
from __future__ import annotations

from typing import Any







class     lowercase		:




							def __init__(    self       ,A__):
												lowercase						     =						num_of_nodes
												lowercase						     =						[]
												lowercase						     =						{}




							def 			A__				(    self       ,A__       ,A__       ,A__):
												self.m_edges.append([u_node, v_node, weight])




							def 			A__				(    self       ,A__):

												if self.m_component[u_node] == u_node:
																	return u_node
												return self.find_component(self.m_component[u_node])




							def 			A__				(    self       ,A__):

												if self.m_component[u_node] != u_node:
																	for k in self.m_component:
																						lowercase						     =						self.find_component(A__)




							def 			A__				(    self       ,A__       ,A__       ,A__):

												if component_size[u_node] <= component_size[v_node]:
																	lowercase						     =						v_node
																	component_size[v_node] += component_size[u_node]
																	self.set_component(A__)

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





							def 			A__				(    self):
												lowercase						     =						[]
												lowercase						     =						0

												lowercase						     =						[-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)

												lowercase						     =						self.m_num_of_nodes

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

																						lowercase						     =						self.m_component[u]
																						lowercase						     =						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
																																):
																																					lowercase						     =						[u, v, w]

																	for edge in minimum_weight_edge:
																						if isinstance(A__       ,A__):
																											lowercase     ,						lowercase     ,						lowercase						     =						edge

																											lowercase						     =						self.m_component[u]
																											lowercase						     =						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

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



def 	UpperCamelCase   (							):
					'''simple docstring'''


if __name__ == "__main__":
							import doctest

							doctest.testmod()







from __future__ import annotations

from decimal import Decimal

from numpy import array



def 	UpperCamelCase   (							lowerCAmelCase__		):
					'''simple docstring'''
					lowercase						     =						Decimal

					# Check if the provided matrix has 2 rows and 2 columns
					# since this implementation only works for 2x2 matrices
					if len(lowerCAmelCase__		) == 2 and len(matrix[0]		) == 2 and len(matrix[1]		) == 2:
										# Calculate the determinant of the matrix
										lowercase						     =						float(
										    d(matrix[0][0]		) * d(matrix[1][1]		) - d(matrix[1][0]		) * d(matrix[0][1]		)		)
										if determinant == 0:
															raise ValueError('''This matrix has no inverse.'''		)

										# Creates a copy of the matrix with swapped positions of the elements
										lowercase						     =						[[0.0, 0.0], [0.0, 0.0]]
										lowercase     ,						lowercase						     =						matrix[1][1], matrix[0][0]
										lowercase     ,						lowercase						     =						-matrix[1][0], -matrix[0][1]

										# Calculate the inverse of the matrix
										return [
										    [(float(d(lowerCAmelCase__		)		) / determinant) or 0.0 for n in row] for row in swapped_matrix
										]
					elif (
					    len(lowerCAmelCase__		) == 3
					    and len(matrix[0]		) == 3
					    and len(matrix[1]		) == 3
					    and len(matrix[2]		) == 3
					):
										# Calculate the determinant of the matrix using Sarrus rule
										lowercase						     =						float(
										    (
										        (d(matrix[0][0]		) * d(matrix[1][1]		) * d(matrix[2][2]		))
										        + (d(matrix[0][1]		) * d(matrix[1][2]		) * d(matrix[2][0]		))
										        + (d(matrix[0][2]		) * d(matrix[1][0]		) * d(matrix[2][1]		))
										    )
										    - (
										        (d(matrix[0][2]		) * d(matrix[1][1]		) * d(matrix[2][0]		))
										        + (d(matrix[0][1]		) * d(matrix[1][0]		) * d(matrix[2][2]		))
										        + (d(matrix[0][0]		) * d(matrix[1][2]		) * d(matrix[2][1]		))
										    )		)
										if determinant == 0:
															raise ValueError('''This matrix has no inverse.'''		)

										# Creating cofactor matrix
										lowercase						     =						[
										    [d(0.0		), d(0.0		), d(0.0		)],
										    [d(0.0		), d(0.0		), d(0.0		)],
										    [d(0.0		), d(0.0		), d(0.0		)],
										]
										lowercase						     =						(d(matrix[1][1]		) * d(matrix[2][2]		)) - (
										    d(matrix[1][2]		) * d(matrix[2][1]		)
										)
										lowercase						     =						-(
										    (d(matrix[1][0]		) * d(matrix[2][2]		)) - (d(matrix[1][2]		) * d(matrix[2][0]		))
										)
										lowercase						     =						(d(matrix[1][0]		) * d(matrix[2][1]		)) - (
										    d(matrix[1][1]		) * d(matrix[2][0]		)
										)
										lowercase						     =						-(
										    (d(matrix[0][1]		) * d(matrix[2][2]		)) - (d(matrix[0][2]		) * d(matrix[2][1]		))
										)
										lowercase						     =						(d(matrix[0][0]		) * d(matrix[2][2]		)) - (
										    d(matrix[0][2]		) * d(matrix[2][0]		)
										)
										lowercase						     =						-(
										    (d(matrix[0][0]		) * d(matrix[2][1]		)) - (d(matrix[0][1]		) * d(matrix[2][0]		))
										)
										lowercase						     =						(d(matrix[0][1]		) * d(matrix[1][2]		)) - (
										    d(matrix[0][2]		) * d(matrix[1][1]		)
										)
										lowercase						     =						-(
										    (d(matrix[0][0]		) * d(matrix[1][2]		)) - (d(matrix[0][2]		) * d(matrix[1][0]		))
										)
										lowercase						     =						(d(matrix[0][0]		) * d(matrix[1][1]		)) - (
										    d(matrix[0][1]		) * d(matrix[1][0]		)
										)

										# Transpose the cofactor matrix (Adjoint matrix)
										lowercase						     =						array(lowerCAmelCase__		)
										for i in range(3		):
															for j in range(3		):
																				lowercase						     =						cofactor_matrix[j][i]

        # Inverse of the matrix using the formula (1/determinant) * adjoint matrix
										lowercase						     =						array(lowerCAmelCase__		)
										for i in range(3		):
															for j in range(3		):
																				inverse_matrix[i][j] /= d(lowerCAmelCase__		)

        # Calculate the inverse of the matrix
										return [[float(d(lowerCAmelCase__		)		) or 0.0 for n in row] for row in inverse_matrix]
					raise ValueError('''Please provide a matrix of size 2x2 or 3x3.'''		)




