maths.integer_square_root
=========================

.. py:module:: maths.integer_square_root

.. autoapi-nested-parse::

   Integer Square Root Algorithm -- An efficient method to calculate the square root of a
   non-negative integer 'num' rounded down to the nearest integer. It uses a binary search
   approach to find the integer square root without using any built-in exponent functions
   or operators.
   * https://en.wikipedia.org/wiki/Integer_square_root
   * https://docs.python.org/3/library/math.html#math.isqrt
   Note:
       - This algorithm is designed for non-negative integers only.
       - The result is rounded down to the nearest integer.
       - The algorithm has a time complexity of O(log(x)).
       - Original algorithm idea based on binary search.



Functions
---------

.. autoapisummary::

   maths.integer_square_root.integer_square_root


Module Contents
---------------

.. py:function:: 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