






import numpy as np
import skfuzzy as fuzz

if __name__ == "__main__":
							# Create universe of discourse in Python using linspace ()
							__UpperCamelCase					:		List[str]	  =						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).
							__UpperCamelCase					:		Tuple	  =						[0, 25, 50]
							__UpperCamelCase					:		str	  =						[25, 50, 75]
							__UpperCamelCase					:		Optional[Any]	  =						fuzz.membership.trimf(X, abca)
							__UpperCamelCase					:		Any	  =						fuzz.membership.trimf(X, abca)

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












from __future__ import annotations

from collections.abc import Iterator
from typing import Any


class   __SCREAMING_SNAKE_CASE:
							def __init__(     self:      int       ,	UpperCamelCase:      Any						)		->		List[Any]:
											snake_case__									=     data
											snake_case__									=     None


class   __SCREAMING_SNAKE_CASE:
							def __init__(     self:      Dict						)		->		Optional[Any]:
											snake_case__									=     None
											snake_case__									=     None
							def __iter__(     self:      Optional[int]						)		->		Iterator[Any]:
											snake_case__									=     self.head
											while self.head:
															yield node.data
															snake_case__									=     node.next
															if node == self.head:
																			break
							def __len__(     self:      int						)		->		int:
											return sum(1 for _ in self						)
							def __repr__(     self:      int						)		->		Optional[int]:
											return "->".join(str(UpperCamelCase						) for item in iter(self						)						)
							def lowerCAmelCase_ (     self:      Union[str, Any]       ,	UpperCamelCase:      Any						)		->		None:
											self.insert_nth(len(self						)       ,	UpperCamelCase						)
							def lowerCAmelCase_ (     self:      Tuple       ,	UpperCamelCase:      Any						)		->		None:
											self.insert_nth(0       ,	UpperCamelCase						)
							def lowerCAmelCase_ (     self:      int       ,	UpperCamelCase:      int       ,	UpperCamelCase:      Any						)		->		None:
											if index < 0 or index > len(self						):
															raise IndexError('list index out of range.'						)
											snake_case__									=     Node(UpperCamelCase						)
											if self.head is None:
															snake_case__									=     new_node  # first node points itself
															snake_case__									=     snake_case__									=     new_node
											elif index == 0:  # insert at head
															snake_case__									=     self.head
															snake_case__									=     snake_case__									=     new_node
											else:
															snake_case__									=     self.head
															for _ in range(index - 1						):
																			snake_case__									=     temp.next
															snake_case__									=     temp.next
															snake_case__									=     new_node
															if index == len(self						) - 1:  # insert at tail
																			snake_case__									=     new_node
							def lowerCAmelCase_ (     self:      Optional[int]						)		->		Union[str, Any]:
											return self.delete_nth(0						)
							def lowerCAmelCase_ (     self:      Union[str, Any]						)		->		Any:
											return self.delete_nth(len(self						) - 1						)
							def lowerCAmelCase_ (     self:      str       ,	UpperCamelCase:      int = 0						)		->		Any:
											if not 0 <= index < len(self						):
															raise IndexError('list index out of range.'						)
											snake_case__									=     self.head
											if self.head == self.tail:  # just one node
															snake_case__									=     snake_case__									=     None
											elif index == 0:  # delete head node
															snake_case__									=     self.tail.next.next
															snake_case__									=     self.head.next
											else:
															snake_case__									=     self.head
															for _ in range(index - 1						):
																			snake_case__									=     temp.next
															snake_case__									=     temp.next
															snake_case__									=     temp.next.next
															if index == len(self						) - 1:  # delete at tail
																			snake_case__									=     temp
											return delete_node.data


							def lowerCAmelCase_ (     self:      Union[str, Any]						)		->		bool:
											return len(self						) == 0


def      a_ (      )			->			None:







				"""simple docstring"""
				snake_case__									=     CircularLinkedList()
				assert len(_A  ) == 0
				assert circular_linked_list.is_empty() is True
				assert str(_A  ) == ""

				try:
								circular_linked_list.delete_front()
								raise AssertionError  # This should not happen
				except IndexError:
								assert True  # This should happen

				try:
								circular_linked_list.delete_tail()
								raise AssertionError  # This should not happen
				except IndexError:
								assert True  # This should happen

				try:
								circular_linked_list.delete_nth(-1  )
								raise AssertionError
				except IndexError:
								assert True

				try:
								circular_linked_list.delete_nth(0  )
								raise AssertionError
				except IndexError:
								assert True

				assert circular_linked_list.is_empty() is True
				for i in range(5  ):
								assert len(_A  ) == i
								circular_linked_list.insert_nth(_A      ,   i + 1  )
				assert str(_A  ) == "->".join(str(_A  ) for i in range(1      ,   6  )  )

				circular_linked_list.insert_tail(6  )
				assert str(_A  ) == "->".join(str(_A  ) for i in range(1      ,   7  )  )
				circular_linked_list.insert_head(0  )
				assert str(_A  ) == "->".join(str(_A  ) for i in range(0      ,   7  )  )

				assert circular_linked_list.delete_front() == 0
				assert circular_linked_list.delete_tail() == 6
				assert str(_A  ) == "->".join(str(_A  ) for i in range(1      ,   6  )  )
				assert circular_linked_list.delete_nth(2  ) == 3

				circular_linked_list.insert_nth(2      ,   3  )
				assert str(_A  ) == "->".join(str(_A  ) for i in range(1      ,   6  )  )

				assert circular_linked_list.is_empty() is False


if __name__ == "__main__":
							import doctest

							doctest.testmod()




