



from __future__ import annotations

from collections.abc import Iterator



class 	lowerCamelCase__      :




		'''simple docstring'''



		def __init__(self		,__lowerCamelCase			)					->      None:

						"""simple docstring"""






						lowerCAmelCase__					:    Optional[Any]												=					value
						lowerCAmelCase__					:    Node | None												=					None
						lowerCAmelCase__					:    Node | None												=					None



class 	lowerCamelCase__      :




		'''simple docstring'''



		def __init__(self		,__lowerCamelCase			)					->      None:

						"""simple docstring"""






						lowerCAmelCase__					:    int												=					tree



		def 		lowerCAmelCase__				(self		,__lowerCamelCase			)					->      int:

						"""simple docstring"""






						if node is None:
										return 0
						return node.value + (
						    self.depth_first_search(node.left			) + self.depth_first_search(node.right			)
						)



		def __iter__(self			)					->      Iterator[int]:

						"""simple docstring"""






						yield self.depth_first_search(self.tree			)


if __name__ == "__main__":
							import doctest

							doctest.testmod()










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






def      lowerCAmelCase__		(   lowerCamelCase_		:		ndarray):





				'''simple docstring'''

				return np.dot(lowerCamelCase_	,lowerCamelCase_)



class 	lowerCamelCase__      :




		'''simple docstring'''



		def __init__(self		,*,
		    __lowerCamelCase = np.inf		,__lowerCamelCase = "linear"		,__lowerCamelCase = 0.0		,)					->      None:

						"""simple docstring"""






						lowerCAmelCase__					:    Any												=					regularization
						lowerCAmelCase__					:    str												=					gamma
						if kernel == "linear":
										lowerCAmelCase__					:    Dict												=					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'''			)
										lowerCAmelCase__					:    Optional[Any]												=					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:
										lowerCAmelCase__					:    List[str]												=					f"""Unknown kernel: {kernel}"""
										raise ValueError(__lowerCamelCase			)



		def 		lowerCAmelCase__				(self		,__lowerCamelCase		,__lowerCamelCase			)					->      float:

						"""simple docstring"""






						return np.dot(__lowerCamelCase		,__lowerCamelCase			)



		def 		lowerCAmelCase__				(self		,__lowerCamelCase		,__lowerCamelCase			)					->      float:

						"""simple docstring"""






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



		def 		lowerCAmelCase__				(self		,__lowerCamelCase		,__lowerCamelCase			)					->      None:

						"""simple docstring"""






						lowerCAmelCase__					:    str												=					observations
						lowerCAmelCase__					:    Optional[int]												=					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

						((lowerCAmelCase__)						,		)					:    List[str]												=					np.shape(__lowerCamelCase			)

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

						lowerCAmelCase__					:    List[str]												=					LinearConstraint(__lowerCamelCase		,0		,0			)
						lowerCAmelCase__					:    List[str]												=					Bounds(0		,self.regularization			)

						lowerCAmelCase__					:    int												=					minimize(
						    __lowerCamelCase		,np.ones(__lowerCamelCase			)		,bounds=__lowerCamelCase		,constraints=[ly_contraint]			).x
						lowerCAmelCase__					:    List[Any]												=					l_star

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



		def 		lowerCAmelCase__				(self		,__lowerCamelCase			)					->      int:

						"""simple docstring"""






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


if __name__ == "__main__":
							import doctest

							doctest.testmod()

