





from __future__ import annotations

from collections.abc import Sequence
from typing import Literal






def 				_UpperCAmelCase			(    A				,							A     ):




   '''simple docstring'''

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






def 				_UpperCAmelCase			(    A     ):




   '''simple docstring'''

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






def 				_UpperCAmelCase			(    A				,							A     ):




   '''simple docstring'''

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






def 				_UpperCAmelCase			(    A				,							A				,							A     ):




   '''simple docstring'''

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






def 				_UpperCAmelCase			(    A				,							A     ):




   '''simple docstring'''

   UpperCAmelCase__						=[]
   UpperCAmelCase__						=[0] * len(snake_case__     )
   for i in range(len(chart[0]     )     ):
      UpperCAmelCase__						=0
      UpperCAmelCase__						=-1
      for j in range(len(snake_case__     )     ):
         if chart[j][i] == 1:
            count += 1
            UpperCAmelCase__						=j
      if count == 1:
         UpperCAmelCase__						=1
   for i in range(len(snake_case__     )     ):
      if select[i] == 1:
         for j in range(len(chart[0]     )     ):
            if chart[i][j] == 1:
               for k in range(len(snake_case__     )     ):
                  UpperCAmelCase__						=0
         temp.append(prime_implicants[i]     )
   while True:
      UpperCAmelCase__						=0
      UpperCAmelCase__						=-1
      UpperCAmelCase__						=0
      for i in range(len(snake_case__     )     ):
         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(snake_case__     )     ):
               UpperCAmelCase__						=0






def 				_UpperCAmelCase			(    A				,							A     ):




   '''simple docstring'''

   UpperCAmelCase__						=[[0 for x in range(len(snake_case__     )     )] for x in range(len(snake_case__     )     )]
   for i in range(len(snake_case__     )     ):
      UpperCAmelCase__						=prime_implicants[i].count("_"     )
      for j in range(len(snake_case__     )     ):
         if is_for_table(prime_implicants[i]				,							binary[j]				,							snake_case__     ):
            UpperCAmelCase__						=1

   return chart






def 				_UpperCAmelCase			(    ):




   '''simple docstring'''

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

   UpperCAmelCase__						=check(snake_case__     )
   print("Prime Implicants are:"     )
   print(snake_case__     )
   UpperCAmelCase__						=prime_implicant_chart(snake_case__				,							snake_case__     )

   UpperCAmelCase__						=selection(snake_case__				,							snake_case__     )
   print("Essential Prime Implicants are:"     )
   print(snake_case__     )


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()











"""simple docstring"""
from __future__ import annotations






def       __UpperCamelCase						(		snake_case__ , snake_case__       ):
	if len(snake_case__       ) == 0:
		return False
	A_		:    Union[str, Any]						     = len(snake_case__       ) // 2
	if a_list[midpoint] == item:
		return True
	if item < a_list[midpoint]:
		return binary_search(a_list[:midpoint] , snake_case__       )
	else:
		return binary_search(a_list[midpoint + 1 :] , snake_case__       )


if __name__ == "__main__":
							_lowerCAmelCase       =				input("Enter numbers separated by comma:\n").strip()
							_lowerCAmelCase       =				[int(item.strip()) for item in user_input.split(",")]
							_lowerCAmelCase       =				int(input("Enter the number to be found in the list:\n").strip())
							_lowerCAmelCase       =				"" if binary_search(sequence, target) else "not "
							print(F'{target} was {not_str}found in {sequence}')

