



"""simple docstring"""






from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def 			_lowercase				(  __snake_case					,__snake_case	)						->   str | Literal[False]:
			__lowerCAmelCase      :  Optional[int]												=       list(lowerCAmelCase_	)
			__lowerCAmelCase      :  Optional[Any]												=       list(lowerCAmelCase_	)
			__lowerCAmelCase      :  Union[str, Any]												=       0
			for i in range(len(lowerCAmelCase_	)	):
						if lista[i] != lista[i]:
									count += 1
									__lowerCAmelCase      :  Optional[int]												=       '_'
			if count > 1:
						return False
			else:
						return "".join(lowerCAmelCase_	)


def 			_lowercase				(  __snake_case	)						->   list[str]:
			__lowerCAmelCase      :  Optional[int]												=       []
			while True:
						__lowerCAmelCase      :  Any												=       ['$'] * len(lowerCAmelCase_	)
						__lowerCAmelCase      :  List[str]												=       []
						for i in range(len(lowerCAmelCase_	)	):
									for j in range(i + 1					,len(lowerCAmelCase_	)	):
												__lowerCAmelCase      :  Optional[int]												=       compare_string(binary[i]					,binary[j]	)
												if k is False:
															__lowerCAmelCase      :  Optional[Any]												=       '*'
															__lowerCAmelCase      :  Optional[Any]												=       '*'
															temp.append("X"	)
						for i in range(len(lowerCAmelCase_	)	):
									if checka[i] == "$":
												pi.append(binary[i]	)
						if len(lowerCAmelCase_	) == 0:
									return pi
						__lowerCAmelCase      :  Any												=       list(set(lowerCAmelCase_	)	)


def 			_lowercase				(  __snake_case					,__snake_case	)						->   list[str]:
			__lowerCAmelCase      :  int												=       []
			for minterm in minterms:
						__lowerCAmelCase      :  Optional[int]												=       ''
						for _ in range(lowerCAmelCase_	):
									__lowerCAmelCase      :  Union[str, Any]												=       str(minterm % 2	) + string
									minterm //= 2
						temp.append(lowerCAmelCase_	)
			return temp


def 			_lowercase				(  __snake_case					,__snake_case					,__snake_case	)						->   bool:
			__lowerCAmelCase      :  int												=       list(lowerCAmelCase_	)
			__lowerCAmelCase      :  Union[str, Any]												=       list(lowerCAmelCase_	)
			__lowerCAmelCase      :  str												=       0
			for i in range(len(lowerCAmelCase_	)	):
						if lista[i] != lista[i]:
									count_n += 1
			return count_n == count


def 			_lowercase				(  __snake_case					,__snake_case	)						->   list[str]:
			__lowerCAmelCase      :  List[Any]												=       []
			__lowerCAmelCase      :  Optional[Any]												=       [0] * len(lowerCAmelCase_	)
			for i in range(len(chart[0]	)	):
						__lowerCAmelCase      :  Union[str, Any]												=       0
						__lowerCAmelCase      :  int												=       -1
						for j in range(len(lowerCAmelCase_	)	):
									if chart[j][i] == 1:
												count += 1
												__lowerCAmelCase      :  int												=       j
						if count == 1:
									__lowerCAmelCase      :  List[Any]												=       1
			for i in range(len(lowerCAmelCase_	)	):
						if select[i] == 1:
									for j in range(len(chart[0]	)	):
												if chart[i][j] == 1:
															for k in range(len(lowerCAmelCase_	)	):
																		__lowerCAmelCase      :  Any												=       0
									temp.append(prime_implicants[i]	)
			while True:
						__lowerCAmelCase      :  Union[str, Any]												=       0
						__lowerCAmelCase      :  List[Any]												=       -1
						__lowerCAmelCase      :  str												=       0
						for i in range(len(lowerCAmelCase_	)	):
									__lowerCAmelCase      :  Union[str, Any]												=       chart[i].count(1	)
									if count_n > max_n:
												__lowerCAmelCase      :  Any												=       count_n
												__lowerCAmelCase      :  int												=       i

						if max_n == 0:
									return temp

						temp.append(prime_implicants[rem]	)

						for i in range(len(chart[0]	)	):
									if chart[rem][i] == 1:
												for j in range(len(lowerCAmelCase_	)	):
															__lowerCAmelCase      :  List[str]												=       0


def 			_lowercase				(  __snake_case					,__snake_case	)						->   list[list[int]]:
			__lowerCAmelCase      :  int												=       [[0 for x in range(len(lowerCAmelCase_	)	)] for x in range(len(lowerCAmelCase_	)	)]
			for i in range(len(lowerCAmelCase_	)	):
						__lowerCAmelCase      :  str												=       prime_implicants[i].count("_"	)
						for j in range(len(lowerCAmelCase_	)	):
									if is_for_table(prime_implicants[i]					,binary[j]					,lowerCAmelCase_	):
												__lowerCAmelCase      :  Optional[Any]												=       1

			return chart


def 			_lowercase				(  )						->   None:
			__lowerCAmelCase      :  Optional[int]												=       int(input("Enter the no. of variables\n"	)	)
			__lowerCAmelCase      :  List[Any]												=       [
			    float(lowerCAmelCase_	)
			    for x in input(
			        "Enter the decimal representation of Minterms \'Spaces Separated\'\n"	).split()
			]
			__lowerCAmelCase      :  List[str]												=       decimal_to_binary(lowerCAmelCase_					,lowerCAmelCase_	)

			__lowerCAmelCase      :  Dict												=       check(lowerCAmelCase_	)
			print("Prime Implicants are:"	)
			print(lowerCAmelCase_	)
			__lowerCAmelCase      :  List[Any]												=       prime_implicant_chart(lowerCAmelCase_					,lowerCAmelCase_	)

			__lowerCAmelCase      :  int												=       selection(lowerCAmelCase_					,lowerCAmelCase_	)
			print("Essential Prime Implicants are:"	)
			print(lowerCAmelCase_	)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()




'''simple docstring'''

from __future__ import annotations

from collections.abc import Sequence
from typing import Literal



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_  )			->      str | Literal[False]:
		_a     :      Optional[int]        =							list(lowerCAmelCase_  )
		_a     :      Optional[Any]        =							list(lowerCAmelCase_  )
		_a     :      Union[str, Any]        =							0
		for i in range(len(lowerCAmelCase_  )  ):
				if lista[i] != lista[i]:
						count += 1
						_a     :      Optional[int]        =							'_'
		if count > 1:
				return False
		else:
				return "".join(lowerCAmelCase_  )



def      __lowerCamelCase     (      lowerCAmelCase_  )			->      list[str]:
		_a     :      Optional[int]        =							[]
		while True:
				_a     :      Any        =							['$'] * len(lowerCAmelCase_  )
				_a     :      List[str]        =							[]
				for i in range(len(lowerCAmelCase_  )  ):
						for j in range(i + 1						,			len(lowerCAmelCase_  )  ):
								_a     :      Optional[int]        =							compare_string(binary[i]						,			binary[j]  )
								if k is False:
										_a     :      Optional[Any]        =							'*'
										_a     :      Optional[Any]        =							'*'
										temp.append('X'  )
				for i in range(len(lowerCAmelCase_  )  ):
						if checka[i] == "$":
								pi.append(binary[i]  )
				if len(lowerCAmelCase_  ) == 0:
						return pi
				_a     :      Any        =							list(set(lowerCAmelCase_  )  )



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_  )			->      list[str]:
		_a     :      int        =							[]
		for minterm in minterms:
				_a     :      Optional[int]        =							''
				for _ in range(lowerCAmelCase_  ):
						_a     :      Union[str, Any]        =							str(minterm % 2  ) + string
						minterm //= 2
				temp.append(lowerCAmelCase_  )
		return temp



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_						,			lowerCAmelCase_  )			->      bool:
		_a     :      int        =							list(lowerCAmelCase_  )
		_a     :      Union[str, Any]        =							list(lowerCAmelCase_  )
		_a     :      str        =							0
		for i in range(len(lowerCAmelCase_  )  ):
				if lista[i] != lista[i]:
						count_n += 1
		return count_n == count



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_  )			->      list[str]:
		_a     :      List[Any]        =							[]
		_a     :      Optional[Any]        =							[0] * len(lowerCAmelCase_  )
		for i in range(len(chart[0]  )  ):
				_a     :      Union[str, Any]        =							0
				_a     :      int        =							-1
				for j in range(len(lowerCAmelCase_  )  ):
						if chart[j][i] == 1:
								count += 1
								_a     :      int        =							j
				if count == 1:
						_a     :      List[Any]        =							1
		for i in range(len(lowerCAmelCase_  )  ):
				if select[i] == 1:
						for j in range(len(chart[0]  )  ):
								if chart[i][j] == 1:
										for k in range(len(lowerCAmelCase_  )  ):
												_a     :      Any        =							0
						temp.append(prime_implicants[i]  )
		while True:
				_a     :      Union[str, Any]        =							0
				_a     :      List[Any]        =							-1
				_a     :      str        =							0
				for i in range(len(lowerCAmelCase_  )  ):
						_a     :      Union[str, Any]        =							chart[i].count(1  )
						if count_n > max_n:
								_a     :      Any        =							count_n
								_a     :      int        =							i

				if max_n == 0:
						return temp

				temp.append(prime_implicants[rem]  )

				for i in range(len(chart[0]  )  ):
						if chart[rem][i] == 1:
								for j in range(len(lowerCAmelCase_  )  ):
										_a     :      List[str]        =							0



def      __lowerCamelCase     (      lowerCAmelCase_						,			lowerCAmelCase_  )			->      list[list[int]]:
		_a     :      int        =							[[0 for x in range(len(lowerCAmelCase_  )  )] for x in range(len(lowerCAmelCase_  )  )]
		for i in range(len(lowerCAmelCase_  )  ):
				_a     :      str        =							prime_implicants[i].count('_'  )
				for j in range(len(lowerCAmelCase_  )  ):
						if is_for_table(prime_implicants[i]						,			binary[j]						,			lowerCAmelCase_  ):
								_a     :      Optional[Any]        =							1

		return chart



def      __lowerCamelCase     (      )			->      None:
		_a     :      Optional[int]        =							int(input('Enter the no. of variables\n'  )  )
		_a     :      List[Any]        =							[
		    float(lowerCAmelCase_  )
		    for x in input(
		        'Enter the decimal representation of Minterms \'Spaces Separated\'\n'  ).split()
		]
		_a     :      List[str]        =							decimal_to_binary(lowerCAmelCase_						,			lowerCAmelCase_  )

		_a     :      Dict        =							check(lowerCAmelCase_  )
		print('Prime Implicants are:'  )
		print(lowerCAmelCase_  )
		_a     :      List[Any]        =							prime_implicant_chart(lowerCAmelCase_						,			lowerCAmelCase_  )

		_a     :      int        =							selection(lowerCAmelCase_						,			lowerCAmelCase_  )
		print('Essential Prime Implicants are:'  )
		print(lowerCAmelCase_  )


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()




