import numpy as np
import skfuzzy as fuzz

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

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






'''simple docstring'''
from __future__ import annotations

from math import ceil, floor, sqrt




def    _UpperCamelCase						(       SCREAMING_SNAKE_CASE__ = 200_0000			)  ->							int:


		'''simple docstring'''


		snake_case  :       list[int]     			=						[0]
		snake_case  :       int

		for idx in range(1 ,       ceil(sqrt(target * 2			) * 1.1			)			):
				triangle_numbers.append(triangle_numbers[-1] + idx			)

		# we want this to be as close as possible to target
		snake_case  :       int     			=						0
		# the area corresponding to the grid that gives the product closest to target
		snake_case  :       int     			=						0
		# an estimate of b, using the quadratic formula
		snake_case  :       float
		# the largest integer less than b_estimate
		snake_case  :       int
		# the largest integer less than b_estimate
		snake_case  :       int
		# the triangle number corresponding to b_floor
		snake_case  :       int
		# the triangle number corresponding to b_ceil
		snake_case  :       int

		for idx_a, triangle_a in enumerate(triangle_numbers[1:] ,       1			):
				snake_case  :       int     			=						(-1 + sqrt(1 + 8 * target / triangle_a			)) / 2
				snake_case  :       Optional[int]     			=						floor(SCREAMING_SNAKE_CASE__			)
				snake_case  :       int     			=						ceil(SCREAMING_SNAKE_CASE__			)
				snake_case  :       Optional[Any]     			=						triangle_numbers[b_floor]
				snake_case  :       Union[str, Any]     			=						triangle_numbers[b_ceil]

				if abs(target - triangle_b_first_guess * triangle_a			) < abs(
				    target - best_product			):
						snake_case  :       str     			=						triangle_b_first_guess * triangle_a
						snake_case  :       int     			=						idx_a * b_floor

				if abs(target - triangle_b_second_guess * triangle_a			) < abs(
				    target - best_product			):
						snake_case  :       List[Any]     			=						triangle_b_second_guess * triangle_a
						snake_case  :       Any     			=						idx_a * b_ceil

		return area


if __name__ == "__main__":
						print(f"{solution() = }")


