
'''simple docstring'''







import matplotlib.pyplot as plt
import numpy as np
def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				Optional[int]   ,   __SCREAMING_SNAKE_CASE      :				Any   ,   __SCREAMING_SNAKE_CASE      :				Any							):



						"""simple docstring"""





						lowercase_			:  List[str]									= len(__lowerCamelCase							)  # Number of training samples
						lowercase_			:  Optional[Any]									= np.eye(__lowerCamelCase							)  # Initialize weights as identity matrix
						for j in range(__lowerCamelCase							):
												lowercase_			:  Union[str, Any]									= point - x_train[j]
												lowercase_			:  Dict									= np.exp(diff @ diff.T / (-2.0 * tau**2)							)

						return weights
def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				Optional[int]   ,   __SCREAMING_SNAKE_CASE      :				str   ,   __SCREAMING_SNAKE_CASE      :				Any   ,   __SCREAMING_SNAKE_CASE      :				Union[str, Any]							):



						"""simple docstring"""





						lowercase_			:  Dict									= weight_matrix(__lowerCamelCase   ,   __lowerCamelCase   ,   __lowerCamelCase							)
						lowercase_			:  Tuple									= np.linalg.inv(x_train.T @ weight_mat @ x_train							) @ (
						    x_train.T @ weight_mat @ y_train.T
						)

						return weight
def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				Optional[int]   ,   __SCREAMING_SNAKE_CASE      :				Tuple   ,   __SCREAMING_SNAKE_CASE      :				Union[str, Any]							):



						"""simple docstring"""





						lowercase_			:  Union[str, Any]									= np.zeros(len(__lowerCamelCase							)							)  # Initialize array of predictions
						for i, item in enumerate(__lowerCamelCase							):
												lowercase_			:  List[Any]									= item @ local_weight(__lowerCamelCase   ,   __lowerCamelCase   ,   __lowerCamelCase   ,   __lowerCamelCase							)

						return y_pred
def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				Optional[int]   ,   __SCREAMING_SNAKE_CASE      :				Optional[Any]   ,   __SCREAMING_SNAKE_CASE      :				List[Any]							):



						"""simple docstring"""





						import seaborn as sns

						lowercase_			:  Union[str, Any]									= sns.load_dataset(__lowerCamelCase							)
						lowercase_			:  List[str]									= np.array(data[x_name]							)
						lowercase_			:  Dict									= np.array(data[y_name]							)

						lowercase_			:  str									= np.ones(len(__lowerCamelCase							)							)

						# pairing elements of one and x_data
						lowercase_			:  List[str]									= np.column_stack((one, x_data)							)

						return x_train, x_data, y_data
def       snake_case_	(       __SCREAMING_SNAKE_CASE      :				Dict   ,   __SCREAMING_SNAKE_CASE      :				Any   ,   __SCREAMING_SNAKE_CASE      :				Any   ,   __SCREAMING_SNAKE_CASE      :				Optional[int]   ,   __SCREAMING_SNAKE_CASE      :				int   ,   __SCREAMING_SNAKE_CASE      :				Union[str, Any]   ,   ):



						"""simple docstring"""





						lowercase_			:  Optional[int]									= np.sort(__lowerCamelCase   ,   axis=0							)
						plt.scatter(__lowerCamelCase   ,   __lowerCamelCase   ,   color='''blue'''							)
						plt.plot(
						    x_train_sorted[:, 1]   ,   preds[x_train[:, 1].argsort(0							)]   ,   color='''yellow'''   ,   linewidth=5   ,   )
						plt.title('''Local Weighted Regression'''							)
						plt.xlabel(__lowerCamelCase							)
						plt.ylabel(__lowerCamelCase							)
						plt.show()


if __name__ == "__main__":
					import doctest

					doctest.testmod()

					# Demo with a dataset from the seaborn module
					_lowercase				:						str												= load_data("tips", "total_bill", "tip")
					_lowercase				:						Union[str, Any]												= local_weight_regression(training_data_x, tip, 5)
					plot_preds(training_data_x, predictions, total_bill, tip, "total_bill", "tip")





'''simple docstring'''







from __future__ import annotations

from queue import Queue






class 				lowerCAmelCase__     :






					def __init__(     self	):


											"""simple docstring"""





											lowercase_			:  dict[int, list[int]]									= {}






					def 			_snake_case					(     self	):


											"""simple docstring"""





											for i in self.vertices:
																	print(__SCREAMING_SNAKE_CASE       ,							''' : '''       ,							''' -> '''.join([str(__SCREAMING_SNAKE_CASE	) for j in self.vertices[i]]	)	)






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE       ,							__SCREAMING_SNAKE_CASE	):


											"""simple docstring"""





											if from_vertex in self.vertices:
																	self.vertices[from_vertex].append(__SCREAMING_SNAKE_CASE	)
											else:
																	lowercase_			:  Optional[Any]									= [to_vertex]






					def 			_snake_case					(     self       ,							__SCREAMING_SNAKE_CASE	):


											"""simple docstring"""





											lowercase_			:  List[Any]									= set()

											# create a first in first out queue to store all the vertices for BFS
											lowercase_			:  Queue									= Queue()

											# mark the source node as visited and enqueue it
											visited.add(__SCREAMING_SNAKE_CASE	)
											queue.put(__SCREAMING_SNAKE_CASE	)

											while not queue.empty():
																	lowercase_			:  List[Any]									= queue.get()

																	# loop through all adjacent vertex and enqueue it if not yet visited
																	for adjacent_vertex in self.vertices[vertex]:
																							if adjacent_vertex not in visited:
																													queue.put(__SCREAMING_SNAKE_CASE	)
																													visited.add(__SCREAMING_SNAKE_CASE	)
											return visited


if __name__ == "__main__":
							from doctest import testmod

							testmod(verbose=True)

							_lowercase				:						Optional[int]												= Graph()
							g.add_edge(0, 1)
							g.add_edge(0, 2)
							g.add_edge(1, 2)
							g.add_edge(2, 0)
							g.add_edge(2, 3)
							g.add_edge(3, 3)

							g.print_graph()
							# 0  :  1 -> 2
							# 1  :  2
							# 2  :  0 -> 3
							# 3  :  3

							assert sorted(g.bfs(2)) == [0, 1, 2, 3]



