





def lowerCAmelCase__(__snake_case ,__snake_case							)       ->   Optional[Any]:







	'''simple docstring'''







	lowerCamelCase__              =	0
	lowerCamelCase__              =	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__              =	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__              =	sorted_collection[point]
		if current_item == item:
			return point
		else:
			if point < left:
				lowerCamelCase__              =	left
				lowerCamelCase__              =	point
			elif point > right:
				lowerCamelCase__              =	right
				lowerCamelCase__              =	point
			else:
				if item < current_item:
					lowerCamelCase__              =	point - 1
				else:
					lowerCamelCase__              =	point + 1
	return None





def lowerCAmelCase__(__snake_case ,__snake_case ,__snake_case ,__snake_case							)       ->   Any:







	'''simple docstring'''







	if sorted_collection[left] == sorted_collection[right]:
		if sorted_collection[left] == item:
			return left
		else:
			return None

	lowerCamelCase__              =	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 lowerCAmelCase__(__snake_case							)       ->   Dict:







	'''simple docstring'''







	if collection != sorted(__snake_case							):
		raise ValueError('''Collection must be ascending sorted'''							)
	return True


if __name__ == "__main__":
			import sys
			_a						=   0
			if debug == 1:
						_a						=   [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")
						_a						=   67

			_a						=   interpolation_search(collection, target)
			if result is not None:
						print(f"""{target} found at positions: {result}""")
			else:
						print("Not found")










import string
from math import logaa





def lowerCAmelCase__(__snake_case ,__snake_case							)       ->   int:







	'''simple docstring'''







	lowerCamelCase__              =	document.translate(
	    str.maketrans('''''' ,'''''' ,string.punctuation							)							).replace('''\n''' ,''''''							)
	lowerCamelCase__              =	document_without_punctuation.split(''' '''							)  # word tokenization
	return len([word for word in tokenize_document if word.lower() == term.lower()]							)





def lowerCAmelCase__(__snake_case ,__snake_case							)       ->   tuple[int, int]:







	'''simple docstring'''







	lowerCamelCase__              =	corpus.lower().translate(
	    str.maketrans('''''' ,'''''' ,string.punctuation							)							)  # strip all punctuation and replace it with ''
	lowerCamelCase__              =	corpus_without_punctuation.split('''\n'''							)
	lowerCamelCase__              =	term.lower()
	return (len([doc for doc in docs if term in doc]							), len(__snake_case							))





def lowerCAmelCase__(__snake_case ,__snake_case ,__snake_case=False							)       ->   float:







	'''simple docstring'''







	if smoothing:
		if n == 0:
			raise ValueError('''log10(0) is undefined.'''							)
		return round(1 + logaa(n / (1 + df)							) ,3							)

	if df == 0:
		raise ZeroDivisionError('''df must be > 0'''							)
	elif n == 0:
		raise ValueError('''log10(0) is undefined.'''							)
	return round(logaa(n / df							) ,3							)





def lowerCAmelCase__(__snake_case ,__snake_case							)       ->   float:







	'''simple docstring'''







	return round(tf * idf ,3							)



