add exponential search algorithm

searches/binary_search.py

@@ -297,6 +297,49 @@ def binary_search_by_recursion(
         return binary_search_by_recursion(sorted_collection, item, midpoint + 1, right)
 
 
+def exponential_search(sorted_collection: list[int], item: int) -> int | None:
+    """Pure implementation of exponential search algorithm in Python
+    Resources used:
+    https://en.wikipedia.org/wiki/Exponential_search
+
+    Be careful collection must be ascending sorted, otherwise result will be
+    unpredictable
+
+    :param sorted_collection: some ascending sorted collection with comparable items
+    :param item: item value to search
+    :return: index of found item or None if item is not found
+
+    the order of this algorithm is O(lg I) where I is index position of item if exist
+
+    Examples:
+    >>> exponential_search([0, 5, 7, 10, 15], 0)
+    0
+
+    >>> exponential_search([0, 5, 7, 10, 15], 15)
+    4
+
+    >>> exponential_search([0, 5, 7, 10, 15], 5)
+    1
+
+    >>> exponential_search([0, 5, 7, 10, 15], 6)
+
+    """
+    bound = 1
+    while bound < len(sorted_collection) and sorted_collection[bound] < item:
+        bound *= 2
+    left = int(bound / 2)
+    right = min(bound, len(sorted_collection) - 1)
+    return binary_search_by_recursion(
+        sorted_collection=sorted_collection, item=item, left=left, right=right
+    )
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+
 if __name__ == "__main__":
     user_input = input("Enter numbers separated by comma:\n").strip()
     collection = sorted(int(item) for item in user_input.split(","))