




"""simple docstring"""




import matplotlib.pyplot as plt
import numpy as np







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

			return weights







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					):
			__lowercase	:       Tuple				=   weight_matrix(__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					)
			__lowercase	:       Any				=   np.linalg.inv(x_train.T @ weight_mat @ x_train					) @ (
			    x_train.T @ weight_mat @ y_train.T
			)

			return weight







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					):
			__lowercase	:       Tuple				=   np.zeros(len(__UpperCamelCase					)					)  # Initialize array of predictions
			for i, item in enumerate(__UpperCamelCase					):
						__lowercase	:       Optional[Any]				=   item @ local_weight(__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					)

			return y_pred







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					):
			import seaborn as sns

			__lowercase	:       Tuple				=   sns.load_dataset(__UpperCamelCase					)
			__lowercase	:       Tuple				=   np.array(data[x_name]					)
			__lowercase	:       List[Any]				=   np.array(data[y_name]					)

			__lowercase	:       List[Any]				=   np.ones(len(__UpperCamelCase					)					)

			# pairing elements of one and x_data
			__lowercase	:       Dict				=   np.column_stack((one, x_data)					)

			return x_train, x_data, y_data







def       __UpperCAmelCase      (				__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							__UpperCamelCase					,							):
			__lowercase	:       int				=   np.sort(__UpperCamelCase					,							axis=0					)
			plt.scatter(__UpperCamelCase					,							__UpperCamelCase					,							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(__UpperCamelCase					)
			plt.ylabel(__UpperCamelCase					)
			plt.show()


if __name__ == "__main__":
			import doctest

			doctest.testmod()

			# Demo with a dataset from the seaborn module
			a_       ,	a_       ,	a_            =   load_data('tips', 'total_bill', 'tip')
			a_            =   local_weight_regression(training_data_x, tip, 5)
			plot_preds(training_data_x, predictions, total_bill, tip, 'total_bill', 'tip')









"""simple docstring"""




# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue







def       __UpperCAmelCase      (				__UpperCamelCase					):
			__lowercase	:       int				=   Queue()
			__lowercase	:       str				=   [False] * len(__UpperCamelCase					)
			__lowercase	:       str				=   [-1] * len(__UpperCamelCase					)

			def bfs():
						while not queue.empty():
									__lowercase	:       int				=   queue.get()
									__lowercase	:       List[str]				=   True

									for neighbour in graph[u]:
												if neighbour == u:
															return False

												if color[neighbour] == -1:
															__lowercase	:       str				=   1 - color[u]
															queue.put(__UpperCamelCase					)

												elif color[neighbour] == color[u]:
															return False

						return True

			for i in range(len(__UpperCamelCase					)					):
						if not visited[i]:
									queue.put(__UpperCamelCase					)
									__lowercase	:       int				=   0
									if bfs() is False:
												return False

			return True


if __name__ == "__main__":
			# Adjacency List of graph
			print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))



