
import math







def        A__					(						lowerCamelCase     ,    lowerCamelCase						)  ->	float:
				if (
				    not isinstance(_lowercase     ,    (int, float)						)
				    or power_factor < -1
				    or power_factor > 1
				):
								raise ValueError("""power_factor must be a valid float value between -1 and 1."""						)
				return apparent_power * power_factor







def        A__					(						lowerCamelCase     ,    lowerCamelCase						)  ->	float:
				if (
				    not isinstance(_lowercase     ,    (int, float)						)
				    or power_factor < -1
				    or power_factor > 1
				):
								raise ValueError("""power_factor must be a valid float value between -1 and 1."""						)
				return apparent_power * math.sqrt(1 - power_factor**2						)


if __name__ == "__main__":
							import doctest

							doctest.testmod()








import random







def        A__					(						lowerCamelCase     ,    lowerCamelCase     ,    lowerCamelCase = False						)  ->	dict:
				UpperCamelCase_:							dict	=						{i: [] for i in range(lowerCamelCase						)}

				# if probability is greater or equal than 1, then generate a complete graph
				if probability >= 1:
								return complete_graph(lowerCamelCase						)
				# if probability is lower or equal than 0, then return a graph without edges
				if probability <= 0:
								return graph

				# for each couple of nodes, add an edge from u to v
				# if the number randomly generated is greater than probability probability
				for i in range(lowerCamelCase						):
								for j in range(i + 1     ,    lowerCamelCase						):
												if random.random() < probability:
																graph[i].append(lowerCamelCase						)
																if not directed:
																				# if the graph is undirected, add an edge in from j to i, either
																				graph[j].append(lowerCamelCase						)
				return graph







def        A__					(						lowerCamelCase						)  ->	dict:
				return {
				    i: [j for j in range(lowerCamelCase						) if i != j] for i in range(lowerCamelCase						)
				}


if __name__ == "__main__":
							import doctest

							doctest.testmod()






