


'''simple docstring'''



from __future__ import annotations

from random import random
from typing import Generic, TypeVar

__lowercase     :						Any	=     TypeVar('KT')
__lowercase     :						Optional[int]	=     TypeVar('VT')





class 							__UpperCamelCase    (		Generic[KT, VT] ):




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

						'''simple docstring'''





						__a      :	Any    =  key
						__a      :	Optional[int]    =  value
						__a      :	list[Node[KT, VT]]    =  []




	def __repr__(       self							):

						'''simple docstring'''





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





	@property
	def 				__UpperCAmelCase							(       self							):

						'''simple docstring'''





						return len(self.forward							)





class 							__UpperCamelCase    (		Generic[KT, VT] ):




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

						'''simple docstring'''





						__a      :	Node[KT, VT]    =  Node[KT, VT]()
						__a      :	str    =  0
						__a      :	List[Any]    =  p
						__a      :	Optional[int]    =  max_level




	def __str__(       self							):

						'''simple docstring'''





						__a      :	List[Any]    =  list(self							)

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

						__a      :	List[str]    =  max((len(str(__lowercase							)							) for item in items)						,    default=4							)
						__a      :	Union[str, Any]    =  max(__lowercase						,    4							) + 4

						__a      :	Optional[int]    =  self.head
						__a      :	Optional[Any]    =  []

						__a      :	List[str]    =  node.forward.copy()
						lines.append(f"""[{node.key}]""".ljust(__lowercase						,    '-'							) + '* ' * len(__lowercase							)							)
						lines.append(' ' * label_size + '| ' * len(__lowercase							)							)

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

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




	def __iter__(       self							):

						'''simple docstring'''





						__a      :	Optional[int]    =  self.head

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




	def 				__UpperCAmelCase							(       self							):

						'''simple docstring'''





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

						return level




	def 				__UpperCAmelCase							(       self						,    __a							):

						'''simple docstring'''





						__a      :	List[Any]    =  []

						__a      :	Dict    =  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:
																__a      :	int    =  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 				__UpperCAmelCase							(       self						,    __a							):

						'''simple docstring'''





						__a      :	Optional[int]    =  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:
																										__a      :	Dict    =  node.forward[i]
																					else:
																										__a      :	List[str]    =  update_node.forward[:i]




	def 				__UpperCAmelCase							(       self						,    __a						,    __a							):

						'''simple docstring'''





						__a      :	Dict    =  self._locate_node(__lowercase							)
						if node is not None:
											__a      :	Tuple    =  value
						else:
											__a      :	Union[str, Any]    =  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							)
																__a      :	Optional[int]    =  level

											__a      :	List[str]    =  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:
																					__a      :	Optional[int]    =  new_node





	def 				__UpperCAmelCase							(       self						,    __a							):

						'''simple docstring'''





						__a      :	int    =  self._locate_node(__lowercase							)

						if node is not None:
											return node.value

						return None






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

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

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






def   lowerCamelCase							():
					__a      :	int    =  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       )

					__a      :	int    =  skip_list.head
					__a      :	Optional[Any]    =  {}
					while node.level != 0:
										__a      :	Union[str, Any]    =  node.forward[0]
										__a      :	Any    =  node.value

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






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






def   lowerCamelCase							():
					__a      :	List[Any]    =  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							():
					__a      :	Union[str, Any]    =  SkipList()
					skip_list.delete('Some key'       )

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






def   lowerCamelCase							():
					__a      :	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'       )
					skip_list.delete('Key2'       )

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






def   lowerCamelCase							():
					__a      :	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   lowerCamelCase							():
					__a      :	Union[str, Any]    =  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				:       List[str]       ):
										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   lowerCamelCase							():







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

					__a      :	Dict    =  SkipList()
					for i in range(10       ):
										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(-12						,				-12       )
					skip_list.insert(77						,				77       )
					assert is_sorted(list(_SCREAMING_SNAKE_CASE       )       )






def   lowerCamelCase							():







					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							():
					__a      :	Union[str, Any]    =  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'''



import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
	# Create universe of discourse in Python using linspace ()
	__lowercase     :						int	=     np.linspace(start=0, stop=75, num=75, endpoint=True, retstep=False)

	# Create two fuzzy sets by defining any membership function
	# (trapmf(), gbellmf(), gaussmf(), etc).
	__lowercase     :						Any	=     [0, 25, 50]
	__lowercase     :						int	=     [25, 50, 75]
	__lowercase     :						List[str]	=     fuzz.membership.trimf(X, abca)
	__lowercase     :						Any	=     fuzz.membership.trimf(X, abca)

	# Compute the different operations using inbuilt functions.
	__lowercase     :						List[Any]	=     np.ones(75)
	__lowercase     :						Any	=     np.zeros((75,))
	# 1. Union = max(µA(x), µB(x))
	__lowercase     :						int	=     fuzz.fuzzy_or(X, young, X, middle_aged)[1]
	# 2. Intersection = min(µA(x), µB(x))
	__lowercase     :						int	=     fuzz.fuzzy_and(X, young, X, middle_aged)[1]
	# 3. Complement (A) = (1- min(µA(x))
	__lowercase     :						str	=     fuzz.fuzzy_not(young)
	# 4. Difference (A/B) = min(µA(x),(1- µB(x)))
	__lowercase     :						List[Any]	=     fuzz.fuzzy_and(X, young, X, fuzz.fuzzy_not(middle_aged)[1])[1]
	# 5. Algebraic Sum = [µA(x) + µB(x) – (µA(x) * µB(x))]
	__lowercase     :						Optional[Any]	=     young + middle_aged - (young * middle_aged)
	# 6. Algebraic Product = (µA(x) * µB(x))
	__lowercase     :						str	=     young * middle_aged
	# 7. Bounded Sum = min[1,(µA(x), µB(x))]
	__lowercase     :						Optional[Any]	=     fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
	# 8. Bounded difference = min[0,(µA(x), µB(x))]
	__lowercase     :						Union[str, Any]	=     fuzz.fuzzy_or(X, zero, X, young - middle_aged)[1]

	# max-min composition
	# max-product composition

	# Plot each set A, set B and each operation result using plot() and subplot().
	from matplotlib import pyplot as plt

	plt.figure()

	plt.subplot(4, 3, 1)
	plt.plot(X, young)
	plt.title('Young')
	plt.grid(True)

	plt.subplot(4, 3, 2)
	plt.plot(X, middle_aged)
	plt.title('Middle aged')
	plt.grid(True)

	plt.subplot(4, 3, 3)
	plt.plot(X, union)
	plt.title('union')
	plt.grid(True)

	plt.subplot(4, 3, 4)
	plt.plot(X, intersection)
	plt.title('intersection')
	plt.grid(True)

	plt.subplot(4, 3, 5)
	plt.plot(X, complement_a)
	plt.title('complement_a')
	plt.grid(True)

	plt.subplot(4, 3, 6)
	plt.plot(X, difference)
	plt.title('difference a/b')
	plt.grid(True)

	plt.subplot(4, 3, 7)
	plt.plot(X, alg_sum)
	plt.title('alg_sum')
	plt.grid(True)

	plt.subplot(4, 3, 8)
	plt.plot(X, alg_product)
	plt.title('alg_product')
	plt.grid(True)

	plt.subplot(4, 3, 9)
	plt.plot(X, bdd_sum)
	plt.title('bdd_sum')
	plt.grid(True)

	plt.subplot(4, 3, 10)
	plt.plot(X, bdd_difference)
	plt.title('bdd_difference')
	plt.grid(True)

	plt.subplots_adjust(hspace=0.5)
	plt.show()



