






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				lowercase__     				=    0
				lowercase__     				=    len(lowerCamelCase_       )

				for i in range(n - 1       ):
								for j in range(i + 1	,     lowerCamelCase_       ):
												if arr[i] > arr[j]:
																num_inversions += 1

				return num_inversions






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				if len(lowerCamelCase_       ) <= 1:
								return arr, 0
				lowercase__     				=    len(lowerCamelCase_       ) // 2
				lowercase__     				=    arr[0:mid]
				lowercase__     				=    arr[mid:]

				lowercase__				,		lowercase__     				=    count_inversions_recursive(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    count_inversions_recursive(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    _count_cross_inversions(lowerCamelCase_	,     lowerCamelCase_       )

				lowercase__     				=    inversion_p + inversions_q + cross_inversions
				return c, num_inversions






def 						a    (		lowerCamelCase_	,     lowerCamelCase_       ):






				'''simple docstring'''
				lowercase__     				=    []
				lowercase__     				=    lowercase__     				=    lowercase__     				=    0
				while i < len(lowerCamelCase_       ) and j < len(lowerCamelCase_       ):
								if p[i] > q[j]:
												# if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
												# These are all inversions. The claim emerges from the
												# property that P is sorted.
												num_inversion += len(lowerCamelCase_       ) - i
												r.append(q[j]       )
												j += 1
								else:
												r.append(p[i]       )
												i += 1

				if i < len(lowerCamelCase_       ):
								r.extend(p[i:]       )
				else:
								r.extend(q[j:]       )

				return r, num_inversion






def 						a    (		):






				'''simple docstring'''
				lowercase__     				=    [10, 2, 1, 5, 5, 2, 11]

				# this arr has 8 inversions:
				# (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

				lowercase__     				=    count_inversions_bf(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    count_inversions_recursive(lowerCamelCase_       )

				assert num_inversions_bf == num_inversions_recursive == 8

				print('''number of inversions = '''	,     lowerCamelCase_       )

				# testing an array with zero inversion (a sorted arr_1)

				arr_a.sort()
				lowercase__     				=    count_inversions_bf(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    count_inversions_recursive(lowerCamelCase_       )

				assert num_inversions_bf == num_inversions_recursive == 0
				print('''number of inversions = '''	,     lowerCamelCase_       )

				# an empty list should also have zero inversions
				lowercase__     				=    []
				lowercase__     				=    count_inversions_bf(lowerCamelCase_       )
				lowercase__				,		lowercase__     				=    count_inversions_recursive(lowerCamelCase_       )

				assert num_inversions_bf == num_inversions_recursive == 0
				print('''number of inversions = '''	,     lowerCamelCase_       )


if __name__ == "__main__":
	main()












from __future__ import annotations






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				lowercase__     				=    0.00
				lowercase__     				=    0
				for resistor in resistors:
								if resistor <= 0:
												lowercase__     				=    F"""Resistor at index {index} has a negative or zero value!"""
												raise ValueError(lowerCamelCase_       )
								first_sum += 1 / float(lowerCamelCase_       )
								index += 1
				return 1 / first_sum






def 						a    (		lowerCamelCase_       ):






				'''simple docstring'''
				lowercase__     				=    0.00
				lowercase__     				=    0
				for resistor in resistors:
								sum_r += resistor
								if resistor < 0:
												lowercase__     				=    F"""Resistor at index {index} has a negative value!"""
												raise ValueError(lowerCamelCase_       )
								index += 1
				return sum_r


if __name__ == "__main__":
							import doctest

							doctest.testmod()




