



from __future__ import annotations

from typing import Any


class 	__snake_case   :
		def __init__(							self    ,a_						):







						"""simple docstring"""
						lowerCAmelCase__		  =  num_of_nodes
						lowerCAmelCase__		  =  []
						lowerCAmelCase__		  =  {}
		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_    ,a_    ,a_						):







						"""simple docstring"""
						self.m_edges.append([u_node, v_node, weight]						)
		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_						):







						"""simple docstring"""

						if self.m_component[u_node] == u_node:
										return u_node
						return self.find_component(self.m_component[u_node]						)
		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_						):







						"""simple docstring"""

						if self.m_component[u_node] != u_node:
										for k in self.m_component:
														lowerCAmelCase__		  =  self.find_component(a_						)
		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_    ,a_    ,a_						):







						"""simple docstring"""

						if component_size[u_node] <= component_size[v_node]:
										lowerCAmelCase__		  =  v_node
										component_size[v_node] += component_size[u_node]
										self.set_component(a_						)

						elif component_size[u_node] >= component_size[v_node]:
										lowerCAmelCase__		  =  self.find_component(a_						)
										component_size[u_node] += component_size[v_node]
										self.set_component(a_						)



		def 						SCREAMING_SNAKE_CASE_					(							self						):







						"""simple docstring"""
						lowerCAmelCase__		  =  []
						lowerCAmelCase__		  =  0

						lowerCAmelCase__		  =  [-1] * self.m_num_of_nodes

						# A list of components (initialized to all of the nodes)
						for node in range(self.m_num_of_nodes						):
										self.m_component.update({node: node}						)
										component_size.append(1						)

						lowerCAmelCase__		  =  self.m_num_of_nodes

						while num_of_components > 1:
										for edge in self.m_edges:
														lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__		  =  edge

														lowerCAmelCase__		  =  self.m_component[u]
														lowerCAmelCase__		  =  self.m_component[v]

														if u_component != v_component:

																		for component in (u_component, v_component):
																						if (
																						    minimum_weight_edge[component] == -1
																						    or minimum_weight_edge[component][2] > w
																						):
																										lowerCAmelCase__		  =  [u, v, w]

										for edge in minimum_weight_edge:
														if isinstance(a_    ,a_						):
																		lowerCAmelCase__  ,   lowerCAmelCase__  ,   lowerCAmelCase__		  =  edge

																		lowerCAmelCase__		  =  self.m_component[u]
																		lowerCAmelCase__		  =  self.m_component[v]

																		if u_component != v_component:
																						mst_weight += w
																						self.union(a_    ,a_    ,a_						)
																						print(f'Added edge [{u} - {v}]\nAdded weight: {w}\n'						)
																						num_of_components -= 1

										lowerCAmelCase__		  =  [-1] * self.m_num_of_nodes
						print(f'The total weight of the minimal spanning tree is: {mst_weight}'						)







def     UpperCAmelCase_		(					)	->     None:



				"""simple docstring"""







if __name__ == "__main__":
	import doctest

	doctest.testmod()





from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__					)	->     Dict:



				"""simple docstring"""





				lowerCAmelCase__		  =  k_size // 2
				lowerCAmelCase__  ,   lowerCAmelCase__		  =  mgrid[0 - center : k_size - center, 0 - center : k_size - center]
				lowerCAmelCase__		  =  1 / (2 * pi * sigma) * exp(-(square(snake_case__					) + square(snake_case__					)) / (2 * square(snake_case__					))					)
				return g







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__					)	->     str:



				"""simple docstring"""





				lowerCAmelCase__  ,   lowerCAmelCase__		  =  image.shape[0], image.shape[1]
				# dst image height and width
				lowerCAmelCase__		  =  height - k_size + 1
				lowerCAmelCase__		  =  width - k_size + 1

				# im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
				lowerCAmelCase__		  =  zeros((dst_height * dst_width, k_size * k_size)					)
				lowerCAmelCase__		  =  0
				for i, j in product(range(snake_case__					)    ,			range(snake_case__					)					):
								lowerCAmelCase__		  =  ravel(image[i : i + k_size, j : j + k_size]					)
								lowerCAmelCase__		  =  window
								row += 1

				#  turn the kernel into shape(k*k, 1)
				lowerCAmelCase__		  =  gen_gaussian_kernel(snake_case__    ,			snake_case__					)
				lowerCAmelCase__		  =  ravel(snake_case__					)

				# reshape and get the dst image
				lowerCAmelCase__		  =  dot(snake_case__    ,			snake_case__					).reshape(snake_case__    ,			snake_case__					).astype(snake_case__					)

				return dst


if __name__ == "__main__":
	# read original image
	_lowerCAmelCase	:   List[str]    =   imread(R"../image_data/lena.jpg")
	# turn image in gray scale value
	_lowerCAmelCase	:   Optional[Any]    =   cvtColor(img, COLOR_BGR2GRAY)

	# get values with two different mask size
	_lowerCAmelCase	:   Optional[int]    =   gaussian_filter(gray, 3, sigma=1)
	_lowerCAmelCase	:   Tuple    =   gaussian_filter(gray, 5, sigma=0.8)

	# show result images
	imshow("gaussian filter with 3x3 mask", gaussianaxa)
	imshow("gaussian filter with 5x5 mask", gaussianaxa)
	waitKey()
