




import numpy as np







def 		lowercase__ (		__A:						Tuple				,__A:						List[Any]				,__A:						int					):





					'''simple docstring'''






					__magic_name__				:						Tuple     				=				n_draws * class_counts / class_counts.sum()
					# floored means we don't overshoot n_samples, but probably undershoot
					__magic_name__				:						List[Any]     				=				np.floor(__A					)
					# we add samples according to how much "left over" probability
					# they had, until we arrive at n_samples
					__magic_name__				:						Optional[int]     				=				int(n_draws - floored.sum()					)
					if need_to_add > 0:
										__magic_name__				:						Optional[Any]     				=				continuous - floored
										__magic_name__				:						List[Any]     				=				np.sort(np.unique(__A					)					)[::-1]
										# add according to remainder, but break ties
										# randomly to avoid biases
										for value in values:
															((__magic_name__)				,     )				:						List[Any]     				=				np.where(remainder == value					)
															# if we need_to_add less than what's in inds
															# we draw randomly from them.
															# if we need to add more, we add them all and
															# go to the next value
															__magic_name__				:						Union[str, Any]     				=				min(len(__A					)				,__A					)
															__magic_name__				:						List[Any]     				=				rng.choice(__A				,size=__A				,replace=__A					)
															floored[inds] += 1
															need_to_add -= add_now
															if need_to_add == 0:
																				break
					return floored.astype(np.intaa					)







def 		lowercase__ (		__A:						List[str]				,__A:						Optional[Any]				,__A:						Union[str, Any]				,__A:						Optional[int]				,__A:						Optional[int]=1_0					):





					'''simple docstring'''






					__magic_name__				,     __magic_name__				:						Dict     				=				np.unique(__A				,return_inverse=__A					)
					__magic_name__				:						int     				=				classes.shape[0]
					__magic_name__				:						Optional[Any]     				=				np.bincount(__A					)
					if np.min(__A					) < 2:
										raise ValueError('''Minimum class count error'''					)
					if n_train < n_classes:
										raise ValueError(
										    '''The train_size = %d should be greater or ''' '''equal to the number of classes = %d''' % (n_train, n_classes)					)
					if n_test < n_classes:
										raise ValueError(
										    '''The test_size = %d should be greater or ''' '''equal to the number of classes = %d''' % (n_test, n_classes)					)
					__magic_name__				:						Any     				=				np.split(np.argsort(__A				,kind='''mergesort'''					)				,np.cumsum(__A					)[:-1]					)
					for _ in range(__A					):
										__magic_name__				:						List[Any]     				=				approximate_mode(__A				,__A				,__A					)
										__magic_name__				:						Optional[int]     				=				class_counts - n_i
										__magic_name__				:						Tuple     				=				approximate_mode(__A				,__A				,__A					)

										__magic_name__				:						Dict     				=				[]
										__magic_name__				:						str     				=				[]

										for i in range(__A					):
															__magic_name__				:						int     				=				rng.permutation(class_counts[i]					)
															__magic_name__				:						str     				=				class_indices[i].take(__A				,mode='''clip'''					)
															train.extend(perm_indices_class_i[: n_i[i]]					)
															test.extend(perm_indices_class_i[n_i[i] : n_i[i] + t_i[i]]					)
										__magic_name__				:						Any     				=				rng.permutation(__A					)
										__magic_name__				:						Dict     				=				rng.permutation(__A					)

										yield train, test









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]]))



