





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




def      a__			(       lowercase__	):






   '''simple docstring'''






   return np.dot(lowercase__	,     lowercase__	)

class   A							:



      def __init__(						self:    List[Any]		,	*,
          _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 						lowerCAmelCase__     (						self:    Dict		,	_lowerCAmelCase:    ndarray		,	_lowerCAmelCase:    ndarray							)    ->     float:
         '''simple docstring'''

         return np.dot(_lowerCAmelCase		,	_lowerCAmelCase							)



      def 						lowerCAmelCase__     (						self:    int		,	_lowerCAmelCase:    ndarray		,	_lowerCAmelCase:    ndarray							)    ->     float:
         '''simple docstring'''

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



      def 						lowerCAmelCase__     (						self:    Any		,	_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 						lowerCAmelCase__     (						self:    Optional[int]		,	_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()











"""simple docstring"""




import math






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       list       ,			_lowercase		:       int = 0       ,			_lowercase		:       int = 0   )					->list:






	'''simple docstring'''






	a :						Optional[Any]      =							end or len(_lowercase   )
	for i in range(_lowercase       ,			_lowercase   ):
		a :						List[str]      =							i
		a :						Any      =							array[i]
		while temp_index != start and temp_index_value < array[temp_index - 1]:
			a :						Optional[Any]      =							array[temp_index - 1]
			temp_index -= 1
		a :						Any      =							temp_index_value
	return array






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       list       ,			_lowercase		:       int       ,			_lowercase		:       int   )					->None:  # Max Heap






	'''simple docstring'''






	a :						Tuple      =							index
	a :						List[Any]      =							2 * index + 1  # Left Node
	a :						Dict      =							2 * index + 2  # Right Node

	if left_index < heap_size and array[largest] < array[left_index]:
		a :						Dict      =							left_index

	if right_index < heap_size and array[largest] < array[right_index]:
		a :						int      =							right_index

	if largest != index:
		a,			a :						List[Any]      =							array[largest], array[index]
		heapify(_lowercase       ,			_lowercase       ,			_lowercase   )






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       list   )					->list:






	'''simple docstring'''






	a :						int      =							len(_lowercase   )

	for i in range(n // 2       ,			-1       ,			-1   ):
		heapify(_lowercase       ,			_lowercase       ,			_lowercase   )

	for i in range(n - 1       ,			0       ,			-1   ):
		a,			a :						str      =							array[0], array[i]
		heapify(_lowercase       ,			0       ,			_lowercase   )

	return array






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       list       ,			_lowercase		:       int       ,			_lowercase		:       int       ,			_lowercase		:       int   )					->int:






	'''simple docstring'''






	if (array[first_index] > array[middle_index]) != (
	    array[first_index] > array[last_index]
	):
		return array[first_index]
	elif (array[middle_index] > array[first_index]) != (
	    array[middle_index] > array[last_index]
	):
		return array[middle_index]
	else:
		return array[last_index]






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       list       ,			_lowercase		:       int       ,			_lowercase		:       int       ,			_lowercase		:       int   )					->int:






	'''simple docstring'''






	a :						List[Any]      =							low
	a :						int      =							high
	while True:
		while array[i] < pivot:
			i += 1
		j -= 1
		while pivot < array[j]:
			j -= 1
		if i >= j:
			return i
		a,			a :						Union[str, Any]      =							array[j], array[i]
		i += 1






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       list   )					->list:






	'''simple docstring'''






	if len(_lowercase   ) == 0:
		return array
	a :						Tuple      =							2 * math.ceil(math.loga(len(_lowercase   )   )   )
	a :						List[str]      =							16
	return intro_sort(_lowercase       ,			0       ,			len(_lowercase   )       ,			_lowercase       ,			_lowercase   )






def  _SCREAMING_SNAKE_CASE						(      _lowercase		:       list       ,			_lowercase		:       int       ,			_lowercase		:       int       ,			_lowercase		:       int       ,			_lowercase		:       int   )					->list:






	'''simple docstring'''






	while end - start > size_threshold:
		if max_depth == 0:
			return heap_sort(_lowercase   )
		max_depth -= 1
		a :						List[str]      =							median_of_a(_lowercase       ,			_lowercase       ,			start + ((end - start) // 2) + 1       ,			end - 1   )
		a :						Tuple      =							partition(_lowercase       ,			_lowercase       ,			_lowercase       ,			_lowercase   )
		intro_sort(_lowercase       ,			_lowercase       ,			_lowercase       ,			_lowercase       ,			_lowercase   )
		a :						Union[str, Any]      =							p
	return insertion_sort(_lowercase       ,			_lowercase       ,			_lowercase   )


if __name__ == "__main__":
		import doctest

		doctest.testmod()

		a		:					Optional[int]	      =     input('''Enter numbers separated by a comma : ''').strip()
		a		:					List[str]	      =     [float(item) for item in user_input.split(''',''')]
		print(sort(unsorted))


