diff --git a/searches/binary_search.py b/searches/binary_search.py index 2e66b672d5b4..519b9c36d936 100644 --- a/searches/binary_search.py +++ b/searches/binary_search.py @@ -243,6 +243,71 @@ 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, + it 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") + + """find lower bounds""" + + def lower_bound(sorted_collection: list[int], item: int) -> int: + 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 + + """find upper bounds""" + + def upper_bound(sorted_collection: list[int], item: int) -> int: + 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: