





'''simple docstring'''



def    _lowerCAmelCase						(				lowerCamelCase_			:  str		,       lowerCamelCase_			:  str				):

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

						return "".join(lowerCamelCase_				)

			# matching characters
			__lowercase										=							get_matched_characters(lowerCamelCase_		,       lowerCamelCase_				)
			__lowercase										=							get_matched_characters(lowerCamelCase_		,       lowerCamelCase_				)
			__lowercase										=							len(lowerCamelCase_				)

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

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

			# common prefix up to 4 characters
			__lowercase										=							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 __future__ import annotations

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

from matplotlib import pyplot as plt




def    _lowerCAmelCase						(				lowerCamelCase_			:  Sequence[float]		,       lowerCamelCase_			:  int		,       lowerCamelCase_			:  int				):
			if not arr:
						return None, None, 0
			if low == high:
						return low, high, arr[low]

			__lowercase										=							(low + high) // 2
			__lowercase						,		__lowercase						,		__lowercase										=							max_subarray(lowerCamelCase_		,       lowerCamelCase_		,       lowerCamelCase_				)
			__lowercase						,		__lowercase						,		__lowercase										=							max_subarray(lowerCamelCase_		,       mid + 1		,       lowerCamelCase_				)
			__lowercase						,		__lowercase						,		__lowercase										=							max_cross_sum(lowerCamelCase_		,       lowerCamelCase_		,       lowerCamelCase_		,       lowerCamelCase_				)
			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						(				lowerCamelCase_			:  Sequence[float]		,       lowerCamelCase_			:  int		,       lowerCamelCase_			:  int		,       lowerCamelCase_			:  int				):
			__lowercase						,		__lowercase										=							float('''-inf'''				), -1
			__lowercase						,		__lowercase										=							float('''-inf'''				), -1

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

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

			return max_left, max_right, (left_sum + right_sum)




def    _lowerCAmelCase						(				lowerCamelCase_			:  int				):
			__lowercase										=							[randint(1		,       lowerCamelCase_				) for _ in range(lowerCamelCase_				)]
			__lowercase										=							time.time()
			max_subarray(lowerCamelCase_		,       0		,       input_size - 1				)
			__lowercase										=							time.time()
			return end - start




def    _lowerCAmelCase						(				):
			__lowercase										=							[1_0, 1_0_0, 1_0_0_0, 1_0_0_0_0, 5_0_0_0_0, 1_0_0_0_0_0, 2_0_0_0_0_0, 3_0_0_0_0_0, 4_0_0_0_0_0, 5_0_0_0_0_0]
			__lowercase										=							[time_max_subarray(lowerCamelCase_				) for input_size in input_sizes]
			print('''No of Inputs\t\tTime Taken'''				)
			for input_size, runtime in zip(lowerCamelCase_		,       lowerCamelCase_				):
						print(lowerCamelCase_		,       '''\t\t'''		,       lowerCamelCase_				)
			plt.plot(lowerCamelCase_		,       lowerCamelCase_				)
			plt.xlabel('''Number of Inputs'''				)
			plt.ylabel('''Time taken in seconds'''				)
			plt.show()


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

	testmod()





