#!/usr/bin/env python3

"""
Pure Python implementation of the exponential search algorithm

For more information, see the Wikipedia page:
https://en.wikipedia.org/wiki/Exponential_search

Run doctests with 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 | None = None,
) -> int:
    """Pure implementation of the binary search algorithm in Python using recursion

    Be careful: the collection must be ascendingly 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 (defaults to the last index)
    :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
    >>> binary_search_by_recursion([0, 5, 7, 10, 15], -1)
    -1
    >>> binary_search_by_recursion([0, 5, 7, 10, 15], 16)
    -1
    """
    if list(sorted_collection) != sorted(sorted_collection):
        raise ValueError("sorted_collection must be sorted in ascending order")
    if right is None:
        right = len(sorted_collection) - 1

    # Recursive core: ``left`` and ``right`` are always concrete indices here, so the
    # window can only shrink. Keeping the recursion flat (no ``None`` sentinel, no
    # re-expansion) is what prevents the runaway recursion when the item sits below
    # ``sorted_collection[0]`` and ``right`` legitimately drops below ``left``.
    def _search(left: int, right: int) -> int:
        if right < left:
            return -1

        midpoint = left + (right - left) // 2

        if sorted_collection[midpoint] == item:
            return midpoint
        elif sorted_collection[midpoint] > item:
            return _search(left, midpoint - 1)
        else:
            return _search(midpoint + 1, right)

    return _search(left, 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 ascendingly 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
    >>> exponential_search([0, 5, 7, 10, 15], -3)
    -1
    >>> exponential_search([0, 5, 7, 10, 15], 20)
    -1
    >>> exponential_search([], 1)  # Empty array edge case
    -1
    """
    if list(sorted_collection) != sorted(sorted_collection):
        raise ValueError("sorted_collection must be sorted in ascending order")

    if not sorted_collection:
        return -1
    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}.")