


import numpy as np
from numpy import ndarray
from scipy.optimize import Bounds, LinearConstraint, minimize
def 	_UpperCamelCase					(    lowerCAmelCase_ )    ->float:
   return np.dot(lowerCAmelCase_	,    lowerCAmelCase_ )






class 	__lowercase					:





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






         """simple docstring"""







         UpperCAmelCase      					=  regularization
         UpperCAmelCase      					=  gamma
         if kernel == "linear":
            UpperCAmelCase      					=  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"""							)
            UpperCAmelCase      					=  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:
            UpperCAmelCase      					=  F"""Unknown kernel: {kernel}"""
            raise ValueError(__lowerCamelCase							)





      def 							_lowercase					(		self    :       int       ,							__lowerCamelCase    :       ndarray       ,							__lowerCamelCase    :       ndarray							)     -> float:






         """simple docstring"""







         return np.dot(__lowerCamelCase       ,							__lowerCamelCase							)





      def 							_lowercase					(		self    :       Optional[int]       ,							__lowerCamelCase    :       ndarray       ,							__lowerCamelCase    :       ndarray							)     -> float:






         """simple docstring"""







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





      def 							_lowercase					(		self    :       Optional[int]       ,							__lowerCamelCase    :       list[ndarray]       ,							__lowerCamelCase    :       ndarray							)     -> None:






         """simple docstring"""







         UpperCAmelCase      					=  observations
         UpperCAmelCase      					=  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

         ((UpperCAmelCase)					,	)      					=  np.shape(__lowerCamelCase							)

         def to_minimize(__lowerCamelCase    :       ndarray							) -> float:
            UpperCAmelCase      					=  0
            ((UpperCAmelCase)					,	)      					=  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							)

         UpperCAmelCase      					=  LinearConstraint(__lowerCamelCase       ,							0       ,							0							)
         UpperCAmelCase      					=  Bounds(0       ,							self.regularization							)

         UpperCAmelCase      					=  minimize(
             __lowerCamelCase       ,							np.ones(__lowerCamelCase							)       ,							bounds=__lowerCamelCase       ,							constraints=[ly_contraint]							).x
         UpperCAmelCase      					=  l_star

         # calculating mean offset of separation plane to points
         UpperCAmelCase      					=  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]							)
         UpperCAmelCase      					=  s / n





      def 							_lowercase					(		self    :       List[str]       ,							__lowerCamelCase    :       ndarray							)     -> int:






         """simple docstring"""







         UpperCAmelCase      					=  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()







__a	 =      256
# Modulus to hash a string
__a	 =      100_0003
def 	_UpperCamelCase					(    lowerCAmelCase_	,    lowerCAmelCase_ )    ->bool:
   UpperCAmelCase      					=  len(lowerCAmelCase_ )
   UpperCAmelCase      					=  len(lowerCAmelCase_ )
   if p_len > t_len:
      return False

   UpperCAmelCase      					=  0
   UpperCAmelCase      					=  0
   UpperCAmelCase      					=  1

   # Calculating the hash of pattern and substring of text
   for i in range(lowerCAmelCase_ ):
      UpperCAmelCase      					=  (ord(pattern[i] ) + p_hash * alphabet_size) % modulus
      UpperCAmelCase      					=  (ord(text[i] ) + text_hash * alphabet_size) % modulus
      if i == p_len - 1:
         continue
      UpperCAmelCase      					=  (modulus_power * alphabet_size) % modulus

   for i in range(0	,    t_len - p_len + 1 ):
      if text_hash == p_hash and text[i : i + p_len] == pattern:
         return True
      if i == t_len - p_len:
         continue
      # Calculate the https://en.wikipedia.org/wiki/Rolling_hash
      UpperCAmelCase      					=  (
          (text_hash - ord(text[i] ) * modulus_power) * alphabet_size
          + ord(text[i + p_len] )
      ) % modulus
   return False
def 	_UpperCamelCase					(    )    ->None:
   UpperCAmelCase      					=  """abc1abc12"""
   UpperCAmelCase      					=  """alskfjaldsabc1abc1abc12k23adsfabcabc"""
   UpperCAmelCase      					=  """alskfjaldsk23adsfabcabc"""
   assert rabin_karp(lowerCAmelCase_	,    lowerCAmelCase_ ) and not rabin_karp(lowerCAmelCase_	,    lowerCAmelCase_ )

   # Test 2)
   UpperCAmelCase      					=  """ABABX"""
   UpperCAmelCase      					=  """ABABZABABYABABX"""
   assert rabin_karp(lowerCAmelCase_	,    lowerCAmelCase_ )

   # Test 3)
   UpperCAmelCase      					=  """AAAB"""
   UpperCAmelCase      					=  """ABAAAAAB"""
   assert rabin_karp(lowerCAmelCase_	,    lowerCAmelCase_ )

   # Test 4)
   UpperCAmelCase      					=  """abcdabcy"""
   UpperCAmelCase      					=  """abcxabcdabxabcdabcdabcy"""
   assert rabin_karp(lowerCAmelCase_	,    lowerCAmelCase_ )

   # Test 5)
   UpperCAmelCase      					=  """Lü"""
   UpperCAmelCase      					=  """Lüsai"""
   assert rabin_karp(lowerCAmelCase_	,    lowerCAmelCase_ )
   UpperCAmelCase      					=  """Lue"""
   assert not rabin_karp(lowerCAmelCase_	,    lowerCAmelCase_ )
   print("""Success.""" )


if __name__ == "__main__":
 test_rabin_karp()



