"""simple docstring"""






from __future__ import annotations



def   a_						( lowerCamelCase ,      lowerCamelCase ,      lowerCamelCase ,      ):
				if not all((nth_term, start_term_a, common_ratio_r)	):
								return []
				UpperCAmelCase__					=							[]
				UpperCAmelCase__					=							1
				UpperCAmelCase__					=							common_ratio_r
				for _ in range(int(snake_case__	)	):
								if not series:
												series.append(snake_case__	)
								else:
												power += 1
												series.append(float(start_term_a * multiple	)	)
												UpperCAmelCase__					=							pow(float(snake_case__	) ,      snake_case__	)
				return series


if __name__ == "__main__":
						import doctest

						doctest.testmod()

						lowerCAmelCase__  :  Optional[Any]											=     float(input('Enter the last number (n term) of the Geometric Series'))
						lowerCAmelCase__  :  List[Any]											=     float(input('Enter the starting term (a) of the Geometric Series'))
						lowerCAmelCase__  :  Union[str, Any]											=     float(
						    input('Enter the common ratio between two terms (r) of the Geometric Series')
						)
						print('Formula of Geometric Series => a + ar + ar^2 ... +ar^n')
						print(geometric_series(nth_term, start_term_a, common_ratio_r))




"""simple docstring"""






from __future__ import annotations
class     snake_case	:




					"""simple docstring"""

					def __init__(    self       :     Tuple   ,lowerCamelCase__       :     int      ):
									UpperCAmelCase__					=							vertices
									UpperCAmelCase__					=							[[0] * vertices for _ in range(lowerCamelCase__      )]







					def 		__lowerCAmelCase						(    self       :     Dict   ,lowerCamelCase__       :     list[int]      ):
									print('Vertex \t Distance from Source'      )
									for vertex in range(self.vertices      ):
													print(lowerCamelCase__   ,'\t\t'   ,distances_from_source[vertex]      )







					def 		__lowerCAmelCase						(    self       :     List[Any]   ,lowerCamelCase__       :     list[int]   ,lowerCamelCase__       :     list[bool]      ):
									UpperCAmelCase__					=							1e7
									UpperCAmelCase__					=							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:
																	UpperCAmelCase__					=							distances_from_source[vertex]
																	UpperCAmelCase__					=							vertex
									return min_index







					def 		__lowerCAmelCase						(    self       :     List[Any]   ,lowerCamelCase__       :     int      ):
									UpperCAmelCase__					=							[int(1e7      )] * self.vertices  # distances from the source
									UpperCAmelCase__					=							0
									UpperCAmelCase__					=							[False] * self.vertices

									for _ in range(self.vertices      ):
													UpperCAmelCase__					=							self.minimum_distance(lowerCamelCase__   ,lowerCamelCase__      )
													UpperCAmelCase__					=							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]
																	):
																					UpperCAmelCase__					=							distances[u] + self.graph[u][v]

									self.print_solution(lowerCamelCase__      )


if __name__ == "__main__":
						lowerCAmelCase__  :  List[str]											=     Graph(9)
						lowerCAmelCase__  :  Tuple											=     [
						    [0, 4, 0, 0, 0, 0, 0, 8, 0],
						    [4, 0, 8, 0, 0, 0, 0, 11, 0],
						    [0, 8, 0, 7, 0, 4, 0, 0, 2],
						    [0, 0, 7, 0, 9, 14, 0, 0, 0],
						    [0, 0, 0, 9, 0, 10, 0, 0, 0],
						    [0, 0, 4, 14, 10, 0, 2, 0, 0],
						    [0, 0, 0, 0, 0, 2, 0, 1, 6],
						    [8, 11, 0, 0, 0, 0, 1, 0, 7],
						    [0, 0, 2, 0, 0, 0, 6, 7, 0],
						]
						graph.dijkstra(0)



