate_node(__SCREAMING_SNAKE_CASE		)

											if node is not None:
																	return node.value

											return None







def  snake_case_		(    ):



						"""simple docstring"""





						lowercase_     :					List[str]													=	SkipList()
						skip_list.insert('''Key1'''				,				3							)
						skip_list.insert('''Key2'''				,				12							)
						skip_list.insert('''Key3'''				,				41							)
						skip_list.insert('''Key4'''				,				-19							)

						lowercase_     :					List[str]													=	skip_list.head
						lowercase_     :					Any													=	{}
						while node.level != 0:
												lowercase_     :					Tuple													=	node.forward[0]
												lowercase_     :					Any													=	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  snake_case_		(    ):



						"""simple docstring"""





						lowercase_     :					Optional[Any]													=	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							)

						lowercase_     :					Dict													=	skip_list.head
						lowercase_     :					Tuple													=	{}
						while node.level != 0:
												lowercase_     :					Union[str, Any]													=	node.forward[0]
												lowercase_     :					Optional[int]													=	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  snake_case_		(    ):



						"""simple docstring"""





						lowercase_     :					Any													=	SkipList()
						assert skip_list.find('''Some key'''							) is None
def  snake_case_		(    ):



						"""simple docstring"""





						lowercase_     :					Dict													=	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  snake_case_		(    ):



						"""simple docstring"""





						lowercase_     :					int													=	SkipList()
						skip_list.delete('''Some key'''							)

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



						"""simple docstring"""





						lowercase_     :					List[Any]													=	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  snake_case_		(    ):



						"""simple docstring"""





						lowercase_     :					List[str]													=	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  snake_case_		(    ):



						"""simple docstring"""





						lowercase_     :					Dict													=	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(__SCREAMING_SNAKE_CASE :			Any							):
												yield node.key
												for forward_node in node.forward:
																		yield from traverse_keys(lowerCAmelCase__							)

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



						"""simple docstring"""





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

						lowercase_     :					Dict													=	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  snake_case_		(    ):



						"""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  snake_case_		(    ):



						"""simple docstring"""





						lowercase_     :					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(lowerCAmelCase__							)


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						main()





'''simple docstring'''







from PIL import Image
def  snake_case_		(    __SCREAMING_SNAKE_CASE :			Image				,				__SCREAMING_SNAKE_CASE :			int							):



						"""simple docstring"""





						lowercase_     :					Optional[int]													=	(259 * (level + 255)) / (255 * (259 - level))

						def contrast(__SCREAMING_SNAKE_CASE :			int							) -> int:
												return int(128 + factor * (c - 128)							)

						return img.point(__SCREAMING_SNAKE_CASE							)


if __name__ == "__main__":
							# Load image
							with Image.open("image_data/lena.jpg") as img:
														# Change contrast to 170
														_lowercase			:  Union[str, Any]   							=	change_contrast(img, 1_7_0)
														cont_img.save("image_data/lena_high_contrast.png", format="png")



