


'''simple docstring'''





import PIL.Image
import PIL.ImageOps
from packaging import version
from PIL import Image


if version.parse(version.parse(PIL.__version__).base_version) >= version.parse('''9.1.0'''):
    __lowerCamelCase												=						{
        '''linear''': PIL.Image.Resampling.BILINEAR,
        '''bilinear''': PIL.Image.Resampling.BILINEAR,
        '''bicubic''': PIL.Image.Resampling.BICUBIC,
        '''lanczos''': PIL.Image.Resampling.LANCZOS,
        '''nearest''': PIL.Image.Resampling.NEAREST,
    }
else:
    __lowerCamelCase												=						{
        '''linear''': PIL.Image.LINEAR,
        '''bilinear''': PIL.Image.BILINEAR,
        '''bicubic''': PIL.Image.BICUBIC,
        '''lanczos''': PIL.Image.LANCZOS,
        '''nearest''': PIL.Image.NEAREST,
    }


def        a__     (					UpperCamelCase_						:      Union[str, Any]						):
   UpperCAmelCase__	:int      =      (images / 2 + 0.5).clamp(0,   1						)
   UpperCAmelCase__	:List[Any]      =      images.cpu().permute(0,   2,   3,   1						).float().numpy()
   UpperCAmelCase__	:Dict      =      numpy_to_pil(UpperCamelCase_						)
   return images


def        a__     (					UpperCamelCase_						:      int						):
   if images.ndim == 3:
      UpperCAmelCase__	:Optional[Any]      =      images[None, ...]
   UpperCAmelCase__	:Union[str, Any]      =      (images * 255).round().astype('''uint8'''						)
   if images.shape[-1] == 1:
      # special case for grayscale (single channel) images
      UpperCAmelCase__	:Dict      =      [Image.fromarray(image.squeeze(),   mode='''L'''						) for image in images]
   else:
      UpperCAmelCase__	:Union[str, Any]      =      [Image.fromarray(UpperCamelCase_						) for image in images]

   return pil_images







'''simple docstring'''





from __future__ import annotations

from collections.abc import Sequence
from typing import Literal


def        a__     (					UpperCamelCase_						:      str,   UpperCamelCase_						:      str						):
   UpperCAmelCase__	:Any      =      list(UpperCamelCase_						)
   UpperCAmelCase__	:Optional[int]      =      list(UpperCamelCase_						)
   UpperCAmelCase__	:str      =      0
   for i in range(len(UpperCamelCase_						)						):
      if lista[i] != lista[i]:
         count += 1
         UpperCAmelCase__	:Union[str, Any]      =      '''_'''
   if count > 1:
      return False
   else:
      return "".join(UpperCamelCase_						)


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


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


def        a__     (					UpperCamelCase_						:      str,   UpperCamelCase_						:      str,   UpperCamelCase_						:      int						):
   UpperCAmelCase__	:Dict      =      list(UpperCamelCase_						)
   UpperCAmelCase__	:str      =      list(UpperCamelCase_						)
   UpperCAmelCase__	:str      =      0
   for i in range(len(UpperCamelCase_						)						):
      if lista[i] != lista[i]:
         count_n += 1
   return count_n == count


def        a__     (					UpperCamelCase_						:      list[list[int]],   UpperCamelCase_						:      list[str]						):
   UpperCAmelCase__	:Optional[Any]      =      []
   UpperCAmelCase__	:List[Any]      =      [0] * len(UpperCamelCase_						)
   for i in range(len(chart[0]						)						):
      UpperCAmelCase__	:Optional[Any]      =      0
      UpperCAmelCase__	:Union[str, Any]      =      -1
      for j in range(len(UpperCamelCase_						)						):
         if chart[j][i] == 1:
            count += 1
            UpperCAmelCase__	:Any      =      j
      if count == 1:
         UpperCAmelCase__	:Any      =      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_						)						):
                  UpperCAmelCase__	:int      =      0
         temp.append(prime_implicants[i]						)
   while True:
      UpperCAmelCase__	:Optional[int]      =      0
      UpperCAmelCase__	:Dict      =      -1
      UpperCAmelCase__	:Optional[Any]      =      0
      for i in range(len(UpperCamelCase_						)						):
         UpperCAmelCase__	:str      =      chart[i].count(1						)
         if count_n > max_n:
            UpperCAmelCase__	:Any      =      count_n
            UpperCAmelCase__	:List[Any]      =      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_						)						):
               UpperCAmelCase__	:Optional[int]      =      0


def        a__     (					UpperCamelCase_						:      list[str],   UpperCamelCase_						:      list[str]						):
   UpperCAmelCase__	:List[str]      =      [[0 for x in range(len(UpperCamelCase_						)						)] for x in range(len(UpperCamelCase_						)						)]
   for i in range(len(UpperCamelCase_						)						):
      UpperCAmelCase__	:Tuple      =      prime_implicants[i].count('''_'''						)
      for j in range(len(UpperCamelCase_						)						):
         if is_for_table(prime_implicants[i],   binary[j],   UpperCamelCase_						):
            UpperCAmelCase__	:List[str]      =      1

   return chart


def        a__     (					):
   UpperCAmelCase__	:int      =      int(input('''Enter the no. of variables\n'''						)						)
   UpperCAmelCase__	:Tuple      =      [
       float(UpperCamelCase_						)
       for x in input(
           '''Enter the decimal representation of Minterms \'Spaces Separated\'\n'''						).split()
   ]
   UpperCAmelCase__	:Union[str, Any]      =      decimal_to_binary(UpperCamelCase_,   UpperCamelCase_						)

   UpperCAmelCase__	:Optional[Any]      =      check(UpperCamelCase_						)
   print('''Prime Implicants are:'''						)
   print(UpperCamelCase_						)
   UpperCAmelCase__	:Optional[int]      =      prime_implicant_chart(UpperCamelCase_,   UpperCamelCase_						)

   UpperCAmelCase__	:Dict      =      selection(UpperCamelCase_,   UpperCamelCase_						)
   print('''Essential Prime Implicants are:'''						)
   print(UpperCamelCase_						)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()



