



"""simple docstring"""






from __future__ import annotations

class 			__SCREAMING_SNAKE_CASE      :


					'''simple docstring'''





					def __init__(			self				:    List[str],    lowerCamelCase				:    int	)->   None:
								lowerCamelCase__						:						Any						      =vertices
								lowerCamelCase__						:						Optional[Any]						      =[[0] * vertices for _ in range(lowerCamelCase	)]



					def 						snake_case			(			self				:    Optional[int],    lowerCamelCase				:    list[int]	)->   None:
								print('''Vertex \t Distance from Source'''	)
								for vertex in range(self.vertices	):
											print(lowerCamelCase,    '''\t\t''',    distances_from_source[vertex]	)



					def 						snake_case			(			self				:    Optional[int],    lowerCamelCase				:    list[int],    lowerCamelCase				:    list[bool]	)->   int:
								lowerCamelCase__						:						Optional[int]						      =1E7
								lowerCamelCase__						:						int						      =0

								# Search not nearest vertex not in the shortest path tree
								for vertex in range(self.vertices	):
											if distances_from_source[vertex] < minimum and visited[vertex] is False:
														lowerCamelCase__						:						Tuple						      =distances_from_source[vertex]
														lowerCamelCase__						:						Any						      =vertex
								return min_index




					def 						snake_case			(			self				:    Any,    lowerCamelCase				:    int	)->   None:
								lowerCamelCase__						:						Union[str, Any]						      =[int(1E7	)] * self.vertices  # distances from the source
								lowerCamelCase__						:						int						      =0
								lowerCamelCase__						:						Optional[int]						      =[False] * self.vertices

								for _ in range(self.vertices	):
											lowerCamelCase__						:						int						      =self.minimum_distance(lowerCamelCase,    lowerCamelCase	)
											lowerCamelCase__						:						List[Any]						      =True

											# Update dist value of the adjacent vertices
											# of the picked vertex only if the current
											# distance is greater than new distance and
											# the vertex in not in the shortest path tree
											for v in range(self.vertices	):
														if (
														    self.graph[u][v] > 0
														    and visited[v] is False
														    and distances[v] > distances[u] + self.graph[u][v]
														):
																	lowerCamelCase__						:						Dict						      =distances[u] + self.graph[u][v]

								self.print_solution(lowerCamelCase	)


if __name__ == "__main__":
		_lowercase					:					List[str] 		=		Graph(9)
		_lowercase					:					Optional[int] 		=		[
		    [0, 4, 0, 0, 0, 0, 0, 8, 0],
		    [4, 0, 8, 0, 0, 0, 0, 1_1, 0],
		    [0, 8, 0, 7, 0, 4, 0, 0, 2],
		    [0, 0, 7, 0, 9, 1_4, 0, 0, 0],
		    [0, 0, 0, 9, 0, 1_0, 0, 0, 0],
		    [0, 0, 4, 1_4, 1_0, 0, 2, 0, 0],
		    [0, 0, 0, 0, 0, 2, 0, 1, 6],
		    [8, 1_1, 0, 0, 0, 0, 1, 0, 7],
		    [0, 0, 2, 0, 0, 0, 6, 7, 0],
		]
		graph.dijkstra(0)










def 		lowercase__ (		__A:						list[list[int]]					):





					'''simple docstring'''






					if len(__A					) == 0 or not all(len(__A					) == 2 for pair in coordinates					):
										raise ValueError('''The program cannot work out a fitting polynomial.'''					)

					if len({tuple(__A					) for pair in coordinates}					) != len(__A					):
										raise ValueError('''The program cannot work out a fitting polynomial.'''					)

					__magic_name__				:						Union[str, Any]     				=				{x for x, _ in coordinates}
					if len(__A					) == 1:
										return F'''x={coordinates[0][0]}'''

					if len(__A					) != len(__A					):
										raise ValueError('''The program cannot work out a fitting polynomial.'''					)

					__magic_name__				:						List[Any]     				=				len(__A					)

					__magic_name__				:						int     				=				0
					__magic_name__				:						list[list[float]]     				=				[]
					# put the x and x to the power values in a matrix
					while count_of_line < x:
										__magic_name__				:						List[Any]     				=				0
										__magic_name__				:						List[str]     				=				coordinates[count_of_line][0]
										__magic_name__				:						list[float]     				=				[]
										while count_in_line < x:
															count_line.append(a ** (x - (count_in_line + 1))					)
															count_in_line += 1
										matrix.append(__A					)
										count_of_line += 1

					__magic_name__				:						Union[str, Any]     				=				0
					# put the y values into a vector
					__magic_name__				:						list[float]     				=				[]
					while count_of_line < x:
										vector.append(coordinates[count_of_line][1]					)
										count_of_line += 1

					__magic_name__				:						int     				=				0

					while count < x:
										__magic_name__				:						int     				=				0
										while zahlen < x:
															if count == zahlen:
																				zahlen += 1
															if zahlen == x:
																				break
															__magic_name__				:						Tuple     				=				matrix[zahlen][count] / matrix[count][count]
															for counting_columns, item in enumerate(matrix[count]					):
																				# manipulating all the values in the matrix
																				matrix[zahlen][counting_columns] -= item * bruch
															# manipulating the values in the vector
															vector[zahlen] -= vector[count] * bruch
															zahlen += 1
										count += 1

					__magic_name__				:						str     				=				0
					# make solutions
					__magic_name__				:						list[str]     				=				[]
					while count < x:
										solution.append(str(vector[count] / matrix[count][count]					)					)
										count += 1

					__magic_name__				:						List[Any]     				=				0
					__magic_name__				:						Union[str, Any]     				=				'''f(x)='''

					while count < x:
										__magic_name__				:						list[str]     				=				solution[count].split('''E'''					)
										if len(__A					) > 1:
															__magic_name__				:						Union[str, Any]     				=				F'''{remove_e[0]}*10^{remove_e[1]}'''
										solved += F'''x^{x - (count + 1)}*{solution[count]}'''
										if count + 1 != x:
															solved += "+"
										count += 1

					return solved


if __name__ == "__main__":
	print(points_to_polynomial([]))
	print(points_to_polynomial([[]]))
	print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
	print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
	print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
	print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
	print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
	print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
	print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
	print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))



