


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


def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







			return np.dot(_UpperCamelCase       ,			_UpperCamelCase  )
class 	lowerCamelCase_       :



					'''simple docstring'''







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







								'''simple docstring'''

								__lowercase 					=   regularization
								__lowercase 					=   gamma
								if kernel == "linear":
											__lowercase 					=   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'''						)
											__lowercase 					=   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:
											__lowercase 					=   F'Unknown kernel: {kernel}'
											raise ValueError(snake_case_						)






					def A      (				self ,       snake_case_ ,       snake_case_						)   ->			float:







								'''simple docstring'''

								return np.dot(snake_case_ ,       snake_case_						)






					def A      (				self ,       snake_case_ ,       snake_case_						)   ->			float:







								'''simple docstring'''

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






					def A      (				self ,       snake_case_ ,       snake_case_						)   ->			None:







								'''simple docstring'''

								__lowercase 					=   observations
								__lowercase 					=   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

								((__lowercase)					, ) 					=   np.shape(snake_case_						)

								def to_minimize(snake_case_						) -> float:
											__lowercase 					=   0
											((__lowercase)					, ) 					=   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_						)

								__lowercase 					=   LinearConstraint(snake_case_ ,       0 ,       0						)
								__lowercase 					=   Bounds(0 ,       self.regularization						)

								__lowercase 					=   minimize(
								    snake_case_ ,       np.ones(snake_case_						) ,       bounds=snake_case_ ,       constraints=[ly_contraint]						).x
								__lowercase 					=   l_star

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






					def A      (				self ,       snake_case_						)   ->			int:







								'''simple docstring'''

								__lowercase 					=   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()






def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







			__lowercase 					=   []
			__lowercase 					=   []
			__lowercase 					=   {
			    '''^''': 3,
			    '''*''': 2,
			    '''/''': 2,
			    '''%''': 2,
			    '''+''': 1,
			    '''-''': 1,
			}  # Priority of each operator
			__lowercase 					=   len(_UpperCamelCase  ) if (len(_UpperCamelCase  ) > 7) else 7

			# Print table header for output
			print(
			    '''Symbol'''.center(8  )       ,			'''Stack'''.center(_UpperCamelCase  )       ,			'''Postfix'''.center(_UpperCamelCase  )       ,			sep=''' | '''       ,			)
			print('''-''' * (print_width * 3 + 7)  )

			for x in infix:
						if x.isalpha() or x.isdigit():
									post_fix.append(_UpperCamelCase  )  # if x is Alphabet / Digit, add it to Postfix
						elif x == "(":
									stack.append(_UpperCamelCase  )  # if x is "(" push to Stack
						elif x == ")":  # if x is ")" pop stack until "(" is encountered
									while stack[-1] != "(":
												post_fix.append(stack.pop()  )  # Pop stack & add the content to Postfix
									stack.pop()
						else:
									if len(_UpperCamelCase  ) == 0:
												stack.append(_UpperCamelCase  )  # If stack is empty, push x to stack
									else:  # while priority of x is not > priority of element in the stack
												while len(_UpperCamelCase  ) > 0 and priority[x] <= priority[stack[-1]]:
															post_fix.append(stack.pop()  )  # pop stack & add to Postfix
												stack.append(_UpperCamelCase  )  # push x to stack

						print(
						    x.center(8  )       ,			(''''''.join(_UpperCamelCase  )).ljust(_UpperCamelCase  )       ,			(''''''.join(_UpperCamelCase  )).ljust(_UpperCamelCase  )       ,			sep=''' | '''       ,			)  # Output in tabular format

			while len(_UpperCamelCase  ) > 0:  # while stack is not empty
						post_fix.append(stack.pop()  )  # pop stack & add to Postfix
						print(
						    ''' '''.center(8  )       ,			(''''''.join(_UpperCamelCase  )).ljust(_UpperCamelCase  )       ,			(''''''.join(_UpperCamelCase  )).ljust(_UpperCamelCase  )       ,			sep=''' | '''       ,			)  # Output in tabular format

			return "".join(_UpperCamelCase  )  # return Postfix as str


def 		lowercase_  (     _UpperCamelCase  ):


			'''simple docstring'''







			__lowercase 					=   list(infix[::-1]  )  # reverse the infix equation

			for i in range(len(_UpperCamelCase  )  ):
						if infix[i] == "(":
									__lowercase 					=   ''')'''  # change "(" to ")"
						elif infix[i] == ")":
									__lowercase 					=   '''('''  # change ")" to "("

			return (infix_2_postfix(''''''.join(_UpperCamelCase  )  ))[
			    ::-1
			]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
	a : Union[str, Any]		=				input('''\nEnter an Infix Equation = ''')  # Input an Infix equation
	a : Optional[Any]		=				''''''.join(Infix.split())  # Remove spaces from the input
	print('''\n\t''', Infix, '''(Infix) -> ''', infix_2_prefix(Infix), '''(Prefix)''')


