




'''simple docstring'''

def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase      )						->   float:

					'''simple docstring'''

					def get_matched_characters(__UpperCAmelCase, __UpperCAmelCase      ) -> str:
										snake_case_		     =							[]
										snake_case_		     =							min(len(_stra      ), len(_stra      )      ) // 2
										for i, l in enumerate(_stra      ):
															snake_case_		     =							int(max(0, i - limit      )      )
															snake_case_		     =							int(min(i + limit + 1, len(_stra      )      )      )
															if l in _stra[left:right]:
																				matched.append(__UpperCAmelCase      )
																				snake_case_		     =							F"{_stra[0:_stra.index(__UpperCAmelCase      )]} {_stra[_stra.index(__UpperCAmelCase      ) + 1:]}"

										return "".join(__UpperCAmelCase      )

					# matching characters
					snake_case_		     =							get_matched_characters(__UpperCAmelCase, __UpperCAmelCase      )
					snake_case_		     =							get_matched_characters(__UpperCAmelCase, __UpperCAmelCase      )
					snake_case_		     =							len(__UpperCAmelCase      )

					# transposition
					snake_case_		     =							(
					    len([(ca, ca) for ca, ca in zip(__UpperCAmelCase, __UpperCAmelCase      ) if ca != ca]      ) // 2
					)

					if not match_count:
										snake_case_		     =							0.0
					else:
										snake_case_		     =							(
										    1
										    / 3
										    * (
										        match_count / len(__UpperCAmelCase      )
										        + match_count / len(__UpperCAmelCase      )
										        + (match_count - transpositions) / match_count
										    )
										)

					# common prefix up to 4 characters
					snake_case_		     =							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'))







'''simple docstring'''

from numpy import exp, pi, sqrt


def 						__magic_name__       (      __UpperCAmelCase, __UpperCAmelCase = 0.0, __UpperCAmelCase = 1.0      )						->   int:

					'''simple docstring'''

					return 1 / sqrt(2 * pi * sigma**2      ) * exp(-((x - mu) ** 2) / (2 * sigma**2)      )


if __name__ == "__main__":
							import doctest

							doctest.testmod()

