






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





def  _a(  UpperCamelCase__				:						ndarray							):




      '''simple docstring'''






      return np.dot(UpperCamelCase__,	UpperCamelCase__							)






class      __SCREAMING_SNAKE_CASE      :




 def __init__(      self	:							Dict					,      *,
     __lowercase	:							float = np.inf					,      __lowercase	:							str = "linear"					,      __lowercase	:							float = 0.0					,      )	->						None:
       SCREAMING_SNAKE_CASE__     :				List[str]									=regularization
       SCREAMING_SNAKE_CASE__     :				Optional[Any]									=gamma
       if kernel == "linear":
             SCREAMING_SNAKE_CASE__     :				List[Any]									=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__     :				List[str]									=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__     :				List[str]									=F"Unknown kernel: {kernel}"
             raise ValueError(__lowercase      )




 def      __magic_name__	(      self	:							List[Any]					,      __lowercase	:							ndarray					,      __lowercase	:							ndarray      )	->						float:
       return np.dot(__lowercase					,      __lowercase      )




 def      __magic_name__	(      self	:							Tuple					,      __lowercase	:							ndarray					,      __lowercase	:							ndarray      )	->						float:
       return np.exp(-(self.gamma * norm_squared(vectora - vectora      ))      )




 def      __magic_name__	(      self	:							Optional[int]					,      __lowercase	:							list[ndarray]					,      __lowercase	:							ndarray      )	->						None:
       SCREAMING_SNAKE_CASE__     :				Tuple									=observations
       SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=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__)		,	)     :				Union[str, Any]									=np.shape(__lowercase      )

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

       SCREAMING_SNAKE_CASE__     :				Optional[int]									=LinearConstraint(__lowercase					,      0					,      0      )
       SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=Bounds(0					,      self.regularization      )

       SCREAMING_SNAKE_CASE__     :				Dict									=minimize(
           __lowercase					,      np.ones(__lowercase      )					,      bounds=__lowercase					,      constraints=[ly_contraint]      ).x
       SCREAMING_SNAKE_CASE__     :				List[Any]									=l_star

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




 def      __magic_name__	(      self	:							Union[str, Any]					,      __lowercase	:							ndarray      )	->						int:
       SCREAMING_SNAKE_CASE__     :				Any									=sum(
           self.optimum[n]
           * self.classes[n]
           * self.kernel(self.observations[n]					,      __lowercase      )
           for n in range(len(self.classes      )      )      )
       return 1 if s + self.offset >= 0 else -1


if __name__ == "__main__":
  import doctest

  doctest.testmod()







'''simple docstring'''
from __future__ import annotations

import sys
from collections import deque
from typing import Generic, TypeVar

a_					= TypeVar('T')






class      __SCREAMING_SNAKE_CASE      (			Generic[T]				):
 snake_case_  							=							42  # Cache store of keys
 snake_case_  							=							42  # References of the keys in cache
 snake_case_  							=							10  # Maximum capacity of cache




 def __init__(      self	:							Dict					,      __lowercase	:							int      )	->						None:
       SCREAMING_SNAKE_CASE__     :				Any									=deque()
       SCREAMING_SNAKE_CASE__     :				str									=set()
       if not n:
             SCREAMING_SNAKE_CASE__     :				Optional[Any]									=sys.maxsize
       elif n < 0:
             raise ValueError('''n should be an integer greater than 0.'''      )
       else:
             SCREAMING_SNAKE_CASE__     :				Optional[Any]									=n




 def      __magic_name__	(      self	:							List[str]					,      __lowercase	:							T      )	->						None:
       if x not in self.key_reference:
             if len(self.dq_store      ) == LRUCache._MAX_CAPACITY:
                   SCREAMING_SNAKE_CASE__     :				int									=self.dq_store.pop()
                   self.key_reference.remove(__lowercase      )
       else:
             self.dq_store.remove(__lowercase      )

       self.dq_store.appendleft(__lowercase      )
       self.key_reference.add(__lowercase      )




 def      __magic_name__	(      self	:							Union[str, Any]      )	->						None:
       for k in self.dq_store:
             print(__lowercase      )




 def __repr__(      self	:							List[Any]      )	->						str:
       return F"LRUCache({self._MAX_CAPACITY}) => {list(self.dq_store      )}"


if __name__ == "__main__":
  import doctest

  doctest.testmod()

  a_					= LRUCache(4)
  lru_cache.refer('A')
  lru_cache.refer(2)
  lru_cache.refer(3)
  lru_cache.refer('A')
  lru_cache.refer(4)
  lru_cache.refer(5)
  lru_cache.display()

  print(lru_cache)
  assert str(lru_cache) == "LRUCache(4) => [5, 4, 'A', 3]"