






import numpy as np
import skfuzzy as fuzz

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

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







				"""simple docstring"""
				# Checks if the entire collection has been sorted
				if len(_A  ) <= 1 or n <= 1:
								return

				insert_next(_A      ,   n - 1  )
				rec_insertion_sort(_A      ,   n - 1  )
def      a_ (      _A      ,   _A  )			->			Tuple:







				"""simple docstring"""
				# Checks order between adjacent elements
				if index >= len(_A  ) or collection[index - 1] <= collection[index]:
								return

				# Swaps adjacent elements since they are not in ascending order
				snake_case__							,						snake_case__									=     (
				    collection[index],
				    collection[index - 1],
				)

				insert_next(_A      ,   index + 1  )


if __name__ == "__main__":
							__UpperCamelCase					:		Optional[int]	  =						input("""Enter integers separated by spaces: """)
							__UpperCamelCase					:		list[int]	  =						[int(num) for num in numbers.split()]
							rec_insertion_sort(number_list, len(number_list))
							print(number_list)




