



from __future__ import annotations

from collections.abc import Sequence
from typing import Literal



def    snake_case_				(    _SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   ):
	__lowercase		       =			list(_SCREAMING_SNAKE_CASE   )
	__lowercase		       =			list(_SCREAMING_SNAKE_CASE   )
	__lowercase		       =			0
	for i in range(len(_SCREAMING_SNAKE_CASE   )   ):
		if lista[i] != lista[i]:
			count += 1
			__lowercase		       =			"_"
	if count > 1:
		return False
	else:
		return "".join(_SCREAMING_SNAKE_CASE   )



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



def    snake_case_				(    _SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   ):
	__lowercase		       =			[]
	for minterm in minterms:
		__lowercase		       =			""
		for _ in range(_SCREAMING_SNAKE_CASE   ):
			__lowercase		       =			str(minterm % 2   ) + string
			minterm //= 2
		temp.append(_SCREAMING_SNAKE_CASE   )
	return temp



def    snake_case_				(    _SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   ):
	__lowercase		       =			list(_SCREAMING_SNAKE_CASE   )
	__lowercase		       =			list(_SCREAMING_SNAKE_CASE   )
	__lowercase		       =			0
	for i in range(len(_SCREAMING_SNAKE_CASE   )   ):
		if lista[i] != lista[i]:
			count_n += 1
	return count_n == count



def    snake_case_				(    _SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   ):
	__lowercase		       =			[]
	__lowercase		       =			[0] * len(_SCREAMING_SNAKE_CASE   )
	for i in range(len(chart[0]   )   ):
		__lowercase		       =			0
		__lowercase		       =			-1
		for j in range(len(_SCREAMING_SNAKE_CASE   )   ):
			if chart[j][i] == 1:
				count += 1
				__lowercase		       =			j
		if count == 1:
			__lowercase		       =			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   )   ):
						__lowercase		       =			0
			temp.append(prime_implicants[i]   )
	while True:
		__lowercase		       =			0
		__lowercase		       =			-1
		__lowercase		       =			0
		for i in range(len(_SCREAMING_SNAKE_CASE   )   ):
			__lowercase		       =			chart[i].count(1   )
			if count_n > max_n:
				__lowercase		       =			count_n
				__lowercase		       =			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   )   ):
					__lowercase		       =			0



def    snake_case_				(    _SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   ):
	__lowercase		       =			[[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   )   ):
		__lowercase		       =			prime_implicants[i].count("_"   )
		for j in range(len(_SCREAMING_SNAKE_CASE   )   ):
			if is_for_table(prime_implicants[i]  ,	binary[j]  ,	_SCREAMING_SNAKE_CASE   ):
				__lowercase		       =			1

	return chart



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

	__lowercase		       =			check(_SCREAMING_SNAKE_CASE   )
	print("Prime Implicants are:"   )
	print(_SCREAMING_SNAKE_CASE   )
	__lowercase		       =			prime_implicant_chart(_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   )

	__lowercase		       =			selection(_SCREAMING_SNAKE_CASE  ,	_SCREAMING_SNAKE_CASE   )
	print("Essential Prime Implicants are:"   )
	print(_SCREAMING_SNAKE_CASE   )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()








def    snake_case_				(    _SCREAMING_SNAKE_CASE   ):

	# bit count represents no. of bits in the gray code
	if bit_count < 0:
		raise ValueError("The given input must be positive"   )

	# get the generated string sequence
	__lowercase		       =			gray_code_sequence_string(_SCREAMING_SNAKE_CASE   )
	#
	# convert them to integers
	for i in range(len(_SCREAMING_SNAKE_CASE   )   ):
		__lowercase		       =			int(sequence[i]  ,	2   )

	return sequence



def    snake_case_				(    _SCREAMING_SNAKE_CASE   ):

	# The approach is a recursive one
	# Base case achieved when either n = 0 or n=1
	if bit_count == 0:
		return ["0"]

	if bit_count == 1:
		return ["0", "1"]

	__lowercase		       =			1 << bit_count  # defines the length of the sequence
	# 1<< n is equivalent to 2^n

	# recursive answer will generate answer for n-1 bits
	__lowercase		       =			gray_code_sequence_string(bit_count - 1   )

	__lowercase		       =			[]

	# append 0 to first half of the smaller sequence generated
	for i in range(seq_len // 2   ):
		__lowercase		       =			"0" + smaller_sequence[i]
		sequence.append(_SCREAMING_SNAKE_CASE   )

	# append 1 to second half ... start from the end of the list
	for i in reversed(range(seq_len // 2   )   ):
		__lowercase		       =			"1" + smaller_sequence[i]
		sequence.append(_SCREAMING_SNAKE_CASE   )

	return sequence


if __name__ == "__main__":
	import doctest

	doctest.testmod()



