from __future__ import annotations

from collections.abc import Sequence
from typing import Literal

def    SCREAMING_SNAKE_CASE_     (						snake_case__   ,  snake_case__							)     ->	List[str]:
							lowerCAmelCase			=		list(_a							)
							lowerCAmelCase			=		list(_a							)
							lowerCAmelCase			=		0
							for i in range(len(_a							)							):
														if lista[i] != lista[i]:
																					count += 1
																					lowerCAmelCase			=		'''_'''
							if count > 1:
														return False
							else:
														return "".join(_a							)

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

def    SCREAMING_SNAKE_CASE_     (						snake_case__   ,  snake_case__							)     ->	Optional[int]:
							lowerCAmelCase			=		[]
							for minterm in minterms:
														lowerCAmelCase			=		''''''
														for _ in range(_a							):
																					lowerCAmelCase			=		str(minterm % 2							) + string
																					minterm //= 2
														temp.append(_a							)
							return temp

def    SCREAMING_SNAKE_CASE_     (						snake_case__   ,  snake_case__   ,  snake_case__							)     ->	Any:
							lowerCAmelCase			=		list(_a							)
							lowerCAmelCase			=		list(_a							)
							lowerCAmelCase			=		0
							for i in range(len(_a							)							):
														if lista[i] != lista[i]:
																					count_n += 1
							return count_n == count

def    SCREAMING_SNAKE_CASE_     (						snake_case__   ,  snake_case__							)     ->	Union[str, Any]:
							lowerCAmelCase			=		[]
							lowerCAmelCase			=		[0] * len(_a							)
							for i in range(len(chart[0]							)							):
														lowerCAmelCase			=		0
														lowerCAmelCase			=		-1
														for j in range(len(_a							)							):
																					if chart[j][i] == 1:
																												count += 1
																												lowerCAmelCase			=		j
														if count == 1:
																					lowerCAmelCase			=		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			=		0
																					temp.append(prime_implicants[i]							)
							while True:
														lowerCAmelCase			=		0
														lowerCAmelCase			=		-1
														lowerCAmelCase			=		0
														for i in range(len(_a							)							):
																					lowerCAmelCase			=		chart[i].count(1							)
																					if count_n > max_n:
																												lowerCAmelCase			=		count_n
																												lowerCAmelCase			=		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			=		0

def    SCREAMING_SNAKE_CASE_     (						snake_case__   ,  snake_case__							)     ->	Tuple:
							lowerCAmelCase			=		[[0 for x in range(len(_a							)							)] for x in range(len(_a							)							)]
							for i in range(len(_a							)							):
														lowerCAmelCase			=		prime_implicants[i].count('''_'''							)
														for j in range(len(_a							)							):
																					if is_for_table(prime_implicants[i]   ,  binary[j]   ,  _a							):
																												lowerCAmelCase			=		1

							return chart

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

							lowerCAmelCase			=		check(_a							)
							print('''Prime Implicants are:'''							)
							print(_a							)
							lowerCAmelCase			=		prime_implicant_chart(_a   ,  _a							)

							lowerCAmelCase			=		selection(_a   ,  _a							)
							print('''Essential Prime Implicants are:'''							)
							print(_a							)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()








"""simple docstring"""

from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403




def __lowercase			(							_a		,			_a		,			_a = "x"		,			_a = 10**-10		,			_a = 1		,			):
    snake_case_ :     Any				=	symbols(_a    )
    snake_case_ :     int				=	lambdify(_a		,			_a    )
    snake_case_ :     Optional[Any]				=	lambdify(_a		,			diff(_a		,			_a    )    )

    snake_case_ :     Optional[Any]				=	starting_point

    while True:
        if diff_function(_a    ) != 0:
            snake_case_ :     Optional[int]				=	prev_guess - multiplicity * func(_a    ) / diff_function(
                _a    )
        else:
            raise ZeroDivisionError('''Could not find root'''    ) from None

        # Precision is checked by comparing the difference of consecutive guesses
        if abs(next_guess - prev_guess    ) < precision:
            return next_guess

        snake_case_ :     int				=	next_guess


# Let's Execute
if __name__ == "__main__":
     # Find root of trigonometric function
     # Find value of pi
     print(f'The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}')

     # Find root of polynomial
     # Find fourth Root of 5
     print(f'The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5j)}')

     # Find value of e
     print(
         '''The root of log(y) - 1 = 0 is ''',
         f'{newton_raphson("log(y) - 1", 2, variable="y")}',
     )

     # Exponential Roots
     print(
         '''The root of exp(x) - 1 = 0 is''',
         f'{newton_raphson("exp(x) - 1", 10, precision=0.005)}',
     )

     # Find root of cos(x)
     print(f'The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}')





