



from __future__ import annotations

def      A_ (		__a       :			list	,						__a       :			list						):

				"""simple docstring"""
				a__			 =						[None] * (len(__a						) + len(__a						))

				a__			 =						0  # pointer to current index for left Half
				a__			 =						0  # pointer to current index for the right Half
				a__			 =						0  # pointer to current index for the sorted array Half

				while pointera < len(__a						) and pointera < len(__a						):
								if left_half[pointera] < right_half[pointera]:
												a__			 =						left_half[pointera]
												pointera += 1
												index += 1
								else:
												a__			 =						right_half[pointera]
												pointera += 1
												index += 1
				while pointera < len(__a						):
								a__			 =						left_half[pointera]
								pointera += 1
								index += 1

				while pointera < len(__a						):
								a__			 =						right_half[pointera]
								pointera += 1
								index += 1

				return sorted_array

def      A_ (		__a       :			list						):

				"""simple docstring"""
				if len(__a						) <= 1:
								return array
				# the actual formula to calculate the middle element = left + (right - left) // 2
				# this avoids integer overflow in case of large N
				a__			 =						0 + (len(__a						) - 0) // 2

				# Split the array into halves till the array length becomes equal to One
				# merge the arrays of single length returned by mergeSort function and
				# pass them into the merge arrays function which merges the array
				a__			 =						array[:middle]
				a__			 =						array[middle:]

				return merge(merge_sort(__a						)	,						merge_sort(__a						)						)


if __name__ == "__main__":
	import doctest

	doctest.testmod()






from __future__ import annotations

def      A_ (		__a       :			list[int | float]						):

				"""simple docstring"""
				if len(__a						) == 0:
								raise ValueError("""find_max() arg is an empty sequence"""						)
				a__			 =						nums[0]
				for x in nums:
								if x > max_num:
												a__			 =						x
				return max_num


if __name__ == "__main__":
	import doctest

	doctest.testmod(verbose=True)

