


from __future__ import annotations

from PIL import Image

# Define glider example
lowercase_	   =     [
    [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
lowercase_	   =     [[0, 1, 0], [0, 1, 0], [0, 1, 0]]
def 				UpperCamelCase__					(  SCREAMING_SNAKE_CASE__						):
 __lowerCamelCase		:							Union[str, Any]		 =						[]
 for i in range(len(SCREAMING_SNAKE_CASE__						)						):
  __lowerCamelCase		:							List[str]		 =						[]
  for j in range(len(cells[i]						)						):
   # Get the number of live neighbours
   __lowerCamelCase		:							int		 =						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(SCREAMING_SNAKE_CASE__						) - 1 and j > 0:
    neighbour_count += cells[i + 1][j - 1]
   if i < len(SCREAMING_SNAKE_CASE__						) - 1:
    neighbour_count += cells[i + 1][j]
   if i < len(SCREAMING_SNAKE_CASE__						) - 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		:							str		 =						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(SCREAMING_SNAKE_CASE__						)
 return next_generation
def 				UpperCamelCase__					(  SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__						):
 __lowerCamelCase		:							str		 =						[]
 for _ in range(SCREAMING_SNAKE_CASE__						):
  # Create output image
  __lowerCamelCase		:							List[Any]		 =						Image.new('RGB'      ,	(len(cells[0]						), len(SCREAMING_SNAKE_CASE__						))						)
  __lowerCamelCase		:							List[Any]		 =						img.load()

  # Save cells to image
  for x in range(len(SCREAMING_SNAKE_CASE__						)						):
   for y in range(len(cells[0]						)						):
    __lowerCamelCase		:							List[Any]		 =						255 - cells[y][x] * 255
    __lowerCamelCase		:							Dict		 =						(colour, colour, colour)

        # Save image
  images.append(SCREAMING_SNAKE_CASE__						)
  __lowerCamelCase		:							Tuple		 =						new_generation(SCREAMING_SNAKE_CASE__						)
 return images


if __name__ == "__main__":
       lowercase_	   =     generate_images(GLIDER, 1_6)
       images[0].save('out.gif', save_all=True, append_images=images[1:])





def 				UpperCamelCase__					(  SCREAMING_SNAKE_CASE__						):
 __lowerCamelCase		:							str		 =						0
 __lowerCamelCase		:							Tuple		 =						len(SCREAMING_SNAKE_CASE__						)

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

 return num_inversions
def 				UpperCamelCase__					(  SCREAMING_SNAKE_CASE__						):
 if len(SCREAMING_SNAKE_CASE__						) <= 1:
  return arr, 0
 __lowerCamelCase		:							Optional[int]		 =						len(SCREAMING_SNAKE_CASE__						) // 2
 __lowerCamelCase		:							Union[str, Any]		 =						arr[0:mid]
 __lowerCamelCase		:							List[Any]		 =						arr[mid:]

 __lowerCamelCase ,					__lowerCamelCase		:							Any		 =						count_inversions_recursive(SCREAMING_SNAKE_CASE__						)
 __lowerCamelCase ,					__lowerCamelCase		:							List[str]		 =						count_inversions_recursive(SCREAMING_SNAKE_CASE__						)
 __lowerCamelCase ,					__lowerCamelCase		:							Dict		 =						_count_cross_inversions(SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__						)

 __lowerCamelCase		:							List[str]		 =						inversion_p + inversions_q + cross_inversions
 return c, num_inversions
def 				UpperCamelCase__					(  SCREAMING_SNAKE_CASE__      ,	SCREAMING_SNAKE_CASE__						):
 __lowerCamelCase		:							Optional[int]		 =						[]
 __lowerCamelCase		:							List[Any]		 =						0
 while i < len(SCREAMING_SNAKE_CASE__						) and j < len(SCREAMING_SNAKE_CASE__						):
  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(SCREAMING_SNAKE_CASE__						) - i
   r.append(q[j]						)
   j += 1
  else:
   r.append(p[i]						)
   i += 1

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

 return r, num_inversion
def 				UpperCamelCase__					(  ):
 __lowerCamelCase		:							Optional[int]		 =						[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(SCREAMING_SNAKE_CASE__						)
 __lowerCamelCase ,					__lowerCamelCase		:							Optional[Any]		 =						count_inversions_recursive(SCREAMING_SNAKE_CASE__						)

 assert num_inversions_bf == num_inversions_recursive == 8

 print('number of inversions = '      ,	SCREAMING_SNAKE_CASE__						)

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

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

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

 # an empty list should also have zero inversions
 __lowerCamelCase		:							List[str]		 =						[]
 __lowerCamelCase		:							Dict		 =						count_inversions_bf(SCREAMING_SNAKE_CASE__						)
 __lowerCamelCase ,					__lowerCamelCase		:							Dict		 =						count_inversions_recursive(SCREAMING_SNAKE_CASE__						)

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


if __name__ == "__main__":
       main()

