Integer Square Root Algorithm  An efficient method to calculate the square root of a nonnegative integer 'num' rounded down to the nearest integer. It uses a binary search approach to find the integer square root without using any builtin exponent functions or operators.  https:en.wikipedia.orgwikiIntegersquareroot  https:docs.python.org3librarymath.htmlmath.isqrt Note:  This algorithm is designed for nonnegative integers only.  The result is rounded down to the nearest integer.  The algorithm has a time complexity of Ologx.  Original algorithm idea based on binary search. Returns the integer square root of a nonnegative integer num. Args: num: A nonnegative integer. Returns: The integer square root of num. Raises: ValueError: If num is not an integer or is negative.  integersquarerooti for i in range18 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4  integersquareroot625 25  integersquareroot2147483647 46340  from math import isqrt  allintegersquarerooti  isqrti for i in range20 True  integersquareroot1 Traceback most recent call last: ... ValueError: num must be nonnegative integer  integersquareroot1.5 Traceback most recent call last: ... ValueError: num must be nonnegative integer  integersquareroot0 Traceback most recent call last: ... ValueError: num must be nonnegative integer
def integer_square_root(num: int) -> int:
    """
    Returns the integer square root of a non-negative integer num.
    Args:
        num: A non-negative integer.
    Returns:
        The integer square root of num.
    Raises:
        ValueError: If num is not an integer or is negative.
    >>> [integer_square_root(i) for i in range(18)]
    [0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4]
    >>> integer_square_root(625)
    25
    >>> integer_square_root(2_147_483_647)
    46340
    >>> from math import isqrt
    >>> all(integer_square_root(i) == isqrt(i) for i in range(20))
    True
    >>> integer_square_root(-1)
    Traceback (most recent call last):
        ...
    ValueError: num must be non-negative integer
    >>> integer_square_root(1.5)
    Traceback (most recent call last):
        ...
    ValueError: num must be non-negative integer
    >>> integer_square_root("0")
    Traceback (most recent call last):
        ...
    ValueError: num must be non-negative integer
    """
    if not isinstance(num, int) or num < 0:
        raise ValueError("num must be non-negative integer")

    if num < 2:
        return num

    left_bound = 0
    right_bound = num // 2

    while left_bound <= right_bound:
        mid = left_bound + (right_bound - left_bound) // 2
        mid_squared = mid * mid
        if mid_squared == num:
            return mid

        if mid_squared < num:
            left_bound = mid + 1
        else:
            right_bound = mid - 1

    return right_bound


if __name__ == "__main__":
    import doctest

    doctest.testmod()
