



from __future__ import annotations

from collections.abc import Sequence
from typing import Literal
def 		UpperCamelCase	(   snake_case__       :    str       ,     snake_case__       :    str	)	->     str | Literal[False]:
   UpperCamelCase    :  Tuple							=	list(snake_case__	)
   UpperCamelCase    :  Optional[Any]							=	list(snake_case__	)
   UpperCamelCase    :  Tuple							=	0
   for i in range(len(snake_case__	)	):
      if lista[i] != lista[i]:
         count += 1
         UpperCamelCase    :  Optional[int]							=	'_'
   if count > 1:
      return False
   else:
      return "".join(snake_case__	)
def 		UpperCamelCase	(   snake_case__       :    list[str]	)	->     list[str]:
   UpperCamelCase    :  Tuple							=	[]
   while True:
      UpperCamelCase    :  Union[str, Any]							=	['$'] * len(snake_case__	)
      UpperCamelCase    :  Tuple							=	[]
      for i in range(len(snake_case__	)	):
         for j in range(i + 1       ,     len(snake_case__	)	):
            UpperCamelCase    :  Optional[int]							=	compare_string(binary[i]       ,     binary[j]	)
            if k is False:
               UpperCamelCase    :  Dict							=	'*'
               UpperCamelCase    :  Dict							=	'*'
               temp.append('X'	)
      for i in range(len(snake_case__	)	):
         if checka[i] == "$":
            pi.append(binary[i]	)
      if len(snake_case__	) == 0:
         return pi
      UpperCamelCase    :  Any							=	list(set(snake_case__	)	)
def 		UpperCamelCase	(   snake_case__       :    int       ,     snake_case__       :    Sequence[float]	)	->     list[str]:
   UpperCamelCase    :  Any							=	[]
   for minterm in minterms:
      UpperCamelCase    :  str							=	''
      for _ in range(snake_case__	):
         UpperCamelCase    :  Dict							=	str(minterm % 2	) + string
         minterm //= 2
      temp.append(snake_case__	)
   return temp
def 		UpperCamelCase	(   snake_case__       :    str       ,     snake_case__       :    str       ,     snake_case__       :    int	)	->     bool:
   UpperCamelCase    :  Optional[int]							=	list(snake_case__	)
   UpperCamelCase    :  Dict							=	list(snake_case__	)
   UpperCamelCase    :  Tuple							=	0
   for i in range(len(snake_case__	)	):
      if lista[i] != lista[i]:
         count_n += 1
   return count_n == count
def 		UpperCamelCase	(   snake_case__       :    list[list[int]]       ,     snake_case__       :    list[str]	)	->     list[str]:
   UpperCamelCase    :  Any							=	[]
   UpperCamelCase    :  str							=	[0] * len(snake_case__	)
   for i in range(len(chart[0]	)	):
      UpperCamelCase    :  Dict							=	0
      UpperCamelCase    :  Tuple							=	-1
      for j in range(len(snake_case__	)	):
         if chart[j][i] == 1:
            count += 1
            UpperCamelCase    :  str							=	j
      if count == 1:
         UpperCamelCase    :  str							=	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    :  str							=	0
         temp.append(prime_implicants[i]	)
   while True:
      UpperCamelCase    :  Dict							=	0
      UpperCamelCase    :  Any							=	-1
      UpperCamelCase    :  Any							=	0
      for i in range(len(snake_case__	)	):
         UpperCamelCase    :  Tuple							=	chart[i].count(1	)
         if count_n > max_n:
            UpperCamelCase    :  str							=	count_n
            UpperCamelCase    :  str							=	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    :  int							=	0
def 		UpperCamelCase	(   snake_case__       :    list[str]       ,     snake_case__       :    list[str]	)	->     list[list[int]]:
   UpperCamelCase    :  int							=	[[0 for x in range(len(snake_case__	)	)] for x in range(len(snake_case__	)	)]
   for i in range(len(snake_case__	)	):
      UpperCamelCase    :  List[str]							=	prime_implicants[i].count('_'	)
      for j in range(len(snake_case__	)	):
         if is_for_table(prime_implicants[i]       ,     binary[j]       ,     snake_case__	):
            UpperCamelCase    :  Any							=	1

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

   UpperCamelCase    :  Tuple							=	check(snake_case__	)
   print('Prime Implicants are:'	)
   print(snake_case__	)
   UpperCamelCase    :  List[Any]							=	prime_implicant_chart(snake_case__       ,     snake_case__	)

   UpperCamelCase    :  int							=	selection(snake_case__       ,     snake_case__	)
   print('Essential Prime Implicants are:'	)
   print(snake_case__	)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()








from __future__ import annotations

__UpperCAmelCase          =       {
    '''A''': ['''B''', '''C''', '''E'''],
    '''B''': ['''A''', '''D''', '''E'''],
    '''C''': ['''A''', '''F''', '''G'''],
    '''D''': ['''B'''],
    '''E''': ['''A''', '''B''', '''D'''],
    '''F''': ['''C'''],
    '''G''': ['''C'''],
}



class 				lowerCAmelCase_		:
       def __init__(			self,			SCREAMING_SNAKE_CASE_,			SCREAMING_SNAKE_CASE_       )     ->		None:
          UpperCamelCase    :  Union[str, Any]							=	graph
          # mapping node to its parent in resulting breadth first tree
          UpperCamelCase    :  dict[str, str | None]							=	{}
          UpperCamelCase    :  Union[str, Any]							=	source_vertex
       def 					snake_case_       (			self       )     ->		None:
          UpperCamelCase    :  str							=	{self.source_vertex}
          UpperCamelCase    :  str							=	None
          UpperCamelCase    :  int							=	[self.source_vertex]  # first in first out queue

          while queue:
             UpperCamelCase    :  Dict							=	queue.pop(0       )
             for adjacent_vertex in self.graph[vertex]:
                if adjacent_vertex not in visited:
                   visited.add(SCREAMING_SNAKE_CASE_       )
                   UpperCamelCase    :  Tuple							=	vertex
                   queue.append(SCREAMING_SNAKE_CASE_       )






       def 					snake_case_       (			self,			SCREAMING_SNAKE_CASE_       )     ->		str:
          if target_vertex == self.source_vertex:
             return self.source_vertex

          UpperCamelCase    :  Optional[Any]							=	self.parent.get(SCREAMING_SNAKE_CASE_       )
          if target_vertex_parent is None:
             UpperCamelCase    :  Union[str, Any]							=	(
                 F"""No path from vertex: {self.source_vertex} to vertex: {target_vertex}"""
             )
             raise ValueError(SCREAMING_SNAKE_CASE_       )

          return self.shortest_path(SCREAMING_SNAKE_CASE_       ) + F"""->{target_vertex}"""


if __name__ == "__main__":
    __UpperCAmelCase          =       Graph(graph, '''G''')
    g.breath_first_search()
    print(g.shortest_path('''D'''))
    print(g.shortest_path('''G'''))
    print(g.shortest_path('''Foo'''))



