

import heapq






def        A       (      _lowerCamelCase						):





							'''simple docstring'''




							_lowerCAmelCase  :							list[list]				     =					[]

							# for each node and his adjacency list add them and the rank of the node to queue
							# using heapq module the queue will be filled like a Priority Queue
							# heapq works with a min priority queue, so I used -1*len(v) to build it
							for key, value in graph.items():
														# O(log(n))
														heapq.heappush(_lowerCamelCase       ,				[-1 * len(_lowerCamelCase						), (key, value)]						)

							# chosen_vertices = set of chosen vertices
							_lowerCAmelCase  :							Tuple				     =					set()

							# while queue isn't empty and there are still edges
							#   (queue[0][0] is the rank of the node with max rank)
							while queue and queue[0][0] != 0:
														# extract vertex with max rank from queue and add it to chosen_vertices
														_lowerCAmelCase  :							List[str]				     =					heapq.heappop(_lowerCamelCase						)[1][0]
														chosen_vertices.add(_lowerCamelCase						)

														# Remove all arcs adjacent to argmax
														for elem in queue:
																					# if v haven't adjacent node, skip
																					if elem[0] == 0:
																												continue
																					# if argmax is reachable from elem
																					# remove argmax from elem's adjacent list and update his rank
																					if argmax in elem[1][1]:
																												_lowerCAmelCase  :							Union[str, Any]				     =					elem[1][1].index(_lowerCamelCase						)
																												del elem[1][1][index]
																												elem[0] += 1
        # re-order the queue
														heapq.heapify(_lowerCamelCase						)
							return chosen_vertices


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						_snake_case	=						{0: [1, 3], 1: [0, 3], 2: [0, 3, 4], 3: [0, 1, 2], 4: [2, 3]}
						print(f'''Minimum vertex cover:\n{greedy_min_vertex_cover(graph)}''')





import numpy as np
from cva import COLOR_BGR2GRAY, CV_8UC3, cvtColor, filteraD, imread, imshow, waitKey






def        A       (      _lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase       ,				_lowerCamelCase						):





							'''simple docstring'''




							if (ksize % 2) == 0:
														_lowerCAmelCase  :							str				     =					ksize + 1
							_lowerCAmelCase  :							List[str]				     =					np.zeros((ksize, ksize)       ,				dtype=np.floataa						)

							# each value
							for y in range(_lowerCamelCase						):
														for x in range(_lowerCamelCase						):
																					# distance from center
																					_lowerCAmelCase  :							int				     =					x - ksize // 2
																					_lowerCAmelCase  :							Dict				     =					y - ksize // 2

																					# degree to radiant
																					_lowerCAmelCase  :							List[Any]				     =					theta / 180 * np.pi
																					_lowerCAmelCase  :							int				     =					np.cos(_theta						)
																					_lowerCAmelCase  :							Optional[int]				     =					np.sin(_theta						)

																					# get kernel x
																					_lowerCAmelCase  :							int				     =					cos_theta * px + sin_theta * py

																					# get kernel y
																					_lowerCAmelCase  :							str				     =					-sin_theta * px + cos_theta * py

																					# fill kernel
																					_lowerCAmelCase  :							Union[str, Any]				     =					np.exp(
																					    -(_x**2 + gamma**2 * _y**2) / (2 * sigma**2)						) * np.cos(2 * np.pi * _x / lambd + psi						)

							return gabor


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						# read original image
						_snake_case	=						imread("../image_data/lena.jpg")
						# turn image in gray scale value
						_snake_case	=						cvtColor(img, COLOR_BGR2GRAY)

						# Apply multiple Kernel to detect edges
						_snake_case	=						np.zeros(gray.shape[:2])
						for theta in [0, 30, 60, 90, 120, 150]:
												_snake_case	=						gabor_filter_kernel(10, 8, theta, 10, 0, 0)
												out += filteraD(gray, CV_8UC3, kernel_aa)
						_snake_case	=						out / out.max() * 255
						_snake_case	=						out.astype(np.uinta)

						imshow("Original", gray)
						imshow("Gabor filter with 20x20 mask and 6 directions", out)

						waitKey(0)
