Implemented Exponential Search with binary search for improved perfor… (#11666)

* Implemented Exponential Search with binary search for improved performance on large sorted arrays.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Added type hints and doctests for binary_search and exponential_search functions. Improved code documentation and ensured testability.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update and rename Exponential_Search.py to exponential_search.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

searches/exponential_search.py

@@ -0,0 +1,113 @@
+#!/usr/bin/env python3
+
+"""
+Pure Python implementation of exponential search algorithm
+
+For more information, see the Wikipedia page:
+https://en.wikipedia.org/wiki/Exponential_search
+
+For doctests run the following command:
+python3 -m doctest -v exponential_search.py
+
+For manual testing run:
+python3 exponential_search.py
+"""
+
+from __future__ import annotations
+
+
+def binary_search_by_recursion(
+    sorted_collection: list[int], item: int, left: int = 0, right: int = -1
+) -> int:
+    """Pure implementation of binary search algorithm in Python using recursion
+
+    Be careful: the collection must be ascending sorted otherwise, the result will be
+    unpredictable.
+
+    :param sorted_collection: some ascending sorted collection with comparable items
+    :param item: item value to search
+    :param left: starting index for the search
+    :param right: ending index for the search
+    :return: index of the found item or -1 if the item is not found
+
+    Examples:
+    >>> binary_search_by_recursion([0, 5, 7, 10, 15], 0, 0, 4)
+    0
+    >>> binary_search_by_recursion([0, 5, 7, 10, 15], 15, 0, 4)
+    4
+    >>> binary_search_by_recursion([0, 5, 7, 10, 15], 5, 0, 4)
+    1
+    >>> binary_search_by_recursion([0, 5, 7, 10, 15], 6, 0, 4)
+    -1
+    """
+    if right < 0:
+        right = len(sorted_collection) - 1
+    if list(sorted_collection) != sorted(sorted_collection):
+        raise ValueError("sorted_collection must be sorted in ascending order")
+    if right < left:
+        return -1
+
+    midpoint = left + (right - left) // 2
+
+    if sorted_collection[midpoint] == item:
+        return midpoint
+    elif sorted_collection[midpoint] > item:
+        return binary_search_by_recursion(sorted_collection, item, left, midpoint - 1)
+    else:
+        return binary_search_by_recursion(sorted_collection, item, midpoint + 1, right)
+
+
+def exponential_search(sorted_collection: list[int], item: int) -> int:
+    """
+    Pure implementation of an exponential search algorithm in Python.
+    For more information, refer to:
+    https://en.wikipedia.org/wiki/Exponential_search
+
+    Be careful: the collection must be ascending sorted, otherwise the result will be
+    unpredictable.
+
+    :param sorted_collection: some ascending sorted collection with comparable items
+    :param item: item value to search
+    :return: index of the found item or -1 if the item is not found
+
+    The time complexity of this algorithm is O(log i) where i is the index of the item.
+
+    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)
+    -1
+    """
+    if list(sorted_collection) != sorted(sorted_collection):
+        raise ValueError("sorted_collection must be sorted in ascending order")
+
+    if sorted_collection[0] == item:
+        return 0
+
+    bound = 1
+    while bound < len(sorted_collection) and sorted_collection[bound] < item:
+        bound *= 2
+
+    left = bound // 2
+    right = min(bound, len(sorted_collection) - 1)
+    return binary_search_by_recursion(sorted_collection, item, left, right)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    # Manual testing
+    user_input = input("Enter numbers separated by commas: ").strip()
+    collection = sorted(int(item) for item in user_input.split(","))
+    target = int(input("Enter a number to search for: "))
+    result = exponential_search(sorted_collection=collection, item=target)
+    if result == -1:
+        print(f"{target} was not found in {collection}.")
+    else:
+        print(f"{target} was found at index {result} in {collection}.")