
import random




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			list						,  _lowerCamelCase :			Optional[Any])					->    int:






							'''simple docstring'''





							__UpperCamelCase   ,						__UpperCamelCase   ,						__UpperCamelCase	:   Optional[Any]			   =					[], [], []
							for element in data:
														if element < pivot:
																					less.append(_lowerCamelCase)
														elif element > pivot:
																					greater.append(_lowerCamelCase)
														else:
																					equal.append(_lowerCamelCase)
							return less, equal, greater




def 	_SCREAMING_SNAKE_CASE					(		_lowerCamelCase :			list						,  _lowerCamelCase :			int)					->    Any:






							'''simple docstring'''





							if index >= len(_lowerCamelCase) or index < 0:
														return None

							__UpperCamelCase	:   Union[str, Any]			   =					items[random.randint(0						,  len(_lowerCamelCase) - 1)]
							__UpperCamelCase	:   Union[str, Any]			   =					0
							__UpperCamelCase   ,						__UpperCamelCase   ,						__UpperCamelCase	:   Optional[int]			   =					_partition(_lowerCamelCase						,  _lowerCamelCase)
							__UpperCamelCase	:   Tuple			   =					len(_lowerCamelCase)
							__UpperCamelCase	:   Dict			   =					len(_lowerCamelCase)

							# index is the pivot
							if m <= index < m + count:
														return pivot
							# must be in smaller
							elif m > index:
														return quick_select(_lowerCamelCase						,  _lowerCamelCase)
							# must be in larger
							else:
														return quick_select(_lowerCamelCase						,  index - (m + count))





from collections.abc import Callable

import numpy as np

def 			_SCREAMING_SNAKE_CASE			(							lowercase	:       Callable	,							lowercase	:       float	,							lowercase	:       float	,							lowercase	:       float	,							lowercase	:       float     ):


      '''simple docstring'''



      lowerCamelCase_		     =    int(np.ceil((x_end - xa) / step_size     )     )
      lowerCamelCase_		     =    np.zeros((n + 1,)     )
      lowerCamelCase_		     =    ya
      lowerCamelCase_		     =    xa

      for k in range(lowercase     ):
            lowerCamelCase_		     =    y[k] + step_size * ode_func(lowercase	,							y[k]     )
            lowerCamelCase_		     =    y[k] + (
                (step_size / 2) * (ode_func(lowercase	,							y[k]     ) + ode_func(x + step_size	,							lowercase     ))
            )
            x += step_size

      return y


if __name__ == "__main__":
 import doctest

 doctest.testmod()



