






"""simple docstring"""





from timeit import timeit

__lowerCamelCase							=  {
    'MALAYALAM': True,
    'String': False,
    'rotor': True,
    'level': True,
    'A': True,
    'BB': True,
    'ABC': False,
    'amanaplanacanalpanama': True,  # "a man a plan a canal panama"
}
# Ensure our test data is valid
assert all((key == key[::-1]) is value for key, value in test_data.items())



def   a    (     __UpperCAmelCase      :    str  )    ->							bool:
						__magic_name__:	List[Any]							=       0
						__magic_name__:	Any							=       len(__UpperCAmelCase  ) - 1
						while start_i < end_i:
												if s[start_i] == s[end_i]:
																		start_i += 1
																		end_i -= 1
												else:
																		return False
						return True



def   a    (     __UpperCAmelCase      :    str  )    ->							bool:
						__magic_name__:	Any							=       len(__UpperCAmelCase  ) // 2
						__magic_name__:	str							=       len(__UpperCAmelCase  )

						# We need to traverse till half of the length of string
						# as we can get access of the i'th last element from
						# i'th index.
						# eg: [0,1,2,3,4,5] => 4th index can be accessed
						# with the help of 1st index (i==n-i-1)
						# where n is length of string
						return all(s[i] == s[n - i - 1] for i in range(__UpperCAmelCase  )  )



def   a    (     __UpperCAmelCase      :    str  )    ->							bool:
						if len(__UpperCAmelCase  ) <= 2:
												return True
						if s[0] == s[len(__UpperCAmelCase  ) - 1]:
												return is_palindrome_recursive(s[1:-1]  )
						else:
												return False



def   a    (     __UpperCAmelCase      :    str  )    ->							bool:
						return s == s[::-1]



def   a    (     __UpperCAmelCase      :    str  )    ->							None:
						__magic_name__:	List[Any]							=       f'all({name}(key) is value for key, value in test_data.items())'
						__magic_name__:	Optional[Any]							=       f'from __main__ import test_data, {name}'
						__magic_name__:	Union[str, Any]							=       5_0_0_0_0_0
						__magic_name__:	Dict							=       timeit(stmt=__UpperCAmelCase      ,   setup=__UpperCAmelCase      ,   number=__UpperCAmelCase  )
						print(f'{name:<35} finished {number:,} runs in {result:.5f} seconds'  )


if __name__ == "__main__":
							for key, value in test_data.items():
														assert is_palindrome(key) is is_palindrome_recursive(key)
														assert is_palindrome(key) is is_palindrome_slice(key)
														print(f'''{key:21} {value}''')
							print('a man a plan a canal panama')

							# finished 500,000 runs in 0.46793 seconds
							benchmark_function('is_palindrome_slice')
							# finished 500,000 runs in 0.85234 seconds
							benchmark_function('is_palindrome')
							# finished 500,000 runs in 1.32028 seconds
							benchmark_function('is_palindrome_recursive')
							# finished 500,000 runs in 2.08679 seconds
							benchmark_function('is_palindrome_traversal')






"""simple docstring"""


from __future__ import annotations

from collections.abc import Sequence
from typing import Literal



def   _A					(	_a	:						str     ,   _a	:						str				):



      """simple docstring"""






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



def   _A					(	_a	:						list[str]				):



      """simple docstring"""






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



def   _A					(	_a	:						int     ,   _a	:						Sequence[float]				):



      """simple docstring"""






      A				  =		[]
      for minterm in minterms:
            A				  =		""""""
            for _ in range(_a				):
                  A				  =		str(minterm % 2				) + string
                  minterm //= 2
            temp.append(_a				)
      return temp



def   _A					(	_a	:						str     ,   _a	:						str     ,   _a	:						int				):



      """simple docstring"""






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



def   _A					(	_a	:						list[list[int]]     ,   _a	:						list[str]				):



      """simple docstring"""






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



def   _A					(	_a	:						list[str]     ,   _a	:						list[str]				):



      """simple docstring"""






      A				  =		[[0 for x in range(len(_a				)				)] for x in range(len(_a				)				)]
      for i in range(len(_a				)				):
            A				  =		prime_implicants[i].count("""_"""				)
            for j in range(len(_a				)				):
                  if is_for_table(prime_implicants[i]     ,   binary[j]     ,   _a				):
                        A				  =		1

      return chart



def   _A					(	):



      """simple docstring"""






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

      A				  =		check(_a				)
      print("""Prime Implicants are:"""				)
      print(_a				)
      A				  =		prime_implicant_chart(_a     ,   _a				)

      A				  =		selection(_a     ,   _a				)
      print("""Essential Prime Implicants are:"""				)
      print(_a				)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()




