[pull] master from TheAlgorithms:master #173

Original file line number	Diff line number	Diff line change
Expand Up		@@ -243,6 +243,81 @@ def binary_search_std_lib(sorted_collection: list[int], item: int) -> int:
		return -1


	def binary_search_with_duplicates(sorted_collection: list[int], item: int) -> list[int]:
	"""Pure implementation of a binary search algorithm in Python that supports
	duplicates.

	Resources used:
	https://stackoverflow.com/questions/13197552/using-binary-search-with-sorted-array-with-duplicates

	The collection must be sorted in ascending order; otherwise the result will be
	unpredictable. If the target appears multiple times, this function returns a
	list of all indexes where the target occurs. If the target is not found,
	this function returns an empty list.

	:param sorted_collection: some ascending sorted collection with comparable items
	:param item: item value to search for
	:return: a list of indexes where the item is found (empty list if not found)

	Examples:
	>>> binary_search_with_duplicates([0, 5, 7, 10, 15], 0)
	[0]
	>>> binary_search_with_duplicates([0, 5, 7, 10, 15], 15)
	[4]
	>>> binary_search_with_duplicates([1, 2, 2, 2, 3], 2)
	[1, 2, 3]
	>>> binary_search_with_duplicates([1, 2, 2, 2, 3], 4)
	[]
	"""
	if list(sorted_collection) != sorted(sorted_collection):
	raise ValueError("sorted_collection must be sorted in ascending order")

	def lower_bound(sorted_collection: list[int], item: int) -> int:
	"""
	Returns the index of the first element greater than or equal to the item.

	:param sorted_collection: The sorted list to search.
	:param item: The item to find the lower bound for.
	:return: The index where the item can be inserted while maintaining order.
	"""
	left = 0
	right = len(sorted_collection)
	while left < right:
	midpoint = left + (right - left) // 2
	current_item = sorted_collection[midpoint]
	if current_item < item:
	left = midpoint + 1
	else:
	right = midpoint
	return left

	def upper_bound(sorted_collection: list[int], item: int) -> int:
	"""
	Returns the index of the first element strictly greater than the item.

	:param sorted_collection: The sorted list to search.
	:param item: The item to find the upper bound for.
	:return: The index where the item can be inserted after all existing instances.
	"""
	left = 0
	right = len(sorted_collection)
	while left < right:
	midpoint = left + (right - left) // 2
	current_item = sorted_collection[midpoint]
	if current_item <= item:
	left = midpoint + 1
	else:
	right = midpoint
	return left

	left = lower_bound(sorted_collection, item)
	right = upper_bound(sorted_collection, item)

	if left == len(sorted_collection) or sorted_collection[left] != item:
	return []
	return list(range(left, right))


		def binary_search_by_recursion(
		sorted_collection: list[int], item: int, left: int = 0, right: int = -1
		) -> int:
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[pull] master from TheAlgorithms:master #173

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