



'''simple docstring'''
from __future__ import annotations

from queue import Queue


def   lowercase_	(   lowerCAmelCase__	:  int			,							lowerCAmelCase__	:  int ):

			"""simple docstring"""





			a ^= b
			b ^= a
			a ^= b
			return a, b


def   lowercase_	(   lowerCAmelCase__	:  int			,							lowerCAmelCase__	:  list[list[int]] ):

			"""simple docstring"""





			__UpperCAmelCase   :      str										=     1
			while (1 << j) < max_node:
						for i in range(1			,							max_node + 1 ):
									__UpperCAmelCase   :      Union[str, Any]										=     parent[j - 1][parent[j - 1][i]]
						j += 1
			return parent


def   lowercase_	(   lowerCAmelCase__	:  int			,							lowerCAmelCase__	:  int			,							lowerCAmelCase__	:  list[int]			,							lowerCAmelCase__	:  list[list[int]] ):

			"""simple docstring"""





			if level[u] < level[v]:
						__UpperCAmelCase   :      Optional[Any]										=     swap(lowerCAmelCase__			,							lowerCAmelCase__ )
			# making depth of u same as depth of v
			for i in range(18			,							-1			,							-1 ):
						if level[u] - (1 << i) >= level[v]:
									__UpperCAmelCase   :      Optional[int]										=     parent[i][u]
    # at the same depth if u==v that mean lca is found
			if u == v:
						return u
			# moving both nodes upwards till lca in found
			for i in range(18			,							-1			,							-1 ):
						if parent[i][u] not in [0, parent[i][v]]:
									__UpperCAmelCase   :      Dict										=     parent[i][u], parent[i][v]
    # returning longest common ancestor of u,v
			return parent[0][u]


def   lowercase_	(   lowerCAmelCase__	:  list[int]			,							lowerCAmelCase__	:  list[list[int]]			,							lowerCAmelCase__	:  int			,							lowerCAmelCase__	:  dict[int, list[int]]			,							lowerCAmelCase__	:  int = 1			,							):

			"""simple docstring"""





			__UpperCAmelCase   :      Optional[Any]										=     0
			__UpperCAmelCase   :      Queue[int]										=     Queue(maxsize=lowerCAmelCase__ )
			q.put(lowerCAmelCase__ )
			while q.qsize() != 0:
						__UpperCAmelCase   :      Union[str, Any]										=     q.get()
						for v in graph[u]:
									if level[v] == -1:
												__UpperCAmelCase   :      Union[str, Any]										=     level[u] + 1
												q.put(lowerCAmelCase__ )
												__UpperCAmelCase   :      int										=     u
			return level, parent


def   lowercase_	(   ):

			"""simple docstring"""





			__UpperCAmelCase   :      Optional[Any]										=     13
			# initializing with 0
			__UpperCAmelCase   :      List[Any]										=     [[0 for _ in range(max_node + 10 )] for _ in range(20 )]
			# initializing with -1 which means every node is unvisited
			__UpperCAmelCase   :      Tuple										=     [-1 for _ in range(max_node + 10 )]
			__UpperCAmelCase   :      dict[int, list[int]]										=     {
			    1: [2, 3, 4],
			    2: [5],
			    3: [6, 7],
			    4: [8],
			    5: [9, 10],
			    6: [11],
			    7: [],
			    8: [12, 13],
			    9: [],
			    10: [],
			    11: [],
			    12: [],
			    13: [],
			}
			__UpperCAmelCase   :      List[Any]										=     breadth_first_search(lowerCAmelCase__			,							lowerCAmelCase__			,							lowerCAmelCase__			,							lowerCAmelCase__			,							1 )
			__UpperCAmelCase   :      Optional[Any]										=     create_sparse(lowerCAmelCase__			,							lowerCAmelCase__ )
			print("""LCA of node 1 and 3 is: """			,							lowest_common_ancestor(1			,							3			,							lowerCAmelCase__			,							lowerCAmelCase__ ) )
			print("""LCA of node 5 and 6 is: """			,							lowest_common_ancestor(5			,							6			,							lowerCAmelCase__			,							lowerCAmelCase__ ) )
			print("""LCA of node 7 and 11 is: """			,							lowest_common_ancestor(7			,							11			,							lowerCAmelCase__			,							lowerCAmelCase__ ) )
			print("""LCA of node 6 and 7 is: """			,							lowest_common_ancestor(6			,							7			,							lowerCAmelCase__			,							lowerCAmelCase__ ) )
			print("""LCA of node 4 and 12 is: """			,							lowest_common_ancestor(4			,							12			,							lowerCAmelCase__			,							lowerCAmelCase__ ) )
			print("""LCA of node 8 and 8 is: """			,							lowest_common_ancestor(8			,							8			,							lowerCAmelCase__			,							lowerCAmelCase__ ) )


if __name__ == "__main__":
						main()









'''simple docstring'''
import numpy as np
from cva import destroyAllWindows, imread, imshow, waitKey



class _A  :





		def __init__(     self ,       __UpperCAmelCase ,       __UpperCAmelCase				)       ->     Union[str, Any]:

					'''simple docstring'''
					__UpperCAmelCase   :      Optional[int]										=     0
					# max greyscale value for #FFFFFF
					__UpperCAmelCase   :      List[Any]										=     int(self.get_greyscale(255 ,       255 ,       255				)				)

					if not self.min_threshold < threshold < self.max_threshold:
								__UpperCAmelCase   :      str										=     f'Factor value should be from 0 to {self.max_threshold}'
								raise ValueError(__UpperCAmelCase				)

					__UpperCAmelCase   :      Tuple										=     input_img
					__UpperCAmelCase   :      Optional[Any]										=     threshold
					__UpperCAmelCase				,  __UpperCAmelCase   :      List[Any]										=     self.input_img.shape[1], self.input_img.shape[0]

					# error table size (+4 columns and +1 row) greater than input image because of
					# lack of if statements
					__UpperCAmelCase   :      Optional[Any]										=     [
					    [0 for _ in range(self.height + 4				)] for __ in range(self.width + 1				)
					]
					__UpperCAmelCase   :      Any										=     np.ones((self.width, self.height, 3) ,       np.uinta				) * 255





		@classmethod
		def 							__A       (     cls ,       __UpperCAmelCase ,       __UpperCAmelCase ,       __UpperCAmelCase				)       ->     float:

					'''simple docstring'''
					return 0.114 * blue + 0.587 * green + 0.2126 * red





		def 							__A       (     self				)       ->     None:

					'''simple docstring'''
					for y in range(self.height				):
								for x in range(self.width				):
											__UpperCAmelCase   :      Optional[Any]										=     int(self.get_greyscale(*self.input_img[y][x]				)				)
											if self.threshold > greyscale + self.error_table[y][x]:
														__UpperCAmelCase   :      List[Any]										=     (0, 0, 0)
														__UpperCAmelCase   :      Union[str, Any]										=     greyscale + self.error_table[x][y]
											else:
														__UpperCAmelCase   :      Optional[Any]										=     (255, 255, 255)
														__UpperCAmelCase   :      Dict										=     greyscale + self.error_table[x][y] - 255
											self.error_table[y][x + 1] += int(8 / 32 * current_error				)
											self.error_table[y][x + 2] += int(4 / 32 * current_error				)
											self.error_table[y + 1][x] += int(8 / 32 * current_error				)
											self.error_table[y + 1][x + 1] += int(4 / 32 * current_error				)
											self.error_table[y + 1][x + 2] += int(2 / 32 * current_error				)
											self.error_table[y + 1][x - 1] += int(4 / 32 * current_error				)
											self.error_table[y + 1][x - 2] += int(2 / 32 * current_error				)


if __name__ == "__main__":
					# create Burke's instances with original images in greyscale
					_UpperCamelCase											=			[
					    Burkes(imread('''image_data/lena.jpg''', 1), threshold)
					    for threshold in (1, 126, 130, 140)
					]

					for burkes in burkes_instances:
										burkes.process()

					for burkes in burkes_instances:
										imshow(
										    F'Original image with dithering threshold: {burkes.threshold}',
										    burkes.output_img,
										)

					waitKey(0)
					destroyAllWindows()




