



"""simple docstring"""







class       UpperCamelCase__			:

			"""simple docstring"""


			def __init__(      self		)      ->	Union[str, Any]:
				A__											=					0
				A__											=					0
				A__											=					{}


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Dict:

				if vertex not in self.adjacency:
					A__											=					{}
					self.num_vertices += 1


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)      ->	Dict:
				self.add_vertex(snake_case__		)
				self.add_vertex(snake_case__		)

				if head == tail:
					return

				A__											=					weight
				A__											=					weight


			def   snake_case__	(      self		)      ->	str:
				A__											=					self.get_edges()
				for edge in edges:
					A__							,							A__							,							A__											=					edge
					edges.remove((tail, head, weight)		)
				for i in range(len(snake_case__		)		):
					A__											=					list(edges[i]		)

				edges.sort(key=lambda SCREAMING_SNAKE_CASE__		: e[2]		)
				for i in range(len(snake_case__		) - 1		):
					if edges[i][2] >= edges[i + 1][2]:
						A__											=					edges[i][2] + 1
				for edge in edges:
					A__							,							A__							,							A__											=					edge
					A__											=					weight
					A__											=					weight


			def __str__(      self		)      ->	Any:
				A__											=					""
				for tail in self.adjacency:
					for head in self.adjacency[tail]:
						A__											=					self.adjacency[head][tail]
						string += f"""{head} -> {tail} == {weight}\n"""
				return string.rstrip("\n"		)


			def   snake_case__	(      self		)      ->	List[str]:
				A__											=					[]
				for tail in self.adjacency:
					for head in self.adjacency[tail]:
						output.append((tail, head, self.adjacency[head][tail])		)
				return output


			def   snake_case__	(      self		)      ->	Any:
				return self.adjacency.keys()


			@staticmethod
			def   snake_case__	(      SCREAMING_SNAKE_CASE__=None						,	SCREAMING_SNAKE_CASE__=None		)      ->	List[Any]:
				A__											=					Graph()
				if vertices is None:
					A__											=					[]
				if edges is None:
					A__											=					[]
				for vertex in vertices:
					g.add_vertex(snake_case__		)
				for edge in edges:
					g.add_edge(*snake_case__		)
				return g






			class       UpperCamelCase__			:

						"""simple docstring"""


						def __init__(      self		)      ->	int:
							A__											=					{}
							A__											=					{}


						def __len__(      self		)      ->	str:
							return len(self.parent		)


						def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Dict:

							if item in self.parent:
								return self.find(snake_case__		)

							A__											=					item
							A__											=					0
							return item


						def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	List[Any]:

							if item not in self.parent:
								return self.make_set(snake_case__		)
							if item != self.parent[item]:
								A__											=					self.find(self.parent[item]		)
							return self.parent[item]







						def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)      ->	Any:
							A__											=					self.find(snake_case__		)
							A__											=					self.find(snake_case__		)

							if roota == roota:
								return roota

							if self.rank[roota] > self.rank[roota]:
								A__											=					roota
								return roota

							if self.rank[roota] < self.rank[roota]:
								A__											=					roota
								return roota

							if self.rank[roota] == self.rank[roota]:
								self.rank[roota] += 1
								A__											=					roota
								return roota
							return None



			@staticmethod
			def   snake_case__	(      SCREAMING_SNAKE_CASE__		)      ->	List[Any]:
				A__											=					graph.num_vertices

				A__											=					Graph.UnionFind()
				A__											=					[]
				while num_components > 1:
					A__											=					{}
					for vertex in graph.get_vertices():
						A__											=					-1

					A__											=					graph.get_edges()
					for edge in edges:
						A__							,							A__							,							A__											=					edge
						edges.remove((tail, head, weight)		)
					for edge in edges:
						A__							,							A__							,							A__											=					edge
						A__											=					union_find.find(snake_case__		)
						A__											=					union_find.find(snake_case__		)
						if seta != seta:
							if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
								A__											=					[head, tail, weight]

							if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
								A__											=					[head, tail, weight]
					for vertex in cheap_edge:
						if cheap_edge[vertex] != -1:
							A__							,							A__							,							A__											=					cheap_edge[vertex]
							if union_find.find(snake_case__		) != union_find.find(snake_case__		):
								union_find.union(snake_case__						,	snake_case__		)
								mst_edges.append(cheap_edge[vertex]		)
								A__											=					num_components - 1
				A__											=					Graph.build(edges=snake_case__		)
				return mst










import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize


def 					_a							(					lowerCAmelCase )->	float:
		return np.dot(lowerCAmelCase    ,						lowerCAmelCase )



class    lowercase_		:



						def __init__(			self	:   int					,							*,
						    snake_case__	:   float = np.inf					,							snake_case__	:   str = "linear"					,							snake_case__	:   float = 0.0					,							):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							regularization
								SCREAMING_SNAKE_CASE_					      =							gamma
								if kernel == "linear":
										SCREAMING_SNAKE_CASE_					      =							self.__linear
								elif kernel == "rbf":
										if self.gamma == 0:
												raise ValueError('rbf kernel requires gamma'  )
										if not isinstance(self.gamma					,							(float, int)  ):
												raise ValueError('gamma must be float or int'  )
										if not self.gamma > 0:
												raise ValueError('gamma must be > 0'  )
										SCREAMING_SNAKE_CASE_					      =							self.__rbf
										# in the future, there could be a default value like in sklearn
										# sklear: def_gamma = 1/(n_features * X.var()) (wiki)
										# previously it was 1/(n_features)
								else:
										SCREAMING_SNAKE_CASE_					      =							f'''Unknown kernel: {kernel}'''
										raise ValueError(snake_case__  )



						def 	__a					(			self	:   Tuple					,							snake_case__	:   ndarray					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								return np.dot(snake_case__					,							snake_case__  )



						def 	__a					(			self	:   int					,							snake_case__	:   ndarray					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								return np.exp(-(self.gamma * norm_squared(vectora - vectora  ))  )



						def 	__a					(			self	:   int					,							snake_case__	:   list[ndarray]					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							observations
								SCREAMING_SNAKE_CASE_					      =							classes

								# using Wolfe's Dual to calculate w.
								# Primal problem: minimize 1/2*norm_squared(w)
								#   constraint: yn(w . xn + b) >= 1
								#
								# With l a vector
								# Dual problem: maximize sum_n(ln) -
								#       1/2 * sum_n(sum_m(ln*lm*yn*ym*xn . xm))
								#   constraint: self.C >= ln >= 0
								#           and sum_n(ln*yn) = 0
								# Then we get w using w = sum_n(ln*yn*xn)
								# At the end we can get b ~= mean(yn - w . xn)
								#
								# Since we use kernels, we only need l_star to calculate b
								# and to classify observations

								((SCREAMING_SNAKE_CASE_)      ,				)					      =							np.shape(snake_case__  )

								def to_minimize(snake_case__	:   ndarray  ) -> float:
										SCREAMING_SNAKE_CASE_					      =							0
										((SCREAMING_SNAKE_CASE_)      ,				)					      =							np.shape(snake_case__  )
										for i in range(snake_case__  ):
												for j in range(snake_case__  ):
														s += (
														    candidate[i]
														    * candidate[j]
														    * classes[i]
														    * classes[j]
														    * self.kernel(observations[i]					,							observations[j]  )
														)
										return 1 / 2 * s - sum(snake_case__  )

								SCREAMING_SNAKE_CASE_					      =							LinearConstraint(snake_case__					,							0					,							0  )
								SCREAMING_SNAKE_CASE_					      =							Bounds(0					,							self.regularization  )

								SCREAMING_SNAKE_CASE_					      =							minimize(
								    snake_case__					,							np.ones(snake_case__  )					,							bounds=snake_case__					,							constraints=[ly_contraint]  ).x
								SCREAMING_SNAKE_CASE_					      =							l_star

								# calculating mean offset of separation plane to points
								SCREAMING_SNAKE_CASE_					      =							0
								for i in range(snake_case__  ):
										for j in range(snake_case__  ):
												s += classes[i] - classes[i] * self.optimum[i] * self.kernel(
												    observations[i]					,							observations[j]  )
								SCREAMING_SNAKE_CASE_					      =							s / n






						def 	__a					(			self	:   Any					,							snake_case__	:   ndarray  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							sum(
								    self.optimum[n]
								    * self.classes[n]
								    * self.kernel(self.observations[n]					,							snake_case__  )
								    for n in range(len(self.classes  )  )  )
								return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
						import doctest

						doctest.testmod()