





"""simple docstring"""






from __future__ import annotations

from collections.abc import Sequence
from typing import Literal

def     __A      (			a_						:str   ,       a_						:str)		->		Dict:
    __a :						int			       =  list(SCREAMING_SNAKE_CASE__)
    __a :						Union[str, Any]			       =  list(SCREAMING_SNAKE_CASE__)
    __a :						List[Any]			       =  0
    for i in range(len(SCREAMING_SNAKE_CASE__)):
        if lista[i] != lista[i]:
            count += 1
            __a :						Tuple			       =  """_"""
    if count > 1:
        return False
    else:
        return "".join(SCREAMING_SNAKE_CASE__)

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

def     __A      (			a_						:int   ,       a_						:Sequence[float])		->		Optional[int]:
    __a :						Tuple			       =  []
    for minterm in minterms:
        __a :						Optional[int]			       =  """"""
        for _ in range(SCREAMING_SNAKE_CASE__):
            __a :						List[str]			       =  str(minterm % 2) + string
            minterm //= 2
        temp.append(SCREAMING_SNAKE_CASE__)
    return temp

def     __A      (			a_						:str   ,       a_						:str   ,       a_						:int)		->		int:
    __a :						Optional[Any]			       =  list(SCREAMING_SNAKE_CASE__)
    __a :						Union[str, Any]			       =  list(SCREAMING_SNAKE_CASE__)
    __a :						Dict			       =  0
    for i in range(len(SCREAMING_SNAKE_CASE__)):
        if lista[i] != lista[i]:
            count_n += 1
    return count_n == count

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

def     __A      (			a_						:list[str]   ,       a_						:list[str])		->		Optional[int]:
    __a :						List[str]			       =  [[0 for x in range(len(SCREAMING_SNAKE_CASE__))] for x in range(len(SCREAMING_SNAKE_CASE__))]
    for i in range(len(SCREAMING_SNAKE_CASE__)):
        __a :						List[str]			       =  prime_implicants[i].count('''_''')
        for j in range(len(SCREAMING_SNAKE_CASE__)):
            if is_for_table(prime_implicants[i]   ,       binary[j]   ,       SCREAMING_SNAKE_CASE__):
                __a :						str			       =  1

    return chart

def     __A      (			)		->		int:
    __a :						Dict			       =  int(input('''Enter the no. of variables\n'''))
    __a :						List[str]			       =  [
        float(SCREAMING_SNAKE_CASE__)
        for x in input(
            '''Enter the decimal representation of Minterms \'Spaces Separated\'\n''').split()
    ]
    __a :						List[Any]			       =  decimal_to_binary(SCREAMING_SNAKE_CASE__   ,       SCREAMING_SNAKE_CASE__)

    __a :						int			       =  check(SCREAMING_SNAKE_CASE__)
    print('''Prime Implicants are:''')
    print(SCREAMING_SNAKE_CASE__)
    __a :						str			       =  prime_implicant_chart(SCREAMING_SNAKE_CASE__   ,       SCREAMING_SNAKE_CASE__)

    __a :						Optional[Any]			       =  selection(SCREAMING_SNAKE_CASE__   ,       SCREAMING_SNAKE_CASE__)
    print('''Essential Prime Implicants are:''')
    print(SCREAMING_SNAKE_CASE__)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()






"""simple docstring"""






from __future__ import annotations

import os
from collections.abc import Mapping

A 			=  tuple[int, int]




class 				__lowercase			:







					'''simple docstring'''




					def __init__(						self	,			_UpperCAmelCase	,			_UpperCAmelCase     ):
									__a :						set[int]			       =  vertices
									__a :						dict[EdgeT, int]			       =  {
									    (min(_UpperCAmelCase     ), max(_UpperCAmelCase     )): weight for edge, weight in edges.items()
									}







					def  _lowerCamelCase		(						self	,			_UpperCAmelCase	,			_UpperCAmelCase     ):
									self.vertices.add(edge[0]     )
									self.vertices.add(edge[1]     )
									__a :						Any			       =  weight







					def  _lowerCamelCase		(						self     ):
									__a :						Graph			       =  Graph({min(self.vertices     )}	,			{}     )
									__a :						EdgeT
									__a :						int
									__a :						EdgeT
									__a :						int

									while len(subgraph.vertices     ) < len(self.vertices     ):
													__a :						List[Any]			       =  max(self.edges.values()     ) + 1
													for edge, weight in self.edges.items():
																	if (edge[0] in subgraph.vertices) ^ (edge[1] in subgraph.vertices):
																					if weight < min_weight:
																									__a :						str			       =  edge
																									__a :						int			       =  weight

													subgraph.add_edge(_UpperCAmelCase	,			_UpperCAmelCase     )

									return subgraph






def     __A      (			a_						:str = "p107_network.txt")		->		int:
				__a :						str			       =  os.path.abspath(os.path.dirname(a_))
				__a :						str			       =  os.path.join(a_   ,       a_)
				__a :						dict[EdgeT, int]			       =  {}
				__a :						list[str]
				__a :						int
				__a :						int

				with open(a_) as f:
								__a :						Any			       =  f.read().strip().split('''\n''')

				__a :						Union[str, Any]			       =  [line.split(''',''') for line in data]

				for edgea in range(1   ,       len(a_)):
								for edgea in range(a_):
												if adjaceny_matrix[edgea][edgea] != "-":
																__a :						int			       =  int(adjaceny_matrix[edgea][edgea])

				__a :						Graph			       =  Graph(set(range(len(a_)))   ,       a_)

				__a :						Graph			       =  graph.prims_algorithm()

				__a :						int			       =  sum(graph.edges.values())
				__a :						int			       =  sum(subgraph.edges.values())

				return initial_total - optimal_total


if __name__ == "__main__":
		print(F'{solution() = }')