


'''simple docstring'''



from __future__ import annotations

from PIL import Image

# Define glider example
A__		:					Dict												=  [
    [0, 1, 0, 0, 0, 0, 0, 0],
    [0, 0, 1, 0, 0, 0, 0, 0],
    [1, 1, 1, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
]

# Define blinker example
A__		:					int												=  [[0, 1, 0], [0, 1, 0], [0, 1, 0]]



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				list[list[int]]							)     ->		list[list[int]]:
     __lowerCamelCase   :	Dict								=		[]
     for i in range(len(UpperCAmelCase_							)							):
          __lowerCamelCase   :	Any								=		[]
          for j in range(len(cells[i]							)							):
               # Get the number of live neighbours
               __lowerCamelCase   :	List[Any]								=		0
               if i > 0 and j > 0:
                    neighbour_count += cells[i - 1][j - 1]
               if i > 0:
                    neighbour_count += cells[i - 1][j]
               if i > 0 and j < len(cells[i]							) - 1:
                    neighbour_count += cells[i - 1][j + 1]
               if j > 0:
                    neighbour_count += cells[i][j - 1]
               if j < len(cells[i]							) - 1:
                    neighbour_count += cells[i][j + 1]
               if i < len(UpperCAmelCase_							) - 1 and j > 0:
                    neighbour_count += cells[i + 1][j - 1]
               if i < len(UpperCAmelCase_							) - 1:
                    neighbour_count += cells[i + 1][j]
               if i < len(UpperCAmelCase_							) - 1 and j < len(cells[i]							) - 1:
                    neighbour_count += cells[i + 1][j + 1]

               # Rules of the game of life (excerpt from Wikipedia):
               # 1. Any live cell with two or three live neighbours survives.
               # 2. Any dead cell with three live neighbours becomes a live cell.
               # 3. All other live cells die in the next generation.
               #    Similarly, all other dead cells stay dead.
               __lowerCamelCase   :	Union[str, Any]								=		cells[i][j] == 1
               if (
                   (alive and 2 <= neighbour_count <= 3)
                   or not alive
                   and neighbour_count == 3
               ):
                    next_generation_row.append(1							)
               else:
                    next_generation_row.append(0							)

          next_generation.append(UpperCAmelCase_							)
     return next_generation



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				list[list[int]]      ,    UpperCAmelCase_    :				int							)     ->		list[Image.Image]:
     __lowerCamelCase   :	List[str]								=		[]
     for _ in range(UpperCAmelCase_							):
          # Create output image
          __lowerCamelCase   :	List[Any]								=		Image.new('RGB'      ,    (len(cells[0]							), len(UpperCAmelCase_							))							)
          __lowerCamelCase   :	int								=		img.load()

          # Save cells to image
          for x in range(len(UpperCAmelCase_							)							):
               for y in range(len(cells[0]							)							):
                    __lowerCamelCase   :	Union[str, Any]								=		2_55 - cells[y][x] * 2_55
                    __lowerCamelCase   :	List[str]								=		(colour, colour, colour)

        # Save image
          images.append(UpperCAmelCase_							)
          __lowerCamelCase   :	Dict								=		new_generation(UpperCAmelCase_							)
     return images


if __name__ == "__main__":
      A__		:					Dict												=  generate_images(GLIDER, 16)
      images[0].save("""out.gif""", save_all=True, append_images=images[1:])










'''simple docstring'''



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[Any]							)     ->		str:
     __lowerCamelCase   :	Tuple								=		0
     __lowerCamelCase   :	Optional[int]								=		len(UpperCAmelCase_							)

     for i in range(n - 1							):
          for j in range(i + 1      ,    UpperCAmelCase_							):
               if arr[i] > arr[j]:
                    num_inversions += 1

     return num_inversions



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				str							)     ->		Optional[int]:
     if len(UpperCAmelCase_							) <= 1:
          return arr, 0
     __lowerCamelCase   :	str								=		len(UpperCAmelCase_							) // 2
     __lowerCamelCase   :	List[Any]								=		arr[0:mid]
     __lowerCamelCase   :	List[str]								=		arr[mid:]

     __lowerCamelCase				,       __lowerCamelCase   :	int								=		count_inversions_recursive(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Optional[Any]								=		count_inversions_recursive(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Any								=		_count_cross_inversions(UpperCAmelCase_      ,    UpperCAmelCase_							)

     __lowerCamelCase   :	Optional[int]								=		inversion_p + inversions_q + cross_inversions
     return c, num_inversions



def 			UpperCAmelCase__					(	UpperCAmelCase_    :				List[Any]      ,    UpperCAmelCase_    :				List[str]							)     ->		Optional[Any]:
     __lowerCamelCase   :	List[str]								=		[]
     __lowerCamelCase   :	Optional[int]								=		0
     while i < len(UpperCAmelCase_							) and j < len(UpperCAmelCase_							):
          if p[i] > q[j]:
               # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
               # These are all inversions. The claim emerges from the
               # property that P is sorted.
               num_inversion += len(UpperCAmelCase_							) - i
               r.append(q[j]							)
               j += 1
          else:
               r.append(p[i]							)
               i += 1

     if i < len(UpperCAmelCase_							):
          r.extend(p[i:]							)
     else:
          r.extend(q[j:]							)

     return r, num_inversion



def 			UpperCAmelCase__					(	)     ->		List[str]:
     __lowerCamelCase   :	Any								=		[10, 2, 1, 5, 5, 2, 11]

     # this arr has 8 inversions:
     # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Dict								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 8

     print('number of inversions = '      ,    UpperCAmelCase_							)

     # testing an array with zero inversion (a sorted arr_1)

     arr_a.sort()
     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	int								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '      ,    UpperCAmelCase_							)

     # an empty list should also have zero inversions
     __lowerCamelCase   :	Dict								=		[]
     __lowerCamelCase   :	Optional[Any]								=		count_inversions_bf(UpperCAmelCase_							)
     __lowerCamelCase				,       __lowerCamelCase   :	Union[str, Any]								=		count_inversions_recursive(UpperCAmelCase_							)

     assert num_inversions_bf == num_inversions_recursive == 0
     print('number of inversions = '      ,    UpperCAmelCase_							)


if __name__ == "__main__":
      main()






