


from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def 		lowercase_  (     _UpperCamelCase       ,			_UpperCamelCase  ):


			'''simple docstring'''







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


def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







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


def 		lowercase_  (     _UpperCamelCase       ,			_UpperCamelCase  ):


			'''simple docstring'''







			__lowercase 					=   []
			for minterm in minterms:
						__lowercase 					=   ''''''
						for _ in range(_UpperCamelCase  ):
									__lowercase 					=   str(minterm % 2  ) + string
									minterm //= 2
						temp.append(_UpperCamelCase  )
			return temp


def 		lowercase_  (     _UpperCamelCase       ,			_UpperCamelCase       ,			_UpperCamelCase  ):


			'''simple docstring'''







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


def 		lowercase_  (     _UpperCamelCase       ,			_UpperCamelCase  ):


			'''simple docstring'''







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


def 		lowercase_  (     _UpperCamelCase       ,			_UpperCamelCase  ):


			'''simple docstring'''







			__lowercase 					=   [[0 for x in range(len(_UpperCamelCase  )  )] for x in range(len(_UpperCamelCase  )  )]
			for i in range(len(_UpperCamelCase  )  ):
						__lowercase 					=   prime_implicants[i].count('''_'''  )
						for j in range(len(_UpperCamelCase  )  ):
									if is_for_table(prime_implicants[i]       ,			binary[j]       ,			_UpperCamelCase  ):
												__lowercase 					=   1

			return chart


def 		lowercase_  (     ):


			'''simple docstring'''







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

			__lowercase 					=   check(_UpperCamelCase  )
			print('''Prime Implicants are:'''  )
			print(_UpperCamelCase  )
			__lowercase 					=   prime_implicant_chart(_UpperCamelCase       ,			_UpperCamelCase  )

			__lowercase 					=   selection(_UpperCamelCase       ,			_UpperCamelCase  )
			print('''Essential Prime Implicants are:'''  )
			print(_UpperCamelCase  )


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()






def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







			__lowercase 					=   len(_UpperCamelCase  )
			__lowercase 					=   len(matrix[0]  )
			__lowercase 					=   min(_UpperCamelCase       ,			_UpperCamelCase  )

			for row in range(_UpperCamelCase  ):
						# Check if diagonal element is not zero
						if matrix[row][row] != 0:
									# Eliminate all the elements below the diagonal
									for col in range(row + 1       ,			_UpperCamelCase  ):
												__lowercase 					=   matrix[col][row] / matrix[row][row]
												for i in range(_UpperCamelCase       ,			_UpperCamelCase  ):
															matrix[col][i] -= multiplier * matrix[row][i]
						else:
									# Find a non-zero diagonal element to swap rows
									__lowercase 					=   True
									for i in range(row + 1       ,			_UpperCamelCase  ):
												if matrix[i][row] != 0:
															__lowercase					, __lowercase 					=   matrix[i], matrix[row]
															__lowercase 					=   False
															break
									if reduce:
												rank -= 1
												for i in range(_UpperCamelCase  ):
															__lowercase 					=   matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
									row -= 1

			return rank


if __name__ == "__main__":
	import doctest

	doctest.testmod()


