



import numpy as np
import skfuzzy as fuzz

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

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

import math
from collections import Counter
from string import ascii_lowercase






def      _A				(UpperCamelCase		:      str )  ->None:



			'''simple docstring'''







			lowerCamelCase__							,lowerCamelCase__ :      List[str]								=		analyze_text(UpperCamelCase )
			lowerCamelCase__ :      Any								=		list(""" """ + ascii_lowercase )
			# what is our total sum of probabilities.
			lowerCamelCase__ :      str								=		sum(single_char_strings.values() )

			# one length string
			lowerCamelCase__ :      Union[str, Any]								=		0
			# for each alpha we go in our dict and if it is in it we calculate entropy
			for ch in my_alphas:
						if ch in single_char_strings:
									lowerCamelCase__ :      List[Any]								=		single_char_strings[ch]
									lowerCamelCase__ :      List[str]								=		my_str / all_sum
									my_fir_sum += prob * math.loga(UpperCamelCase )  # entropy formula.

    # print entropy
			print(f"{round(-1 * my_fir_sum ):.1f}" )

			# two len string
			lowerCamelCase__ :      str								=		sum(two_char_strings.values() )
			lowerCamelCase__ :      int								=		0
			# for each alpha (two in size) calculate entropy.
			for cha in my_alphas:
						for cha in my_alphas:
									lowerCamelCase__ :      str								=		cha + cha
									if sequence in two_char_strings:
												lowerCamelCase__ :      str								=		two_char_strings[sequence]
												lowerCamelCase__ :      int								=		int(UpperCamelCase ) / all_sum
												my_sec_sum += prob * math.loga(UpperCamelCase )

    # print second entropy
			print(f"{round(-1 * my_sec_sum ):.1f}" )

			# print the difference between them
			print(f"{round((-1 * my_sec_sum) - (-1 * my_fir_sum) ):.1f}" )






def      _A				(UpperCamelCase		:      str )  ->tuple[dict, dict]:



			'''simple docstring'''







			lowerCamelCase__ :      Optional[int]								=		Counter()  # type: ignore
			lowerCamelCase__ :      List[Any]								=		Counter()  # type: ignore
			single_char_strings[text[-1]] += 1

			# first case when we have space at start.
			two_char_strings[" " + text[0]] += 1
			for i in range(0      ,			len(UpperCamelCase ) - 1 ):
						single_char_strings[text[i]] += 1
						two_char_strings[text[i : i + 2]] += 1
			return single_char_strings, two_char_strings






def      _A				()  ->List[str]:



			'''simple docstring'''







			import doctest

			doctest.testmod()
			# text = (
			#     "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
			#     "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
			#     "jointure saw horrible. He private he on be imagine suppose. Fertile "
			#     "beloved evident through no service elderly is. Blind there if every no so "
			#     "at. Own neglected you preferred way sincerity delivered his attempted. To "
			#     "of message cottage windows do besides against uncivil.  Delightful "
			#     "unreserved impossible few estimating men favourable see entreaties. She "
			#     "propriety immediate was improving. He or entrance humoured likewise "
			#     "moderate. Much nor game son say feel. Fat make met can must form into "
			#     "gate. Me we offending prevailed discovery. "
			# )

			# calculate_prob(text)


if __name__ == "__main__":
				main()



