





"""simple docstring"""




def  a_       (							_lowercase ,		_lowercase ,		_lowercase     ):
						if right <= left:
												return
						_UpperCamelCase    :      int						     =					left
						_UpperCamelCase    :      Any						     =					right
						_UpperCamelCase    :      int						     =					sorting[left]
						while i <= b:
												if sorting[i] < pivot:
																		_UpperCamelCase     ,							_UpperCamelCase    :      str						     =					sorting[i], sorting[a]
																		a += 1
																		i += 1
												elif sorting[i] > pivot:
																		_UpperCamelCase     ,							_UpperCamelCase    :      List[Any]						     =					sorting[i], sorting[b]
																		b -= 1
												else:
																		i += 1
						quick_sort_apartition(_lowercase ,		_lowercase ,		a - 1     )
						quick_sort_apartition(_lowercase ,		b + 1 ,		_lowercase     )





def  a_       (							_lowercase ,		_lowercase ,		_lowercase     ):
						if left < right:
												_UpperCamelCase    :      int						     =					lomuto_partition(_lowercase ,		_lowercase ,		_lowercase     )
												quick_sort_lomuto_partition(_lowercase ,		_lowercase ,		pivot_index - 1     )
												quick_sort_lomuto_partition(_lowercase ,		pivot_index + 1 ,		_lowercase     )





def  a_       (							_lowercase ,		_lowercase ,		_lowercase     ):
						_UpperCamelCase    :      Tuple						     =					sorting[right]
						_UpperCamelCase    :      Optional[int]						     =					left
						for i in range(_lowercase ,		_lowercase     ):
												if sorting[i] < pivot:
																		_UpperCamelCase     ,							_UpperCamelCase    :      Tuple						     =					sorting[i], sorting[store_index]
																		store_index += 1
						_UpperCamelCase     ,							_UpperCamelCase    :      int						     =					sorting[store_index], sorting[right]
						return store_index





def  a_       (							_lowercase     ):
						if len(_lowercase     ) <= 1:
												return sorting
						return (
						    three_way_radix_quicksort([i for i in sorting if i < sorting[0]]     )
						    + [i for i in sorting if i == sorting[0]]
						    + three_way_radix_quicksort([i for i in sorting if i > sorting[0]]     )
						)


if __name__ == "__main__":
						import doctest

						doctest.testmod(verbose=True)

						UpperCamelCase_     =input("""Enter numbers separated by a comma:\n""").strip()
						UpperCamelCase_     =[int(item) for item in user_input.split(""",""")]
						quick_sort_apartition(unsorted, 0, len(unsorted) - 1)
						print(unsorted)










"""simple docstring"""




UpperCamelCase_     =1_000





def  a_       (							_lowercase     ):
						return x * x





def  a_       (							_lowercase ,		_lowercase ,		_lowercase ,		_lowercase = 4     ):
						assert callable(
						    _lowercase     ), F"""the function(object) passed should be callable your input : {function}"""
						assert isinstance(_lowercase ,		(float, int)     ), F"""a should be float or integer your input : {a}"""
						assert isinstance(function(_lowercase     ) ,		(float, int)     ), (
						    "the function should return integer or float return type of your function, "
						    F"""{type(_lowercase     )}"""
						)
						assert isinstance(_lowercase ,		(float, int)     ), F"""b should be float or integer your input : {b}"""
						assert (
						    isinstance(_lowercase ,		_lowercase     ) and precision > 0
						), F"""precision should be positive integer your input : {precision}"""

						# just applying the formula of simpson for approximate integration written in
						# mentioned article in first comment of this file and above this function

						_UpperCamelCase    :      str						     =					(b - a) / N_STEPS
						_UpperCamelCase    :      Dict						     =					function(_lowercase     ) + function(_lowercase     )

						for i in range(1 ,		_lowercase     ):
												_UpperCamelCase    :      List[Any]						     =					a + h * i
												result += function(_lowercase     ) * (4 if i % 2 else 2)

						result *= h / 3
						return round(_lowercase ,		_lowercase     )


if __name__ == "__main__":
						import doctest

						doctest.testmod()



