
"""simple docstring"""




from collections.abc import Callable

import numpy as np



def        _lowerCamelCase ( __a,							__a,							__a,							__a,							__a    ):
		SCREAMING_SNAKE_CASE_						 = int(np.ceil((x_end - xa) / step_size    )    )
		SCREAMING_SNAKE_CASE_						 = np.zeros((n + 1,)    )
		SCREAMING_SNAKE_CASE_						 = ya
		SCREAMING_SNAKE_CASE_						 = xa

		for k in range(__a    ):
				SCREAMING_SNAKE_CASE_						 = y[k] + step_size * ode_func(__a,							y[k]    )
				x += step_size

		return y


if __name__ == "__main__":
						import doctest

						doctest.testmod()

"""simple docstring"""




from __future__ import annotations



def        _lowerCamelCase ( __a,							__a    ):
		SCREAMING_SNAKE_CASE_						 = 0
		SCREAMING_SNAKE_CASE_						 = len(__a    ) - 1

		while i < j:
				if nums[i] + nums[j] == target:
						return [i, j]
				elif nums[i] + nums[j] < target:
						SCREAMING_SNAKE_CASE_						 = i + 1
				else:
						SCREAMING_SNAKE_CASE_						 = j - 1

		return []


if __name__ == "__main__":
						import doctest

						doctest.testmod()
						print(f'''{two_pointer([2, 7, 11, 15], 9) = }''')