"""simple docstring"""






import numpy as np
import skfuzzy as fuzz

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

						# Compute the different operations using inbuilt functions.
						lowerCAmelCase__						:						List[Any]		  =			np.ones(75)
						lowerCAmelCase__						:						Any		  =			np.zeros((75,))
						# 1. Union = max(µA(x), µB(x))
						lowerCAmelCase__						:						Dict		  =			fuzz.fuzzy_or(X, young, X, middle_aged)[1]
						# 2. Intersection = min(µA(x), µB(x))
						lowerCAmelCase__						:						Tuple		  =			fuzz.fuzzy_and(X, young, X, middle_aged)[1]
						# 3. Complement (A) = (1- min(µA(x))
						lowerCAmelCase__						:						Dict		  =			fuzz.fuzzy_not(young)
						# 4. Difference (A/B) = min(µA(x),(1- µB(x)))
						lowerCAmelCase__						:						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))]
						lowerCAmelCase__						:						Dict		  =			young + middle_aged - (young * middle_aged)
						# 6. Algebraic Product = (µA(x) * µB(x))
						lowerCAmelCase__						:						str		  =			young * middle_aged
						# 7. Bounded Sum = min[1,(µA(x), µB(x))]
						lowerCAmelCase__						:						Union[str, Any]		  =			fuzz.fuzzy_and(X, one, X, young + middle_aged)[1]
						# 8. Bounded difference = min[0,(µA(x), µB(x))]
						lowerCAmelCase__						:						Tuple		  =			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 						a_		(      lowerCamelCase = 2_0_0_0_0_0_0 ):
				UpperCAmelCase__    =							[0]
				UpperCAmelCase__    =							42

				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
				UpperCAmelCase__    =							0
				# the area corresponding to the grid that gives the product closest to target
				UpperCAmelCase__    =							0
				# an estimate of b, using the quadratic formula
				UpperCAmelCase__    =							42
				# the largest integer less than b_estimate
				UpperCAmelCase__    =							42
				# the largest integer less than b_estimate
				UpperCAmelCase__    =							42
				# the triangle number corresponding to b_floor
				UpperCAmelCase__    =							42
				# the triangle number corresponding to b_ceil
				UpperCAmelCase__    =							42

				for idx_a, triangle_a in enumerate(triangle_numbers[1:]      ,    1 ):
								UpperCAmelCase__    =							(-1 + sqrt(1 + 8 * target / triangle_a )) / 2
								UpperCAmelCase__    =							floor(lowerCamelCase )
								UpperCAmelCase__    =							ceil(lowerCamelCase )
								UpperCAmelCase__    =							triangle_numbers[b_floor]
								UpperCAmelCase__    =							triangle_numbers[b_ceil]

								if abs(target - triangle_b_first_guess * triangle_a ) < abs(
								    target - best_product ):
												UpperCAmelCase__    =							triangle_b_first_guess * triangle_a
												UpperCAmelCase__    =							idx_a * b_floor

								if abs(target - triangle_b_second_guess * triangle_a ) < abs(
								    target - best_product ):
												UpperCAmelCase__    =							triangle_b_second_guess * triangle_a
												UpperCAmelCase__    =							idx_a * b_ceil

				return area


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



