



"""simple docstring"""






def      _lowercase							(    __snake_case   ,__snake_case      )		->  Optional[int]:
			__lowerCAmelCase :    int				=			0
			__lowerCAmelCase :    Any				=			len(__snake_case      ) - 1

			while left <= right:
						# avoid divided by 0 during interpolation
						if sorted_collection[left] == sorted_collection[right]:
									if sorted_collection[left] == item:
												return left
									else:
												return None

						__lowerCAmelCase :    Union[str, Any]				=			left + ((item - sorted_collection[left]) * (right - left)) // (
						    sorted_collection[right] - sorted_collection[left]
						)

						# out of range check
						if point < 0 or point >= len(__snake_case      ):
									return None

						__lowerCAmelCase :    List[str]				=			sorted_collection[point]
						if current_item == item:
									return point
						else:
									if point < left:
												__lowerCAmelCase :    Union[str, Any]				=			left
												__lowerCAmelCase :    str				=			point
									elif point > right:
												__lowerCAmelCase :    Any				=			right
												__lowerCAmelCase :    List[Any]				=			point
									else:
												if item < current_item:
															__lowerCAmelCase :    Union[str, Any]				=			point - 1
												else:
															__lowerCAmelCase :    Tuple				=			point + 1
			return None


def      _lowercase							(    __snake_case   ,__snake_case   ,__snake_case   ,__snake_case      )		->  Tuple:

			# avoid divided by 0 during interpolation
			if sorted_collection[left] == sorted_collection[right]:
						if sorted_collection[left] == item:
									return left
						else:
									return None

			__lowerCAmelCase :    Dict				=			left + ((item - sorted_collection[left]) * (right - left)) // (
			    sorted_collection[right] - sorted_collection[left]
			)

			# out of range check
			if point < 0 or point >= len(__snake_case      ):
						return None

			if sorted_collection[point] == item:
						return point
			elif point < left:
						return interpolation_search_by_recursion(__snake_case   ,__snake_case   ,__snake_case   ,__snake_case      )
			elif point > right:
						return interpolation_search_by_recursion(__snake_case   ,__snake_case   ,__snake_case   ,__snake_case      )
			else:
						if sorted_collection[point] > item:
									return interpolation_search_by_recursion(
									    __snake_case   ,__snake_case   ,__snake_case   ,point - 1      )
						else:
									return interpolation_search_by_recursion(
									    __snake_case   ,__snake_case   ,point + 1   ,__snake_case      )


def      _lowercase							(    __snake_case      )		->  Optional[Any]:
			if collection != sorted(__snake_case      ):
						raise ValueError("Collection must be ascending sorted"      )
			return True


if __name__ == "__main__":
	import sys
	__snake_case				:  Optional[Any] =       0
	if debug == 1:
		__snake_case				:  List[Any] =       [10, 30, 40, 45, 50, 66, 77, 93]
		try:
			__assert_sorted(collection)
		except ValueError:
			sys.exit('Sequence must be ascending sorted to apply interpolation search')
		__snake_case				:  Optional[int] =       67

	__snake_case				:  Tuple =       interpolation_search(collection, target)
	if result is not None:
		print(F"""{target} found at positions: {result}""")
	else:
		print('Not found')




"""simple docstring"""






def      _lowercase							(    __snake_case   ,__snake_case      )		->  Tuple:
			# "extended trapezoidal rule"
			# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
			__lowerCAmelCase :    Optional[Any]				=			(boundary[1] - boundary[0]) / steps
			__lowerCAmelCase :    List[Any]				=			boundary[0]
			__lowerCAmelCase :    Any				=			boundary[1]
			__lowerCAmelCase :    Dict				=			make_points(__snake_case   ,__snake_case   ,__snake_case      )
			__lowerCAmelCase :    List[str]				=			0.0
			y += (h / 2.0) * f(__snake_case      )
			for i in x_i:
						# print(i)
						y += h * f(__snake_case      )
			y += (h / 2.0) * f(__snake_case      )
			return y


def      _lowercase							(    __snake_case   ,__snake_case   ,__snake_case      )		->  Union[str, Any]:
			__lowerCAmelCase :    int				=			a + h
			while x < (b - h):
						yield x
						__lowerCAmelCase :    List[str]				=			x + h


def      _lowercase							(    __snake_case      )		->  Tuple:  # enter your function here
			__lowerCAmelCase :    int				=			(x - 0) * (x - 0)
			return y


def      _lowercase							(    )		->  int:
			__lowerCAmelCase :    Tuple				=			0.0  # Lower bound of integration
			__lowerCAmelCase :    Union[str, Any]				=			1.0  # Upper bound of integration
			__lowerCAmelCase :    Dict				=			10.0  # define number of steps or resolution
			__lowerCAmelCase :    Optional[Any]				=			[a, b]  # define boundary of integration
			__lowerCAmelCase :    Optional[int]				=			method_a(__snake_case   ,__snake_case      )
			print(F"""y = {y}"""      )


if __name__ == "__main__":
	main()