

'''simple docstring'''




from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : str							, SCREAMING_SNAKE_CASE   : str    ):
  UpperCAmelCase    				=						list(SCREAMING_SNAKE_CASE    )
  UpperCAmelCase    				=						list(SCREAMING_SNAKE_CASE    )
  UpperCAmelCase    				=						0
  for i in range(len(SCREAMING_SNAKE_CASE    )    ):
    if lista[i] != lista[i]:
      count += 1
      UpperCAmelCase    				=						'_'
  if count > 1:
    return False
  else:
    return "".join(SCREAMING_SNAKE_CASE    )


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


def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : int							, SCREAMING_SNAKE_CASE   : Sequence[float]    ):
  UpperCAmelCase    				=						[]
  for minterm in minterms:
    UpperCAmelCase    				=						''
    for _ in range(SCREAMING_SNAKE_CASE    ):
      UpperCAmelCase    				=						str(minterm % 2    ) + string
      minterm //= 2
    temp.append(SCREAMING_SNAKE_CASE    )
  return temp


def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : str							, SCREAMING_SNAKE_CASE   : str							, SCREAMING_SNAKE_CASE   : int    ):
  UpperCAmelCase    				=						list(SCREAMING_SNAKE_CASE    )
  UpperCAmelCase    				=						list(SCREAMING_SNAKE_CASE    )
  UpperCAmelCase    				=						0
  for i in range(len(SCREAMING_SNAKE_CASE    )    ):
    if lista[i] != lista[i]:
      count_n += 1
  return count_n == count


def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : list[list[int]]							, SCREAMING_SNAKE_CASE   : list[str]    ):
  UpperCAmelCase    				=						[]
  UpperCAmelCase    				=						[0] * len(SCREAMING_SNAKE_CASE    )
  for i in range(len(chart[0]    )    ):
    UpperCAmelCase    				=						0
    UpperCAmelCase    				=						-1
    for j in range(len(SCREAMING_SNAKE_CASE    )    ):
      if chart[j][i] == 1:
        count += 1
        UpperCAmelCase    				=						j
    if count == 1:
      UpperCAmelCase    				=						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    )    ):
            UpperCAmelCase    				=						0
      temp.append(prime_implicants[i]    )
  while True:
    UpperCAmelCase    				=						0
    UpperCAmelCase    				=						-1
    UpperCAmelCase    				=						0
    for i in range(len(SCREAMING_SNAKE_CASE    )    ):
      UpperCAmelCase    				=						chart[i].count(1    )
      if count_n > max_n:
        UpperCAmelCase    				=						count_n
        UpperCAmelCase    				=						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    )    ):
          UpperCAmelCase    				=						0


def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : list[str]							, SCREAMING_SNAKE_CASE   : list[str]    ):
  UpperCAmelCase    				=						[[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    )    ):
    UpperCAmelCase    				=						prime_implicants[i].count('_'    )
    for j in range(len(SCREAMING_SNAKE_CASE    )    ):
      if is_for_table(prime_implicants[i]							, binary[j]							, SCREAMING_SNAKE_CASE    ):
        UpperCAmelCase    				=						1

  return chart


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

  UpperCAmelCase    				=						check(SCREAMING_SNAKE_CASE    )
  print('Prime Implicants are:'    )
  print(SCREAMING_SNAKE_CASE    )
  UpperCAmelCase    				=						prime_implicant_chart(SCREAMING_SNAKE_CASE							, SCREAMING_SNAKE_CASE    )

  UpperCAmelCase    				=						selection(SCREAMING_SNAKE_CASE							, SCREAMING_SNAKE_CASE    )
  print('Essential Prime Implicants are:'    )
  print(SCREAMING_SNAKE_CASE    )


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()





'''simple docstring'''




def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : List[Any]							, SCREAMING_SNAKE_CASE   : Union[str, Any]    ):
  # "extended trapezoidal rule"
  # int(f) = dx/2 * (f1 + 2f2 + ... + fn)
  UpperCAmelCase    				=						(boundary[1] - boundary[0]) / steps
  UpperCAmelCase    				=						boundary[0]
  UpperCAmelCase    				=						boundary[1]
  UpperCAmelCase    				=						make_points(SCREAMING_SNAKE_CASE							, SCREAMING_SNAKE_CASE							, SCREAMING_SNAKE_CASE    )
  UpperCAmelCase    				=						0.0
  y += (h / 2.0) * f(SCREAMING_SNAKE_CASE    )
  for i in x_i:
    # print(i)
    y += h * f(SCREAMING_SNAKE_CASE    )
  y += (h / 2.0) * f(SCREAMING_SNAKE_CASE    )
  return y


def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : Tuple							, SCREAMING_SNAKE_CASE   : Dict							, SCREAMING_SNAKE_CASE   : Tuple    ):
  UpperCAmelCase    				=						a + h
  while x < (b - h):
    yield x
    UpperCAmelCase    				=						x + h


def    lowerCamelCase__		(    SCREAMING_SNAKE_CASE   : Optional[Any]    ):  # enter your function here
  UpperCAmelCase    				=						(x - 0) * (x - 0)
  return y


def    lowerCamelCase__		(    ):
  UpperCAmelCase    				=						0.0  # Lower bound of integration
  UpperCAmelCase    				=						1.0  # Upper bound of integration
  UpperCAmelCase    				=						10.0  # define number of steps or resolution
  UpperCAmelCase    				=						[a, b]  # define boundary of integration
  UpperCAmelCase    				=						method_a(SCREAMING_SNAKE_CASE							, SCREAMING_SNAKE_CASE    )
  print(f'''y = {y}'''    )


if __name__ == "__main__":
  main()


