





from __future__ import annotations

import math







def    __lowerCamelCase					(							__a   :int    ,     __a   :int    ,     __a   :bool    ,     __a   :list[int]    ,     __a   :float    )		->				int:






		"""simple docstring"""

		if depth < 0:
				raise ValueError("""Depth cannot be less than 0"""    )

		if len(__a    ) == 0:
				raise ValueError("""Scores cannot be empty"""    )

		if depth == height:
				return scores[node_index]

		if is_max:
				return max(
				    minimax(depth + 1    ,     node_index * 2    ,     __a    ,     __a    ,     __a    )    ,     minimax(depth + 1    ,     node_index * 2 + 1    ,     __a    ,     __a    ,     __a    )    ,     )

		return min(
		    minimax(depth + 1    ,     node_index * 2    ,     __a    ,     __a    ,     __a    )    ,     minimax(depth + 1    ,     node_index * 2 + 1    ,     __a    ,     __a    ,     __a    )    ,     )







def    __lowerCamelCase					(							)		->				None:






		"""simple docstring"""

		A__        =   [9_0, 2_3, 6, 3_3, 2_1, 6_5, 1_2_3, 3_4_4_2_3]
		A__        =   math.log(len(__a    )    ,     2    )
		print("""Optimal value : """    ,     end=""""""    )
		print(minimax(0    ,     0    ,     __a    ,     __a    ,     __a    )    )


if __name__ == "__main__":
					import doctest

					doctest.testmod()
					main()










from __future__ import annotations

from PIL import Image

# Define glider example
A    :					Any =      [
    [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    :					Optional[Any] =      [[0, 1, 0], [0, 1, 0], [0, 1, 0]]







def    __lowerCamelCase					(							__a   :list[list[int]]    )		->				list[list[int]]:






		"""simple docstring"""

		A__        =   []
		for i in range(len(__a    )    ):
				A__        =   []
				for j in range(len(cells[i]    )    ):
						# Get the number of live neighbours
						A__        =   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(__a    ) - 1 and j > 0:
								neighbour_count += cells[i + 1][j - 1]
						if i < len(__a    ) - 1:
								neighbour_count += cells[i + 1][j]
						if i < len(__a    ) - 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.
						A__        =   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(__a    )
		return next_generation







def    __lowerCamelCase					(							__a   :list[list[int]]    ,     __a   :int    )		->				list[Image.Image]:






		"""simple docstring"""

		A__        =   []
		for _ in range(__a    ):
				# Create output image
				A__        =   Image.new("""RGB"""    ,     (len(cells[0]    ), len(__a    ))    )
				A__        =   img.load()

				# Save cells to image
				for x in range(len(__a    )    ):
						for y in range(len(cells[0]    )    ):
								A__        =   2_5_5 - cells[y][x] * 2_5_5
								A__        =   (colour, colour, colour)

        # Save image
				images.append(__a    )
				A__        =   new_generation(__a    )
		return images


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



