
def     __lowerCAmelCase			(			a__						,    a__  )       ->  float:

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

								return "".join(a__  )

				# matching characters
				__a										=    get_matched_characters(a__						,    a__  )
				__a										=    get_matched_characters(a__						,    a__  )
				__a										=    len(a__  )

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

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

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

from __future__ import annotations

import time
from collections.abc import Sequence
from random import randint

from matplotlib import pyplot as plt


def     __lowerCAmelCase			(			a__						,    a__						,    a__  )       ->  tuple[int | None, int | None, float]:
				if not arr:
								return None, None, 0
				if low == high:
								return low, high, arr[low]

				__a										=    (low + high) // 2
				__a							,     __a							,     __a										=    max_subarray(a__						,    a__						,    a__  )
				__a							,     __a							,     __a										=    max_subarray(a__						,    mid + 1						,    a__  )
				__a							,     __a							,     __a										=    max_cross_sum(a__						,    a__						,    a__						,    a__  )
				if left_sum >= right_sum and left_sum >= cross_sum:
								return left_low, left_high, left_sum
				elif right_sum >= left_sum and right_sum >= cross_sum:
								return right_low, right_high, right_sum
				return cross_left, cross_right, cross_sum


def     __lowerCAmelCase			(			a__						,    a__						,    a__						,    a__  )       ->  tuple[int, int, float]:
				__a							,     __a										=    float('''-inf'''  ), -1
				__a							,     __a										=    float('''-inf'''  ), -1

				__a										=    0
				for i in range(a__						,    low - 1						,    -1  ):
								summ += arr[i]
								if summ > left_sum:
												__a										=    summ
												__a										=    i

				__a										=    0
				for i in range(mid + 1						,    high + 1  ):
								summ += arr[i]
								if summ > right_sum:
												__a										=    summ
												__a										=    i

				return max_left, max_right, (left_sum + right_sum)


def     __lowerCAmelCase			(			a__  )       ->  float:
				__a										=    [randint(1						,    a__  ) for _ in range(a__  )]
				__a										=    time.time()
				max_subarray(a__						,    0						,    input_size - 1  )
				__a										=    time.time()
				return end - start


def     __lowerCAmelCase			(			)       ->  None:
				__a										=    [10, 100, 1000, 1_0000, 5_0000, 10_0000, 20_0000, 30_0000, 40_0000, 50_0000]
				__a										=    [time_max_subarray(a__  ) for input_size in input_sizes]
				print('''No of Inputs\t\tTime Taken'''  )
				for input_size, runtime in zip(a__						,    a__  ):
								print(a__						,    '''\t\t'''						,    a__  )
				plt.plot(a__						,    a__  )
				plt.xlabel('''Number of Inputs'''  )
				plt.ylabel('''Time taken in seconds'''  )
				plt.show()


if __name__ == "__main__":
					from doctest import testmod

					testmod()