




"""simple docstring"""


from __future__ import annotations


def 					UpperCAmelCase__       (snake_case__							:					list[int]		,   snake_case__							:					int    ):
  """simple docstring"""

  _snake_case							:		List[str]								=  0
  _snake_case							:		Optional[int]								=  len(snake_case__    ) - 1

  while i < j:
    if nums[i] + nums[j] == target:
      return [i, j]
    elif nums[i] + nums[j] < target:
      _snake_case							:		int								=  i + 1
    else:
      _snake_case							:		List[str]								=  j - 1

  return []


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     print(F'''{two_pointer([2, 7, 11, 15], 9) = }''')








"""simple docstring"""


from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def 					UpperCAmelCase__       (snake_case__							:					str		,   snake_case__							:					str    ):
  """simple docstring"""

  _snake_case							:		Optional[Any]								=  list(snake_case__    )
  _snake_case							:		List[Any]								=  list(snake_case__    )
  _snake_case							:		List[Any]								=  0
  for i in range(len(snake_case__    )    ):
    if lista[i] != lista[i]:
      count += 1
      _snake_case							:		Any								=  """_"""
  if count > 1:
    return False
  else:
    return "".join(snake_case__    )


def 					UpperCAmelCase__       (snake_case__							:					list[str]    ):
  """simple docstring"""

  _snake_case							:		int								=  []
  while True:
    _snake_case							:		Union[str, Any]								=  ["""$"""] * len(snake_case__    )
    _snake_case							:		int								=  []
    for i in range(len(snake_case__    )    ):
      for j in range(i + 1		,   len(snake_case__    )    ):
        _snake_case							:		List[Any]								=  compare_string(binary[i]		,   binary[j]    )
        if k is False:
          _snake_case							:		Dict								=  """*"""
          _snake_case							:		List[Any]								=  """*"""
          temp.append("""X"""    )
    for i in range(len(snake_case__    )    ):
      if checka[i] == "$":
        pi.append(binary[i]    )
    if len(snake_case__    ) == 0:
      return pi
    _snake_case							:		Optional[int]								=  list(set(snake_case__    )    )


def 					UpperCAmelCase__       (snake_case__							:					int		,   snake_case__							:					Sequence[float]    ):
  """simple docstring"""

  _snake_case							:		Optional[int]								=  []
  for minterm in minterms:
    _snake_case							:		Any								=  """"""
    for _ in range(snake_case__    ):
      _snake_case							:		Optional[Any]								=  str(minterm % 2    ) + string
      minterm //= 2
    temp.append(snake_case__    )
  return temp


def 					UpperCAmelCase__       (snake_case__							:					str		,   snake_case__							:					str		,   snake_case__							:					int    ):
  """simple docstring"""

  _snake_case							:		Dict								=  list(snake_case__    )
  _snake_case							:		List[str]								=  list(snake_case__    )
  _snake_case							:		Tuple								=  0
  for i in range(len(snake_case__    )    ):
    if lista[i] != lista[i]:
      count_n += 1
  return count_n == count


def 					UpperCAmelCase__       (snake_case__							:					list[list[int]]		,   snake_case__							:					list[str]    ):
  """simple docstring"""

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


def 					UpperCAmelCase__       (snake_case__							:					list[str]		,   snake_case__							:					list[str]    ):
  """simple docstring"""

  _snake_case							:		int								=  [[0 for x in range(len(snake_case__    )    )] for x in range(len(snake_case__    )    )]
  for i in range(len(snake_case__    )    ):
    _snake_case							:		Any								=  prime_implicants[i].count("""_"""    )
    for j in range(len(snake_case__    )    ):
      if is_for_table(prime_implicants[i]		,   binary[j]		,   snake_case__    ):
        _snake_case							:		Tuple								=  1

  return chart


def 					UpperCAmelCase__       ():
  """simple docstring"""

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

  _snake_case							:		str								=  check(snake_case__    )
  print("""Prime Implicants are:"""    )
  print(snake_case__    )
  _snake_case							:		int								=  prime_implicant_chart(snake_case__		,   snake_case__    )

  _snake_case							:		str								=  selection(snake_case__		,   snake_case__    )
  print("""Essential Prime Implicants are:"""    )
  print(snake_case__    )


if __name__ == "__main__":
     import doctest

     doctest.testmod()
     main()


