






'''simple docstring'''







def 		_UpperCAmelCase   (							__A							:   int						,		__A							:   list      ):
				_enforce_args(__A						,		__A      )
				if n == 0:
								return 0
				a_		:  List[str]											=      float('''-inf'''      )
				for i in range(1						,		n + 1      ):
								a_		:  Dict											=      max(
								    __A						,		prices[i - 1] + naive_cut_rod_recursive(n - i						,		__A      )      )

				return max_revue





def 		_UpperCAmelCase   (							__A							:   int						,		__A							:   list      ):
				_enforce_args(__A						,		__A      )
				a_		:  List[str]											=      [float('''-inf'''      ) for _ in range(n + 1      )]
				return _top_down_cut_rod_recursive(__A						,		__A						,		__A      )





def 		_UpperCAmelCase   (							__A							:   int						,		__A							:   list						,		__A							:   list      ):
				if max_rev[n] >= 0:
								return max_rev[n]
				elif n == 0:
								return 0
				else:
								a_		:  int											=      float('''-inf'''      )
								for i in range(1						,		n + 1      ):
												a_		:  List[str]											=      max(
												    __A						,		prices[i - 1] + _top_down_cut_rod_recursive(n - i						,		__A						,		__A      )						,		)

								a_		:  Optional[int]											=      max_revenue

				return max_rev[n]





def 		_UpperCAmelCase   (							__A							:   int						,		__A							:   list      ):
				_enforce_args(__A						,		__A      )

				# length(max_rev) = n + 1, to accommodate for the revenue obtainable from a rod of
				# length 0.
				a_		:  Any											=      [float('''-inf'''      ) for _ in range(n + 1      )]
				a_		:  int											=      0

				for i in range(1						,		n + 1      ):
								a_		:  Union[str, Any]											=      max_rev[i]
								for j in range(1						,		i + 1      ):
												a_		:  List[Any]											=      max(__A						,		prices[j - 1] + max_rev[i - j]      )

								a_		:  int											=      max_revenue_i

				return max_rev[n]





def 		_UpperCAmelCase   (							__A							:   int						,		__A							:   list      ):
				if n < 0:
								a_		:  List[str]											=      f'n must be greater than or equal to 0. Got n = {n}'
								raise ValueError(__A      )

				if n > len(__A      ):
								a_		:  str											=      (
								    '''Each integral piece of rod must have a corresponding price. '''
								    f'Got n = {n} but length of prices = {len(__A      )}'
								)
								raise ValueError(__A      )





def 		_UpperCAmelCase   (							):
				a_		:  str											=      [6, 10, 12, 15, 20, 23]
				a_		:  Tuple											=      len(__A      )

				# the best revenue comes from cutting the rod into 6 pieces, each
				# of length 1 resulting in a revenue of 6 * 6 = 36.
				a_		:  Optional[int]											=      36

				a_		:  Optional[Any]											=      top_down_cut_rod(__A						,		__A      )
				a_		:  List[str]											=      bottom_up_cut_rod(__A						,		__A      )
				a_		:  List[Any]											=      naive_cut_rod_recursive(__A						,		__A      )

				assert expected_max_revenue == max_rev_top_down
				assert max_rev_top_down == max_rev_bottom_up
				assert max_rev_bottom_up == max_rev_naive


if __name__ == "__main__":
		main()












'''simple docstring'''







def 		_UpperCAmelCase   (							__A							:   str						,		__A							:   str      ):

				def get_matched_characters(__A							:   str						,		__A							:   str      ) -> str:
								a_		:  Union[str, Any]											=      []
								a_		:  int											=      min(len(_stra      )						,		len(_stra      )      ) // 2
								for i, l in enumerate(_stra      ):
												a_		:  Any											=      int(max(0						,		i - limit      )      )
												a_		:  Union[str, Any]											=      int(min(i + limit + 1						,		len(_stra      )      )      )
												if l in _stra[left:right]:
																matched.append(__A      )
																a_		:  Any											=      f'{_stra[0:_stra.index(__A      )]} {_stra[_stra.index(__A      ) + 1:]}'

								return "".join(__A      )

				# matching characters
				a_		:  Optional[Any]											=      get_matched_characters(__A						,		__A      )
				a_		:  int											=      get_matched_characters(__A						,		__A      )
				a_		:  Any											=      len(__A      )

				# transposition
				a_		:  List[Any]											=      (
				    len([(ca, ca) for ca, ca in zip(__A						,		__A      ) if ca != ca]      ) // 2
				)

				if not match_count:
								a_		:  Dict											=      0.0
				else:
								a_		:  Optional[int]											=      (
								    1
								    / 3
								    * (
								        match_count / len(__A      )
								        + match_count / len(__A      )
								        + (match_count - transpositions) / match_count
								    )
								)

				# common prefix up to 4 characters
				a_		:  List[str]											=      0
				for ca, ca in zip(stra[:4]						,		stra[:4]      ):
								if ca == ca:
												prefix_len += 1
								else:
												break

				return jaro + 0.1 * prefix_len * (1 - jaro)


if __name__ == "__main__":
		import doctest

		doctest.testmod()
		print(jaro_winkler('hello', 'world'))




