import numpy as np
import skfuzzy as fuzz

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

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


def       __magic_name__(  __UpperCAmelCase ,						__UpperCAmelCase		)						->    bool:



      '''simple docstring'''

      _lowerCamelCase			    =				len(__UpperCAmelCase		)
      _lowerCamelCase			    =				[[False] * (required_sum + 1) for _ in range(arr_len + 1		)]

      # for each arr value, a sum of zero(0) can be formed by not taking any element
      # hence True/1
      for i in range(arr_len + 1		):
            _lowerCamelCase			    =				True

      # sum is not zero and set is empty then false
      for i in range(1 ,						required_sum + 1		):
            _lowerCamelCase			    =				False

      for i in range(1 ,						arr_len + 1		):
            for j in range(1 ,						required_sum + 1		):
                  if arr[i - 1] > j:
                        _lowerCamelCase			    =				subset[i - 1][j]
                  if arr[i - 1] <= j:
                        _lowerCamelCase			    =				subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

      return subset[arr_len][required_sum]


if __name__ == "__main__":
     import doctest

     doctest.testmod()