




class    lowercase_		:



						def __init__(			self	:   Dict  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							0
								SCREAMING_SNAKE_CASE_					      =							0
								SCREAMING_SNAKE_CASE_					      =							{}



						def 	__a					(			self	:   int					,							snake_case__	:   List[Any]  ):

								"""simple docstring"""

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



						def 	__a					(			self	:   Optional[int]					,							snake_case__	:   str					,							snake_case__	:   Tuple					,							snake_case__	:   Union[str, Any]  ):

								"""simple docstring"""

								self.add_vertex(snake_case__  )
								self.add_vertex(snake_case__  )

								if head == tail:
										return

								SCREAMING_SNAKE_CASE_					      =							weight
								SCREAMING_SNAKE_CASE_					      =							weight



						def 	__a					(			self	:   Optional[Any]  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							self.get_edges()
								for edge in edges:
										SCREAMING_SNAKE_CASE_      ,				SCREAMING_SNAKE_CASE_      ,				SCREAMING_SNAKE_CASE_					      =							edge
										edges.remove((tail, head, weight)  )
								for i in range(len(snake_case__  )  ):
										SCREAMING_SNAKE_CASE_					      =							list(edges[i]  )

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



						def __str__(			self	:   Union[str, Any]  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							''
								for tail in self.adjacency:
										for head in self.adjacency[tail]:
												SCREAMING_SNAKE_CASE_					      =							self.adjacency[head][tail]
												string += f'''{head} -> {tail} == {weight}\n'''
								return string.rstrip('\n'  )



						def 	__a					(			self	:   List[str]  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							[]
								for tail in self.adjacency:
										for head in self.adjacency[tail]:
												output.append((tail, head, self.adjacency[head][tail])  )
								return output



						def 	__a					(			self	:   Dict  ):

								"""simple docstring"""

								return self.adjacency.keys()



						@staticmethod
						def 	__a					(			snake_case__	:   Union[str, Any]=None					,							snake_case__	:   Dict=None  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							Graph()
								if vertices is None:
										SCREAMING_SNAKE_CASE_					      =							[]
								if edges is None:
										SCREAMING_SNAKE_CASE_					      =							[]
								for vertex in vertices:
										g.add_vertex(snake_case__  )
								for edge in edges:
										g.add_edge(*snake_case__  )
								return g



						class    lowercase_		:



												def __init__(			self	:   Dict  ):

														"""simple docstring"""

														SCREAMING_SNAKE_CASE_					      =							{}
														SCREAMING_SNAKE_CASE_					      =							{}



												def __len__(			self	:   List[str]  ):

														"""simple docstring"""

														return len(self.parent  )



												def 	__a					(			self	:   List[Any]					,							snake_case__	:   Optional[int]  ):

														"""simple docstring"""

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

														SCREAMING_SNAKE_CASE_					      =							item
														SCREAMING_SNAKE_CASE_					      =							0
														return item



												def 	__a					(			self	:   Dict					,							snake_case__	:   Optional[int]  ):

														"""simple docstring"""

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






												def 	__a					(			self	:   Tuple					,							snake_case__	:   int					,							snake_case__	:   List[Any]  ):

														"""simple docstring"""

														SCREAMING_SNAKE_CASE_					      =							self.find(snake_case__  )
														SCREAMING_SNAKE_CASE_					      =							self.find(snake_case__  )

														if roota == roota:
																return roota

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

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

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



						@staticmethod
						def 	__a					(			snake_case__	:   Union[str, Any]  ):

								"""simple docstring"""

								SCREAMING_SNAKE_CASE_					      =							graph.num_vertices

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

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

														if cheap_edge[seta] == -1 or cheap_edge[seta][2] > weight:
																SCREAMING_SNAKE_CASE_					      =							[head, tail, weight]
										for vertex in cheap_edge:
												if cheap_edge[vertex] != -1:
														SCREAMING_SNAKE_CASE_      ,				SCREAMING_SNAKE_CASE_      ,				SCREAMING_SNAKE_CASE_					      =							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]  )
																SCREAMING_SNAKE_CASE_					      =							num_components - 1
								SCREAMING_SNAKE_CASE_					      =							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()