






from __future__ import annotations

from collections.abc import Callable
from typing import Any, Generic, TypeVar

SCREAMING_SNAKE_CASE 							=						TypeVar('T')
class 							A_    (						Generic[T]			):






 '''simple docstring'''




 def __init__(	self							,  _A							,  _A) ->		None:

     """simple docstring"""



     _UpperCAmelCase				:      Any | T			  =				None

     _UpperCAmelCase				:      int			  =				len(_A)
     _UpperCAmelCase				:      list[T]			  =				[any_type for _ in range(self.N)] + arr
     _UpperCAmelCase				:      Dict			  =				fnc
     self.build()


 def  snake_case__				(	self) ->		None:

     """simple docstring"""



     for p in range(self.N - 1							,  0							,  -1):
         _UpperCAmelCase				:      List[Any]			  =				self.fn(self.st[p * 2]							,  self.st[p * 2 + 1])


 def  snake_case__				(	self							,  _A							,  _A) ->		None:

     """simple docstring"""



     p += self.N
     _UpperCAmelCase				:      List[str]			  =				v
     while p > 1:
         _UpperCAmelCase				:      Optional[int]			  =				p // 2
         _UpperCAmelCase				:      List[Any]			  =				self.fn(self.st[p * 2]							,  self.st[p * 2 + 1])


 def  snake_case__				(	self							,  _A							,  _A) ->		T | None:  # noqa: E741

     """simple docstring"""



     _UpperCAmelCase				:      Dict			  =				l + self.N, r + self.N

     _UpperCAmelCase				:      T | None			  =				None
     while l <= r:
         if l % 2 == 1:
             _UpperCAmelCase				:      Dict			  =				self.st[l] if res is None else self.fn(_A							,  self.st[l])
         if r % 2 == 0:
             _UpperCAmelCase				:      List[Any]			  =				self.st[r] if res is None else self.fn(_A							,  self.st[r])
         _UpperCAmelCase				:      Union[str, Any]			  =				(l + 1) // 2, (r - 1) // 2
     return res


if __name__ == "__main__":
 from functools import reduce

 SCREAMING_SNAKE_CASE 							=						[1, 10, -2, 9, -3, 8, 4, -7, 5, 6, 11, -12]

 SCREAMING_SNAKE_CASE 							=						{
     0: 7,
     1: 2,
     2: 6,
     3: -14,
     4: 5,
     5: 4,
     6: 7,
     7: -10,
     8: 9,
     9: 10,
     10: 12,
     11: 1,
 }

 SCREAMING_SNAKE_CASE 							=						SegmentTree(test_array, min)
 SCREAMING_SNAKE_CASE 							=						SegmentTree(test_array, max)
 SCREAMING_SNAKE_CASE 							=						SegmentTree(test_array, lambda a, b: a + b)

 def      _lowerCamelCase	(						)      ->					None:
     for i in range(len(__A ) ):
         for j in range(__A		,		len(__A ) ):
             _UpperCAmelCase				:      Any			  =				reduce(__A		,		test_array[i : j + 1] )
             _UpperCAmelCase				:      List[str]			  =				reduce(__A		,		test_array[i : j + 1] )
             _UpperCAmelCase				:      Optional[int]			  =				reduce(lambda __A		,		__A : a + b		,		test_array[i : j + 1] )
             assert min_range == min_segment_tree.query(__A		,		__A )
             assert max_range == max_segment_tree.query(__A		,		__A )
             assert sum_range == sum_segment_tree.query(__A		,		__A )

 test_all_segments()

 for index, value in test_updates.items():
  SCREAMING_SNAKE_CASE 							=						value
  min_segment_tree.update(index, value)
  max_segment_tree.update(index, value)
  sum_segment_tree.update(index, value)
  test_all_segments()












import numpy as np
import skfuzzy as fuzz

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

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




