


'''simple docstring'''



from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def    lowerCamelCase__   ( A     :    Dict   ,     A     :    Union[str, Any]  ):




						'''simple docstring'''






						UpperCAmelCase         =			list(_lowerCamelCase  )
						UpperCAmelCase         =			list(_lowerCamelCase  )
						UpperCAmelCase         =			0
						for i in range(len(_lowerCamelCase  )  ):
												if lista[i] != lista[i]:
																		count += 1
																		UpperCAmelCase         =			"_"
						if count > 1:
												return False
						else:
												return "".join(_lowerCamelCase  )


def    lowerCamelCase__   ( A     :    str  ):




						'''simple docstring'''






						UpperCAmelCase         =			[]
						while True:
												UpperCAmelCase         =			["$"] * len(_lowerCamelCase  )
												UpperCAmelCase         =			[]
												for i in range(len(_lowerCamelCase  )  ):
																		for j in range(i + 1   ,     len(_lowerCamelCase  )  ):
																								UpperCAmelCase         =			compare_string(binary[i]   ,     binary[j]  )
																								if k is False:
																														UpperCAmelCase         =			"*"
																														UpperCAmelCase         =			"*"
																														temp.append('''X'''  )
												for i in range(len(_lowerCamelCase  )  ):
																		if checka[i] == "$":
																								pi.append(binary[i]  )
												if len(_lowerCamelCase  ) == 0:
																		return pi
												UpperCAmelCase         =			list(set(_lowerCamelCase  )  )


def    lowerCamelCase__   ( A     :    Any   ,     A     :    Any  ):




						'''simple docstring'''






						UpperCAmelCase         =			[]
						for minterm in minterms:
												UpperCAmelCase         =			""
												for _ in range(_lowerCamelCase  ):
																		UpperCAmelCase         =			str(minterm % 2  ) + string
																		minterm //= 2
												temp.append(_lowerCamelCase  )
						return temp


def    lowerCamelCase__   ( A     :    List[Any]   ,     A     :    Optional[int]   ,     A     :    Union[str, Any]  ):




						'''simple docstring'''






						UpperCAmelCase         =			list(_lowerCamelCase  )
						UpperCAmelCase         =			list(_lowerCamelCase  )
						UpperCAmelCase         =			0
						for i in range(len(_lowerCamelCase  )  ):
												if lista[i] != lista[i]:
																		count_n += 1
						return count_n == count


def    lowerCamelCase__   ( A     :    Dict   ,     A     :    List[Any]  ):




						'''simple docstring'''






						UpperCAmelCase         =			[]
						UpperCAmelCase         =			[0] * len(_lowerCamelCase  )
						for i in range(len(chart[0]  )  ):
												UpperCAmelCase         =			0
												UpperCAmelCase         =			-1
												for j in range(len(_lowerCamelCase  )  ):
																		if chart[j][i] == 1:
																								count += 1
																								UpperCAmelCase         =			j
												if count == 1:
																		UpperCAmelCase         =			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  )  ):
																																				UpperCAmelCase         =			0
																		temp.append(prime_implicants[i]  )
						while True:
												UpperCAmelCase         =			0
												UpperCAmelCase         =			-1
												UpperCAmelCase         =			0
												for i in range(len(_lowerCamelCase  )  ):
																		UpperCAmelCase         =			chart[i].count(1  )
																		if count_n > max_n:
																								UpperCAmelCase         =			count_n
																								UpperCAmelCase         =			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  )  ):
																														UpperCAmelCase         =			0


def    lowerCamelCase__   ( A     :    Optional[Any]   ,     A     :    Tuple  ):




						'''simple docstring'''






						UpperCAmelCase         =			[[0 for x in range(len(_lowerCamelCase  )  )] for x in range(len(_lowerCamelCase  )  )]
						for i in range(len(_lowerCamelCase  )  ):
												UpperCAmelCase         =			prime_implicants[i].count('''_'''  )
												for j in range(len(_lowerCamelCase  )  ):
																		if is_for_table(prime_implicants[i]   ,     binary[j]   ,     _lowerCamelCase  ):
																								UpperCAmelCase         =			1

						return chart


def    lowerCamelCase__   ( ):




						'''simple docstring'''






						UpperCAmelCase         =			int(input('''Enter the no. of variables\n'''  )  )
						UpperCAmelCase         =			[
						    float(_lowerCamelCase  )
						    for x in input(
						        '''Enter the decimal representation of Minterms \'Spaces Separated\'\n'''  ).split()
						]
						UpperCAmelCase         =			decimal_to_binary(_lowerCamelCase   ,     _lowerCamelCase  )

						UpperCAmelCase         =			check(_lowerCamelCase  )
						print('''Prime Implicants are:'''  )
						print(_lowerCamelCase  )
						UpperCAmelCase         =			prime_implicant_chart(_lowerCamelCase   ,     _lowerCamelCase  )

						UpperCAmelCase         =			selection(_lowerCamelCase   ,     _lowerCamelCase  )
						print('''Essential Prime Implicants are:'''  )
						print(_lowerCamelCase  )


if __name__ == "__main__":
			import doctest

			doctest.testmod()
			main()









'''simple docstring'''



from ..utils import DummyObject, requires_backends






class  UpperCamelCase__(     metaclass=lowerCAmelCase ):
				__magic_name__       :   List[str]							= ["note_seq"]




				def __init__(	self    :				Any   ,					*lowerCAmelCase    :				List[str]   ,					**lowerCAmelCase    :				int   )->  Optional[int]:

										"""simple docstring"""




										requires_backends(self   ,					['''note_seq''']   )




				@classmethod
				def   a__(	cls    :				Dict   ,					*lowerCAmelCase    :				int   ,					**lowerCAmelCase    :				Optional[int]   )->  Dict:

										"""simple docstring"""




										requires_backends(cls   ,					['''note_seq''']   )





				@classmethod
				def   a__(	cls    :				int   ,					*lowerCAmelCase    :				Tuple   ,					**lowerCAmelCase    :				Optional[Any]   )->  Union[str, Any]:

										"""simple docstring"""




										requires_backends(cls   ,					['''note_seq''']   )





