"""simple docstring"""







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()


"""simple docstring"""







__SCREAMING_SNAKE_CASE    	={}



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     int     ,			__SCREAMING_SNAKE_CASE							:     int     ,			__SCREAMING_SNAKE_CASE							:     int      ):

     # if we are absent twice, or late 3 consecutive days,
     # no further prize strings are possible
     if late == 3 or absent == 2:
          return 0

     # if we have no days left, and have not failed any other rules,
     # we have a prize string
     if days == 0:
          return 1

     # No easy solution, so now we need to do the recursive calculation

     # First, check if the combination is already in the cache, and
     # if yes, return the stored value from there since we already
     # know the number of possible prize strings from this point on
     lowercase_	:				Any													=	(days, absent, late)
     if key in cache:
          return cache[key]

     # now we calculate the three possible ways that can unfold from
     # this point on, depending on our attendance today

     # 1) if we are late (but not absent), the "absent" counter stays as
     # it is, but the "late" counter increases by one
     lowercase_	:				Optional[int]													=	_calculate(days - 1     ,			__SCREAMING_SNAKE_CASE     ,			late + 1      )

     # 2) if we are absent, the "absent" counter increases by 1, and the
     # "late" counter resets to 0
     lowercase_	:				Any													=	_calculate(days - 1     ,			absent + 1     ,			0      )

     # 3) if we are on time, this resets the "late" counter and keeps the
     # absent counter
     lowercase_	:				Dict													=	_calculate(days - 1     ,			__SCREAMING_SNAKE_CASE     ,			0      )

     lowercase_	:				str													=	state_late + state_absent + state_ontime

     lowercase_	:				Tuple													=	prizestrings
     return prizestrings



def 			lowercase__(       __SCREAMING_SNAKE_CASE							:     int = 30      ):
     return _calculate(__SCREAMING_SNAKE_CASE     ,			absent=0     ,			late=0      )


if __name__ == "__main__":
       print(solution())

