





from __future__ import annotations

from collections.abc import Sequence
from typing import Literal






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






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






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






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






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






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

     return chart






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

     lowerCAmelCase_					:       List[str]    =		check(_a			)
     print("""Prime Implicants are:"""			)
     print(_a			)
     lowerCAmelCase_					:       str    =		prime_implicant_chart(_a					,   _a			)

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


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      main()







from __future__ import annotations






def 							_lowerCAmelCase (  _a   :					list[int]			)	->			list[int]:  # This function is recursive
     lowerCAmelCase_					:       List[Any]    =		len(_a			)
     # If the array contains only one element, we return it (it's the stop condition of
     # recursion)
     if array_length <= 1:
          return array
          # Else
     lowerCAmelCase_					:       Union[str, Any]    =		array[0]
     lowerCAmelCase_					:       str    =		False
     lowerCAmelCase_					:       Optional[int]    =		1
     lowerCAmelCase_					:       list[int]    =		[]
     while not is_found and i < array_length:
          if array[i] < pivot:
               lowerCAmelCase_					:       Optional[Any]    =		True
               lowerCAmelCase_					:       Tuple    =		[element for element in array[i:] if element >= array[i]]
               lowerCAmelCase_					:       Any    =		longest_subsequence(_a			)
               if len(_a			) > len(_a			):
                    lowerCAmelCase_					:       List[Any]    =		temp_array
          else:
               i += 1

     lowerCAmelCase_					:       Tuple    =		[element for element in array[1:] if element >= pivot]
     lowerCAmelCase_					:       List[Any]    =		[pivot, *longest_subsequence(_a			)]
     if len(_a			) > len(_a			):
          return temp_array
     else:
          return longest_subseq


if __name__ == "__main__":
      import doctest

      doctest.testmod()
